GLOSSARY OF FINANCIAL DERIVATIVES TERMS

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Exact Matches:

BINARY OPTION

Unlike simple options, which have continuous pay-out profiles, that of a binary option is discontinuous and pays out a fixed amount if the underlying satisfies a predetermined trigger condition but nothing otherwise. Binary options are also known as digital or all-or-nothing options.

There are two major forms: at maturity and one-touch. At maturity binaries, also known as European binaries or at expiry binaries, pay out only if the spot trades above (or below) the trigger level at expiry. One-touch binary options, also known as American binaries, pay out if the spot rate trades through the trigger level at any time up to and including expiry. The pay-out of a one-touch binary may be due as soon as the trigger condition is satisfied or alternatively at expiry (one-touch immediate or one-touch deferred binaries). As with barrier options, variations on the theme include discrete binaries, stepped binaries, etc. Binary options are frequently combined with other instruments to create structured products, such as contingent premium options.

Partial Matches:

ACCRUAL CORRIDOR

The range within which an underlying reference rate must trade for coupon payments to accrue in a range note or corridor option.

ALL-OR-NOTHING OPTION

See binary option

AMERICAN-STYLE OPTION

The holder of an American-style option has the right to exercise the option at any time during the life of the option, up to and including the expiry date.

See also option styles

ASIAN OPTION

See average option

AT-THE-MONEY

1. At-the-money forward: An option whose strike is set at the same level as the prevailing market price of the underlying forward contract. With a Black-Scholes model , the delta of a European-style, at-the-money forward option will be close to 50%.
2. At-the-money spot: An option whose strike is set the same as the prevailing market price of the underlying. Because forwards commonly trade at a premium or discount to the spot, the delta may not be close to 50%.

AUction rate securities

A debt instrument used by tax-exempt and corporate issuers with a long term maturity for which the interest rate is adjusted either daily, or every seven, 28 or 35 days. The interest rate adjustments are determined by an auction, in which the remarketing agent (typically a securities dealer) takes bids from investors in the form of a yield and amount. The remarketing agent then determines the lowest rate to clear the outstanding amount of auction rate securities (ARS).

In early 2008, as the credit crunch continued, Wall Street firms which served as the remarketing agent for the auctions stopped bidding on the auctions themselves, and the auctions failed. A failed auction simply means that there were not enough ‘buy’ orders to fill the number of ‘sell’ orders. In the relatively opaque bidding process, many dealers were supporting auctions by bidding on the ARS to prevent the auction from failing. The result was that many investors who held this paper were not able to sell it, and the investments became illiquid. Because ARS have no bank liquidity facility, there is no put option available for the investor. In the event of a failed auction, the interest rates jump to a pre-determined max rate. The max rates can be absolute, such as 12%, or formulaic, such as 6-month commercial paper + 100 basis points, for example. In the spring of 2008, there were widespread auction failures in the $165 billion municipal ARS market. Many issuers were experiencing borrowing costs that greatly exceeded their budget, and by the summer of 2008, over half of the outstanding municipal ARS had been converted to another debt mode, such as fixed rate, or variable rate bonds.

AUTOCAP

A standard cap consists of a series of caplets hedging future floating rate payments. However, autocaps only provide a hedge for the first pre-specified number of in-the-money caplets after which the option expires, and so are a cheaper alternative to caps.

AVERAGE OPTION

A plain vanilla option pays out the difference between its predetermined strike price and the spot rate (or price) of the underlying at the time of expiry. The purchaser of an average option (average price, average strike, average hybrid, average ratio), on the other hand, will receive a pay-out which depends on the average value of the underlying. The average can be calculated in a number of ways (arithmetic or geometric, weighted or simple) from the spot rate on a predetermined series of dates (usually official fixing rates). An average rate (also known as average price) option is a cash-settled option with a predetermined (i.e., fixed) strike which is exercised at expiry against the average value of the underlying over the option’s life. In general, hedging with an average option is cheaper than using a portfolio of vanilla options, since the averaging process offsets high values with low ones and therefore lowers volatility and premium. Average rate options, also known as Asian options, are particularly popular in the currency and commodity markets.

In contrast, the strike for an average strike option is not fixed until the end of the averaging period which is typically much before the expiry. When the strike is set, the option is exercised against the prevailing spot rate. Unlike average price options, average strike options may be either cash or physically settled. In the case of an average hybrid option (also known as an average-in/average-out option), both the strike and settlement price of the option are determined using the average, where the strike averaging period typically precedes the settlement price averaging period. For the average ratio option, both the strike and settlement price of the option are determined using the average as in the hybrid case. The final payoff is determined by comparing the ratio of settlement price to strike and a fixed percent strike.

AVERAGE PRICE OPTION

See average option

AVERAGE RATE OPTION

See average option

AVERAGE STRIKE OPTION

See average option

BARRIER OPTION

Barrier options, also known as knock-out, knock-in or trigger options, are path-dependent options which are either activated (knocked-in) or terminated (knocked-out) if a specified spot rate reaches a specified trigger level (or levels) between inception and expiry. Before termination knock-out options behave identically to standard European-style options, but carry lower initial premiums because they may be extinguished before reaching maturity. In contrast, knock-in options behave identically to European-style options only if they are activated/knocked-in and so also command a lower premium.

  The standard barrier options have barrier levels that are monitored continually during the lifetime of the option. Single barrier options that have a barrier level above current spot are classified as up-and-out or up-and-in options. For single barriers below spot the usual terminology is down-and-out for the knock-out barrier option, and down-and-in for the knock-in barrier option.

  An alternative terminology for single barrier options classifies barrier options where the barrier is out-of-the money with respect to the strike price as regular barrier options. In-the-money barrier options are further differentiated into reverse barrier options (for cases where the barrier may be breached as the underlying asset’s spot rate moves deeper in-the-money) and geared barrier options (examples where the barrier is in-the-money and lies between the strike and the underlying spot rate) A double barrier option has both an upper and lower barrier.

  Many variations on the barrier theme are available. Barrier levels can be monitored continually, at discrete fixing times (discrete barrier options) or only at the final expiry date of the option (at-expiry barrier options). Barriers may be active only during distinct time intervals (window barrier options) or may change value at fixed points during the lifetime of the option (stepped barrier options). Barriers may need to be breached for a certain time before they are considered triggered (Parisian Barrier Options) or may allow for partial triggering depending upon how far beyond the trigger level the underlying asset is observed (Soft Barrier options). Barriers may reference a different underlying to that of the option itself – such barriers are known as outside barriers.

BARRIER RISK

The value and sensitivities (Greeks) of barrier options can be subject to large swings when the spot rate is at, or near, the trigger level. This is particularly true for reverse barrier options and geared barrier options, where the option has positive intrinsic value at the Barrier. The specific nature of these swings can make the management of such products riskier, hence barrier risk.

BASKET OPTION

An option that enables a purchaser to buy or sell a basket of currencies, equities or bonds.

BEAR SPREAD

An option spread trade that reflects a bearish view on the market. It is usually understood as the purchase of a put spread.

BERMUDAN OPTION

The holder of a Bermudan option, also known as a mid-Atlantic or semi-American option, has the right to exercise it on one or more possible dates prior to its expiry.

See also option styles

BETA

1. The beta of an instrument is its standardized covariance with its class of instruments as a whole. Thus the beta of a stock is the extent to which that stock follows movements in the overall market. If a stock has a beta greater than one, it is more volatile than the market; if less than one, it is less volatile.
2. Beta trading is used by currency traders if they take the volatility risk of one currency in another. For example, rather than hedge a sterling/yen option with another sterling/yen option, a trader, either because of liquidity constraints or because of lower volatility, might hedge with euro/yen options. The beta risk indicates the likelihood of the two currencies’ volatilities diverging.

BETTER-OF-TWO-ASSETS OPTION

See outperformance option

BILATERAL NETTING

Agreement between two counterparties whereby the value of all in-the-money contracts is offset by the value of all out-of-the money contracts, resulting in a single net exposure amount owed by one counterparty to the other. Bilateral netting can be multi-product and encompass portfolios of swaps, interest rate options, and forward foreign exchange.

BINARY PAY-OUT

See binary option, credit default swap, exotic option

BINOMIAL TREE

Also called a binomial lattice. A discrete time model for describing the evolution of a random variable that is permitted to rise or fall with given probabilities. After the initial rise, two branches will each have two possible outcomes and so the process will continue. The process is usually specified so that an upward movement followed by a downward movement results in the same price, so that the branches recombine. If the branches do not recombine it is known as a bushy, or exploded, tree. The size of the movements and the probabilities are chosen so that the discrete binomial model tends to the normal distribution assumed in option models as the number of discrete steps is increased. Options can be evaluated by discounting the terminal pay-off back through the tree using the determined probabilities. Interest in binomial trees arises from their ability to deal with American-style features and to price interest rate options. For example, American-style options can readily be priced because the early exercise condition can be tested at each point in the tree.

BLACK-SCHOLES MODEL

The original closed-form solution to option pricing developed by Fischer Black and Myron Scholes in 1973. In its simplest form it offers a solution to pricing European-style options on assets with interim cash pay-outs over the life of the option. The model calculates the theoretical, or fair value for the option by constructing an instantaneously riskless hedge: that is, one whose performance is the mirror image of the option pay-out. The portfolio of option and hedge can then be assumed to earn the risk-free rate of return.

Central to the model is the assumption that market returns are normally distributed (i.e., have lognormal prices), that there are no transaction costs, that volatility and interest rates remain constant throughout the life of the option, and that the market follows a diffusion process. The model has five major inputs: the risk-free interest rate, the option’s strike price, the price of the underlying, the option’s maturity, and the volatility assumed. Since the first four are usually determined by the market, options traders tend to trade the implied volatility of the option.

BOND FUTURE

A futures contract on a bond. The underlying can be of two types. The first is a notional (theoretical) bond, for example the 10-year government bond futures contract on Marché à Terme International de France (Matif), which has a notional seven- to 10-year underlying government bond with a 10% coupon. The second type is a futures contract on a specific bond, for example, the futures contract on the Danish government bond 8% 2000, listed on the Guarantee Fund for Danish Options and Futures. The notional type is more common.

The theoretical price of a bond futures contract equals the spot price of the underlying bond plus its net cost of carry. The higher the cost of carry (measured by its implied repo rate) for the cash bond, the more value there is in holding a futures contract instead, which is simply another way of buying a cash bond but at a future date. If the financing costs of holding a bond are lower than the bond’s yield, the bond will have positive carry and the futures contract will trade at a discount. If the financing costs of the bond are higher than the bond’s yield, the futures will trade at a premium. Hence bond futures normally trade at a discount to the cash in an upward-sloping yield curve and at a premium in a downward-sloping one. The degree of premium or discount will decrease the closer the futures contract is to expiry.

When futures are based on a notional bond, the exchange has to specify which bonds are deliverable into the futures contract. These can change periodically as outstanding issues get shorter and reach maturity. Because bonds have differing coupons, the exchange has to specify a conversion factor that allows those bonds to be compared on an equal basis to the notional underlying. A bond’s conversion factor is the value of one unit of that bond were it to trade at a yield to maturity equal to that of the notional bond. Because of demand/supply conditions, some bonds will be cheaper to deliver than others. The cheapest to deliver will be those where the greatest profit can be made from holding the bond and delivering it into the futures contract (called cash-and-carry arbitrage). This is dependent on the supply of bonds in the market, and on a bond’s maturity and coupon.

BOND OPTION

An option offered on debt, usually government securities, although OTC options are available on corporate debt. The options can either be ex-change-traded, listed or OTC. Bond options have traditionally been standard European-style or American-style puts and calls. There is more interest in exotic structures such as yield curve options, inter-market spread options, and quanto options.

BOX

To buy/sell mispriced options and hedge the market risk using only options, unlike the conversion or the reversal, which use futures contracts. If a certain strike put is underpriced, the trader buys the put and sells a call at the same strike, creating a synthetic short futures position. To get rid of the market risk, he sells another put and buys another call, but at different strike prices.

BREAK FORWARD/CAPPED FORWARD

A strategy that involves buying a synthetic off-market currency forward (buying and selling a put and a call at the same strike price) and the simultaneous purchase of another option, allowing a purchaser to benefit from favorable exchange rate movements. The transaction is usually constructed for zero cost because the premium from the off-market forward pays for the option.

BULL SPREAD

An option spread trade that reflects a bullish view on the market. It is usually understood as the purchase of a call spread.

CALENDAR SPREAD

A strategy that involves buying and selling options or futures with the same (strike) price but different maturities. Such a strategy is used in futures when one contract month is theoretically cheap and another is expensive. With options, the strategy is often used to play expected changes in the shape of the volatility term structure. For example, if one-month volatility is high and one-year volatility low, arbitrageurs might buy one-year straddles and sell short-term straddles, thereby selling short-term volatility and buying long-term volatility. If, all else being equal, short-term volatility declines relative to long-term volatility, the strategy makes money.

CALL OPTION

See option

CALL SPREAD

A strategy that reduces the cost of buying a call option by selling another call at a higher level. This limits potential gain if the underlying goes up, but the premium received from selling the out-of-the-money call partly finances the at-the-money call. A call spread may be advantageous if the purchaser thinks there is only limited upside in the underlying.

See also bear spread, bull spread, put spread

CALLABLE SWAP

An interest rate swap in which the fixed-rate payer has the right to terminate the swap after a certain time if rates fall. Often done in conjunction with callable debt issues where an issuer is more concerned with the cost of debt than the maturity. The embedded option is, in effect, a swaption sold by the fixed-rate receiver which enables the fixed-rate payer to receive the same high fixed rate for the remaining years of the swap in the event that interest rates fall. The fixed rate received under the swaption offsets the fixed rate paid under the original swap effectively cancelling the swap. In some definitions of a callable swap, the fixed-rate receiver has the right to terminate the swap. Also known as a cancellable swap.

CAP

A contract whereby the seller agrees to pay to the purchaser, in return for an upfront premium or a series of annuity payments, the difference between a reference rate and an agreed strike rate when the reference exceeds the strike. Commonly, the reference rate is three- or six-month Libor. A cap is therefore a strip of interest rate guarantees that allows the purchaser to take advantage of a reduction in interest rates and to be protected if they rise. They are priced as the sum of the cost of the individual options, known as caplets.

CAPTION

An option on a cap. A type of compound option in which the purchaser has the right, but not the obligation, to buy or sell a cap at a predetermined price on a predetermined date. Captions can be a cheap way of leveraging into the more expensive option.

CATASTROPHE EQUITY PUTS

A put option purchased by an insurance firm, giving it the right to sell a portion of equity to the investor in the event of a catastrophe-related trigger. These instruments are often written to increase liquidity at times when there are lots of claims.

CATASTROPHE OPTION

These options can be American-style or European-style, either paying out if a single specified catastrophe such as a hurricane or earthquake occurs, or alternatively, having a pay-out dependent on an index. For example, the index may represent the number of claims received by property insurance companies.

CHOOSER OPTION

A chooser option offers purchasers the choice, after a predetermined period, between a put and a call option. The pay-outs are similar to those of a straddle but chooser options are cheaper because purchasers must choose before expiry whether they want the put or the call. Also known as a hermaphrodite, or AC-DC option.

CLIQUET OPTION

Also known as a ratchet or reset option. A path-dependent+option that allows buyers to lock-in gains on the underlying security during chosen intervals over the life time of the option. Cliquet options were developed in France with the CAC 40 stock index as the underlying, although they are used in structured retail products elsewhere in Europe. The option’s strike price is effectively reset on predetermined dates. Gains, if any, are locked in. So if an index rises from 100 to 110 in year one, the buyer locks in 10 points and the strike price is reset at 110. If it falls to 97 in the next year the strike price is reset at that lower level, no further profits are locked in, but the accrued profit is kept.

CLOSED-FORM SOLUTION

Also called an analytical solution. An explicit solution of, for example, an option pricing problem by the use of formulae involving only simple mathematical functions, such as Black-Scholes or Vasicek models. Closed-form models can usually be evaluated much more quickly than numerical models, which are sometimes far more computationally intensive.

COLLAR

The simultaneous purchase of an out-of-the-money call and sale of an out-of-the-money put (or cap and floor in the case of interest rate options). The premium from selling the put reduces the cost of purchasing the call. The amount saved depends on the strike rate of the two options. If the premium raised by the sale of the put exactly matches the cost of the call, the strategy is known as a zero cost collar. When used to hedge an outright position in the underlying, this locks the hedger into a range of values; this hedging strategy is known as a cylinder.

COMPOUND OPTION

An option on an option, permitting the purchaser to buy (or sell) an option on an underlying at a fixed price over a predetermined period. Usually sold on interest rate instruments (e.g., captions or floortions), or currencies. They are also used as components of more complex trades. Compound options are often bought to protect against increases in standard option prices during periods of high volatility. The upfront premium for a compound option is less than for a normal European-style option but if the option is exercised, the overall cost will be greater. Due to their greater flexibility the cost, if both options are exercised, is greater than a conventional option.

Compound options can also be constructed on options other than European style options (e.g., barrier options) or portfolios of options (e.g., compound on a cylinder). Indeed compound options on compound options, otherwise known as installment options are common (often as part of more complex structures). An installment option requires the holder to pay fixed amounts of premium (installment) at certain installment dates to benefit from the right of exercise of the underlying option. At any point that holder can elect to let the installment payments lapse and loses any right of exercise.

CONSTANT MATURITY TREASURY DERIVATIVE

Over-the-counter swaps and options which use longer-term, Treasury-based instruments for their floating rate reference than money market indexes, such as Libor. “Constant Maturity Treasury” (CMT) refers to the par yield that would be paid by a treasury bill, note or bond which matures in exactly one, two, three, five, seven, 10, 20 or 30 years. Since there may not be treasury issues in the market with exactly these maturities, the yield is interpolated from the yields on treasuries that are available. In the US, such rates have been calculated and published by the Federal Reserve Bank of New York and the US Treasury department on a daily basis every day for more than 30 years. The H.15 Report from the Federal Reserve Bank is often used as a source for CMT rates.

It is then possible for this interpolated yield to form the index rate for instruments such as floating rate notes, which pay interest linked to the CMT yield, options, which pay the difference between a strike price and the CMT yield, and swaps and swaptions, in which one of the cashflows exchanged is the CMT yield. Where necessary, the reference rate is reset at each settlement date. Typical uses of CMT derivatives as hedging tools include the purchase of CMT floors by mortgage servicing companies to protect the value of purchased mortgage servicing portfolios, and the purchase of CMT caps to protect investors with negatively convex mortgage-backed securities portfolios. It is possible to enter into derivatives in other currencies that are based, by analogy, on a “constant maturity interest rate swap” interpolated from the swap curve in the relevant currency. Such derivatives are known as constant maturity swap (CMS) derivatives. Unlike CMT derivatives, CMS derivatives incorporate the spread component of swaps.

CONTINGENT PREMIUM OPTION

An option for which the purchaser pays no premium unless the option is exercised. As a rule of thumb, the premium eventually paid is equal to the premium payable on a normal option divided by the option delta, hence the price increases dramatically for out-of-the-money options. Contingent options can usually be broken down into one or more binary options plus a conventional option. For example, a purchaser could synthesize a contingent call by buying a European-style call and selling enough European binary options with the same strike to pay for the premium on the call. If the options are not in-the-money at expiry, both the total premium paid and the total pay-out are zero. If they are in-the-money, the pay-out on the binary options is simply subtracted from the pay-out on the call. Further flexibility can be obtained by setting the strike for the digitals further out-of-the-money than the call.

CONVERSION

1) A way of taking advantage of mispriced options by creating a synthetic short futures position and hedging market risk by buying a futures contract against it. Thus if a put is undervalued, a trader buys it, at the same time selling a fairly valued call and buying a futures contract. The same strategy can be applied if the call is mispriced. If the option is truly undervalued, the trader earns a riskless profit. The whole exercise relies on put-call+parity. 2) The act of converting a convertible bond into equity.

CONVERTIBLE BOND

A bond issued by a company that may be exchanged by the holder for a set number of that company’s shares at a predetermined price. Because the bond embeds a call option on the company’s equity, convertibles carry much lower rates of interest than traditional debt and are therefore a cheap way for companies to raise debt. The problem for existing shareholders is that conversion dilutes the company’s outstanding shares. Typically, bonds are convertible into a company’s own stock. There are however “third party convertibles”, which convert into shares of another company.

CONVEXITY

A bond’s convexity is the amount that its price sensitivity differs from that implied by the bond’s duration. Fixed-rate bonds and swaps have positive convexity: when rates rise the rate of change in their price is slower than suggested by their duration; when rates fall it is faster. Positive convexity is therefore a welcome attribute. The higher the bond’s duration, the more its convexity. Bonds or swaps with call options or embedded call options, e.g., collateralized mortgage obligations, have negative convexity: when rates rise their price fall is faster relative to the interest rate move. Convexity effectively describes the same attribute as gamma.

CORRELATION

Correlation is a measure of the degree to which changes in two variables are related. It is normally expressed as a coefficient between plus one, which means variables are perfectly correlated (in that they move in the same direction to the same degree) and minus one, which means they are perfectly negatively correlated (in that they move in opposite directions to the same degree). In financial markets correlation is important in three areas:
1. The model used for global asset allocation decisions, Sharpe’s capital asset pricing model (CAPM), has, as its linchpin, a covariance matrix that measures correlations between markets.
2. Correlation is also central to the pricing of some options, where two-factor or multi-factor models are used. For spread options, yield curve options and cross-currency caps, estimating the correlation between the underlying assets is of primary importance, the degree of correlation between them having a direct influence on the option price. For quantos such as guaranteed exchange rate options, or differential swaps, the correlation effect is the extent to which there is a relationship between movements in the underlying and movements in the ex-change rate, which has a secondary effect on the price of the option.
3. Correlation between markets is also used to offset an option position in one market against another with similar direction and volatility. Such a strategy might be used to reduce cost – to avoid hedging the positions separately, or because implied volatility in the second market is lower – or because hedging is difficult in the first market. Correlation can be estimated historically (like volatility) but tends to be unstable, and historic estimations may be poor predictors of future realized correlations.

CORRIDOR OPTION

The holder of a corridor option receives a coupon at the end of the lifetime of the corridor whose magnitude depends upon the behavior of a specified spot rate during the lifetime of the corridor. For each day on which the spot rate (typically an official fixing rate observation) remains within the chosen spot range (the accrual corridor) the holder accrues one day’s worth of coupon interest. At the end of the lifetime the accrued coupon is paid out. Its value is calculated according to the following formula:

A variation is the knockout corridor option. In this structure, the holder ceases to accrue coupon interest as soon as the spot rate leaves the range. Even if the spot rate subsequently re-enters the range, the holder does not continue to accrue coupon interest. At the end of the option’s lifetime, the accrued coupon is calculated according to the following formula:

If the accrual corridor is one-sided (the other side of the range being open-ended), it is known as a wall option. Typically, corridor options are imbedded in a structured note, sometimes called a range note, that pays a higher yield than the corresponding vanilla debt as long as the underlying rate remains sufficiently long within the accrual corridor. A similar option to the corridor option is the range binary, a binary option which pays a fixed coupon amount if the range is not breached but nothing if it is breached.

COVERED CALL

To sell a call option while owning the underlying security on which the option is written. The technique is used by fund managers to increase income by receiving option premium. It would be used for securities they are willing to sell, only if the underlying went up sufficiently for the option to be exercised. Generally, covered call writers would undertake the strategy only if they thought volatility was overpriced in the market. The lower the volatility, the less the covered call writer gains in return for giving up upside in the underlying. It provides downside protection only to the extent that the option premium offsets a market downturn.

COVERED PUT

To sell a put option while holding cash. This technique is used to increase income by receiving option premium. If the market goes down and the option is exercised, the cash can be used to buy the underlying to cover. Covered put writing is often used as a way of target buying: if an investor has a target price at which he wants to buy, he can set the strike price of the option at that level and receive option premium to increase the yield of the asset. Investors also sell covered puts if markets have fallen rapidly but seem to have bottomed, because of the high volatility typically received on the option.

COX-INGERSOLL-ROSS MODEL

In its simplest form this is a lognormal one-factor model of the term structure of interest rates, which has the short rate of interest as its single source of uncertainty. The model allows for interest rate mean reversion and is also known as the square root model because of the assumptions made about the volatility of the short-term rate. The model provides closed-form solutions for prices of zero-coupon bonds, and put and call options on those bonds.

CREDIT DERIVATIVE

A bilateral financial contract which isolates credit risk from an underlying instrument and transfers that credit risk from one party to the contract (the Protection Buyer) to the other (the Protection Seller). There are two main categories of credit derivatives: the first consists of instruments such as credit default swaps in which contingent payments occur as a result of a credit event; the second, which includes credit spread options, seeks to isolate the credit spread component of an instrument’s market yield.

CREDIT OPTION

Put or call options on the price of either (a) a floating rate note, bond, or loan, or (b) an asset swap package, consisting of a credit-risky instrument with any payment characteristics and a corresponding derivative contract that exchanges the cashflows of that instrument for a floating rate cashflow stream, typically three- or six-month Libor plus a spread.

CREDIT RISK ASSESSMENT

The process of determining the extent of the credit risk inherent in a financial instrument or portfolio of financial instruments. Such extent is usually measured in terms of exposure, which can be analyzed in several ways:
    •     The current exposure associated with a derivative instrument, its replacement cost, is the present value of the expected future net cash flows of that instrument.
    •     The potential exposure is an estimate of the future replacement cost of a derivative transaction, calculated using probability analysis (e.g., Monte Carlo or historical simulation, option valuation models) over the remaining term of the transaction.
    •     The potential exposure is an estimate of the future replacement cost of a derivative transaction, calculated using probability analysis (e.g., Monte Carlo or historical simulation, option valuation models) over the remaining term of the transaction.
    •     The most likely potential exposure is known as the expected exposure, which is found by taking the mean of all possible replacement costs (weighted by probability), where the replacement cost in any outcome is taken as being equal to the mark-to-market present value if positive, and zero if negative.
    •     It is also possible to calculate a worst case exposure, an estimate of the exposure that might be expected if the market were to move through an amount dictated by a specified confidence interval. This calculation allows capital to be held to protect against possible, but relatively unlikely market moves.

  If the expected or worst case exposures of an instrument are calculated over time, the resulting graph reveals a credit risk exposure profile. The highest point on the profile is the “peak expected (or worst case) exposure” generated by the instrument. This would be the largest possible loss that could occur, to the probability dictated by the confidence interval.

CREDIT SPREAD OPTION

An option on the credit spread between two debt issues. The option will pay out the difference between the credit spread at maturity and a strike spread determined at the outset.

CURRENCY FORWARD

An agreement to exchange a specified amount of one currency for another at a future date at a certain rate. The exchange of currencies is priced so as to allow no risk-free arbitrage. In other words, pricing is not a market estimate of the spot rate at that date, but is made according to the two currencies’ respective interest rates. For example, assuming that Eurosterling interest rates are 10% and Eurodollar 5%, and the US dollar/sterling spot rate is 1.75, the forward rate should reflect the 5% interest rate advantage of depositing money in sterling. Thus the 12-month forward rate should be 1.6695.

Forwards are more appropriate than options if a company has a strong directional view of expected movements in exchange rates. But certainty is rare and hedging entirely with forwards may leave a company locked into unfavorable exchange rates. Unlike options, forwards do not enable companies to take advantage of favorable currency movements. The purchaser of a forward, unlike the purchaser of a future, carries the credit risk of the firm from which it makes the purchase. Since the contracts are not easily reassignable, it is difficult to reduce this risk.

CURRENCY PROTECTED OPTION

The same as guaranteed exchange rate option.

CURRENCY STRUCK OPTION

This is same as joint option

CYLINDER

Also known as range forward or risk-reversal. The simultaneous purchase of an out-of-the-money currency put option and sale of an out-of-the-money currency call option (or vice versa). The choice of strike prices is usually made to result in a zero cost strategy. This strategy enables purchasers to hedge their downside at reduced (or no) cost. This is at the expense of forgoing upside beyond a certain level since the purchase of the put is financed by the sale of the call.

DAILY CALL OPTION

Common in the natural gas markets, this option allows the buyer to take additional volumes of gas with a single day’s notice.

DEBT service fund

Debt service funds are usually required to be deposited with a trustee or in another segregated manner on a monthly basis to meet semi-annual debt service interest payments (1/6 per month) and annual principal payments (1/12 per month). Traditional investment techniques result in these monies being invested short-term and earning short-term rates of interest.

  As an alternative, a debt service fund forward purchase agreement offers an issuer a higher rate of return on invested monies, along with the option of receiving an up-front payment equaling the present value of that future stream of income.

  These agreements can be structured on either a delivery versus payment (DVP) or swap basis. On a DVP basis, the counterparty will deliver to the issuer or issuer’s trustee a U.S. Treasury security maturing prior to the semi-annual debt service payment date with a face value equaling the debt service amount deposited with the counterparty. On a swap basis, the issuer transmits the actual semi-annual earnings on U.S. Treasury Bill investments (variable) in exchange for the guaranteed rate (fixed). On this basis, the counterparty can deliver an upfront payment of a fixed yield over time.

  Collateral on the agreements can range from treasury securities to agency securities to commercial paper to uncollateralized. The collateral requirement corresponds directly with the yield.

  In the event the issue is refunded, a breakage fee may be incurred requiring a payment to the counterparty, thereby reducing the earlier received cash payment. For instance, if an issuer were to enter into an agreement and receive an up-front payment of the cash flow for thirty years, the issuer is contracting to deliver a 20-year stream of monthly cash payments. If the issuer later chooses to call the bonds after seven years, the issuer will be subject to a breakage fee because the issuer will be unable to deliver this stream of cash. To avoid this the issuer can limit the agreement to the first call date rather than out to the final maturity of the issue.

DEBT service reserve fund

The Debt Service Reserve Fund (“DSRF”) has traditionally been invested in a long term treasury security combined with a simultaneous purchase of a par put option to insure liquidity and par value of the treasury. The problem with purchasing the treasury put is that it can be expensive (up to 100 bps), reducing the overall yield of the DSRF. Furthermore, once purchased, a treasury put is relatively illiquid with little resale value. Sometimes, the long term treasury is bought “naked,” that is, without the put option, which eminently sets up the issuer for a probable underfunded DSRF sometime in the future.

The DSRF Forward Purchase Agreement (“FPA”) provides essentially the same long term rate as long term treasuries, while eliminating the need for a treasury put option. The DSRF FPA works as follows: A FPA provider would initially deliver a 90 day T-Bill to the trustee. When that T-bill matured the FPA provider would deliver a new 90 day T-Bill in exchange for the cash resulting from the previous maturing T-Bill. This cycle would continue for the term of the agreement. The yield for this type of instrument is fixed for the term of the agreement. The agreement is extremely safe, as the issuer always has either cash or a T-Bill in the trustee possession, and will be approved by most bond counsel.

If allowed by the indenture, the interest to be earned for the term of the FPA can be taken over time or taken up front as a lump sum payment. An issuer can partially fund the DSRF by taking earnings up-front which reduces the overall bond issuance amount. The up-front payment can represent 25-50% of the total DSRF requirement. Similarly, if an issuer had bought a long term treasury in a lower interest rate environment to fund a DSRF which is now underfunded, a partial up-front payment from an FPA can bring the DSRF back to par, eliminating the need to look to other sources of monies to fill the requirement. The remaining interest can then be taken over time or be taken up-front to release locked DSRF funds for other uses.

DEFERRED PAY-OUT OPTION

A deferred pay-out option is a variation on American-style options similar to a shout option. The holder of the option may exercise it at any time, for the value taken by the underlying at that time, but the pay-out is delayed until the expiry date. This term is also applied to certain digital options whose pay-out is not paid when triggered, but deferred until the final maturity.

See also option styles

DEFERRED PREMIUM OPTION

See pay-later option

DEFERRED START OPTION

See forward start option

DELTA

The delta of an option describes its premium’s sensitivity to changes in the price of the underlying. In other words, an option’s delta will be the amount of the underlying necessary to hedge changes in the option price for small movements in the underlying. The delta of an option changes with changes in the price of the underlying. An at-the-money option will have a delta of close to 50%. It falls for out-of-the-money options and increases for in-the-money options, but the change is non-linear: it changes much faster when the option is close-to-the-money. The rate of change of delta is an option’s gamma.

DELTA-HEDGING

An option is said to be delta-hedged if a position has been taken in the underlying in proportion to its delta. For example, if one is short a call option on an underlying with a face value of $1 million and a delta of 25%, a long position of $250,000 in the underlying will leave one delta-neutral with no exposure to small changes in the price of the underlying. Such a hedge is only effective instantaneously, however. Since the delta of an option is itself altered by changes in the price of the underlying, interest rates, the option’s volatility and its time to expiry, changes in any of these factors will shift the net position away from delta-neutrality. In practice, therefore, a delta-hedge must be rebalanced continuously if it is to be effective.

DERIVATIVE

A derivative instrument or product is one whose value changes with changes in one or more underlying market variables, such as equity or commodity prices, interest rates or foreign exchange rates. Basic derivatives include, forwards, futures, swaps, options, warrants and convertible bonds. In mathematical models of financial markets, derivatives are known as contingent claims.

DETERMINISTIC VOLATILITY

The family of options pricing models (including those of Dupire, Derman, Kani and Zou) that seek to incorporate the volatility skew and assume that the local volatility of the underlying stock is a deterministic function of time and the stock price itself.

DIFFERENCE OPTION

See spread option

DIGITAL OPTIONS

See binary option

DISCRETE BARRIER OPTION

Barrier options where the trigger level is only active for part of the option’s lifetime. This includes barrier options where the trigger is only valid on certain fixing dates, as well as cases where the trigger is valid for sub-intervals of the option’s lifetime.

DISTRIBUTION

The probability distribution of a variable describes the probability of the variable attaining a certain value. Assumptions about the distribution of the underlying are crucial to option models because the distribution determines how likely it is that the option will be exercised. Many models assume the logarithm of the relative return has a normal distribution, which can be described by two parameters.

The first is the distribution’s mean; the second its standard deviation (equivalent, if annualized, to volatility). In practice, most empirically observed asset distributions depart from normality. This departure can be described in terms of the skew (how much it tilts to one side or the other) and kurtosis, which describes how fat or thin are the tails at either side. Most markets tend to have fat tails (to be leptokurtic) rather than thin tails (platykurtic). This pushes up the price of out-of-the-money options.

DUAL CURRENCY SWAP

Dual currency swaps are currency swaps that incorporate the foreign exchange options necessary to hedge the interest payments back into the principal currency for dual currency bonds.

DUAL-STRIKE OPTION

See multiple-strike option

DYNAMIC REPLICATION

To replicate the pay-out of an option by buying or selling the underlying (or for some markets, because of cheaper transaction costs, futures) in proportion to an option’s delta. If replicating a short call position, the replicator would, as the underlying went up, buy increasing amounts in proportion to the theoretical option’s delta, and likewise decrease the hedge amount as the market falls. Dynamic replicators are at risk from increases in volatility, as this makes it more difficult for the necessary hedge amounts to be transacted at the desired rate.

EMBEDDED OPTION

An option, often an interest rate option, embedded in a debt instrument that affects its redemption. Examples include mortgage-backed securities and callable and putable bonds. Embedded options do not have to be interest rate options; some are linked to the price of an equity index (Nikkei 225 puts embedded in Nikkei-linked bonds) or a commodity (usually gold). Many so-called guaranteed products contain zero-coupon bonds and call options.

EQUITY WARRANT

A warrant which gives the purchaser the right, but not the obligation, to buy shares in a company at a specific price for a given period of time. One type is issued by a company and gives purchasers the right to buy its stock at a given price for a fixed period. The warrants are usually issued attached to a bond; the stock option lowers the interest on the bond but, if exercised, dilutes the existing equity. The bond and warrant components are sometimes stripped and traded separately. The other type is a covered warrant.

EUROPEAN-STYLE OPTION

A European-style option is one which may only be exercised on the expiry date.

See also option styles

EXCHANGE OPTION

Depending on the context, this can either refer to an outperformance option, or, alternatively an option giving the purchaser the right to exchange one asset for another. The latter type of options are useful if there isn’t a cross-market, as with a barrel of oil priced in Euros. The purchaser of a Euro-oil exchange option would have the right to exchange a certain amount of Euros for a certain number of barrels of oil.

EXCHANGE-TRADED OPTION

See option

EXERCISE period

In an option contract, the period of time in which a party has the right to exercise its option and effect a pre-negotiated transaction.

EXOTIC OPTION

Any option with a more complicated pay-out structure than a plain vanilla put or call option. The pay-out of a plain vanilla option is simply the difference between the strike price of the option and the spot price of the underlying at the time of exercise. For a European-style option, the exercise time is always the expiry date; other option styles offer greater flexibility.

  There are a number of ways in which an option pay-out can differ from that of a plain vanilla. The pay-out could also be a function of:
    •     the difference between a strike and an average rate for the underlying (average options)
    •     the difference between prices for two different underlyings (difference options, exchange options), the same underlying at different times (high-low options)
    •     the correlation between two or more underlyings (outperformance options, outside barrier options)
    •     the difference between a strike and the spot rate at some time other than expiry (deferred pay-out options, shout options, lookback options, cliquet options, ladder options – see diagram
    •     a fixed amount (binary options)

  Alternatively, or additionally, a pay-out may be conditional on certain trigger conditions being met. For example, barrier options are activated or nullified if a spot rate falls or rises through a predetermined trigger level. Multiple trigger conditions are possible (as the in case of corridor or mini-premium options).

EXPLODED TREE

A tree (binomial or trinomial) in which an up step followed by a down step gives a different outcome to a down step followed by an up step. Consequently, the number of nodes increases exponentially, compared with a recombining tree, in which the number increases quadratically. This makes their evaluation exceptionally computer-intensive. The advantage is that they can be used to price path-dependent options and they are important for modeling interest rate options. See binomial+tree for diagram.

EXTENDIBLE SWAP

A swap in which the fixed-rate payer has an option to extend the swap. A three-year swap extendible for a further two years would simply use a three-year swap in conjunction with a swaption on a two-year swap with a maturity of three years.

FLEXIBLE OPTION

A flexible option (also known as a flexible exchange or flex option) is a customizable exchange-traded option which allows the buyer to customize contract terms such as expiry date and contract size in addition to the strike price. Flexible options with single stock, index, or even currency underlyings are traded on several major exchanges.

FLOORTION

An option on a floor. The purchaser has the right, but not the obligation, to buy or sell a floor at a predetermined price on a predetermined date.

FORWARD EXTRA

The Forward Extra structure has been developed primarily for hedging purposes, and is essentially a European option that becomes a synthetic forward contract at the strike level of the option if a trigger level is reached. For zero cost, the purchaser of the structure acquires protection against an adverse exchange rate move and can benefit from a favorable limited move on the underlying (provided that the trigger level is not hit). The Forward Extra Plus offers the protection of the Forward Extra. However, if a pre-determined trigger level is reached, the Forward Extra becomes a synthetic forward contract struck at the initial forward outright rate.

See also trigger forward, weekly reset forward

FORWARD START OPTION

An option that gives the purchaser the right to receive, after a specified time, a standard put or call option. The option’s strike price is set at the time the option is activated, rather than when it is purchased. The strike level is usually set at a certain fixed percentage in or out-of-the-money relative to the prevailing spot rate at the time the strike is activated.

FUTURE

A future is a contract to buy or sell a standard quantity of a given instrument, at an agreed price, on a given date. A future is similar to a forward contract and differs from an option in that both parties are obliged to abide by the transaction. Futures are traded on a range of underlying instruments including commodities, bonds, currencies, stock indices and even pollution.

  The most important difference between futures and forwards is that futures are almost always traded on an exchange and cleared by a clearing house, whereas forwards are over-the-counter instruments. Furthermore, futures, unlike forwards, have standard delivery dates and trading units. Most futures contracts expire on a quarterly basis. Contracts specify either physical delivery of the underlying instrument or cash settlement at expiry. Cash settlement involves the company paying or being paid the difference between the price struck at the outset and the expiry price of the contract.

  The clearing house is crucial, acting as the counterparty to all transactions; that is, it acts as the buyer to the seller of the future, and as the seller to the buyer. Since for every long futures position there must be a short position, the clearing house has a net position of zero at the end of each day. It also operates a system known as margining. On entering a transaction, a company will be required to lodge a specified sum of money (initial margin) with the clearing house. The amount depends on how much the clearing house considers prudent to set aside to protect against a dramatic move in the underlying market. Each day, the company also gives or receives variation margin, which is the difference between the original contractual price and the daily closing price.

  In pricing futures, an important distinction is between futures on assets held for investment and those held almost exclusively for consumption (such as pork bellies or soya beans). The price of futures on investment assets is determined by the relative interest rates or dividend yields of the asset and cash, such as to eliminate riskless arbitrage through buying the future and selling the asset or vice versa. By contrast, futures on commodities not held for investment cannot readily be priced by an arbitrage approach – perceived supply and demand considerations are much more significant.

  Futures provide a formalized method of transferring risk from those wanting to reduce their market exposure to those wanting to increase it. For example, futures markets allow commodity producers to hedge against falling prices, or fund managers to weight their stock, bond or currency portfolios according to their required risk profiles.

  For fund managers, futures also provide a way of entering and exiting markets with typically much lower transaction costs (friction) than would be the case with cash alternatives. This is especially true in equity markets. Because of their standardized nature, however, futures contracts may not match precise hedging needs. Instead the hedger may incur basis risk, the risk that the return on the futures position may differ from that on the spot.

FUTURES OPTION

An option, either a put or a call, on any futures contract. Also known as an option on a future.

GAMMA

The rate of change in the delta of an option for a small change in the underlying. The rate of change is greatest when an option is at-the-money and decreases as the price of the underlying moves further away from the strike price in either direction – gamma is therefore -shaped. A long gamma position is one in which a trader is long options. For a position that is short gamma, the opposite holds. Gamma can be hedged by mirroring the options position. Alternatively, a trader may choose to adjust the position in the underlying continually in order to maintain delta neutrality.

GARMAN-KOHLHAGEN MODEL

A model developed to price European-style options on spot foreign exchange rates. The model is based upon the Black-Scholes model with the addition of an extra interest rate factor for the foreign currency.

GARMAN-KOHLHAGEN MODEL

GEARED KNOCK-OUT/IN OPTION

See barrier option

GEARING

The price of the underlying divided by the price of the derivative contract, which can be used for crude assessments of leverage and option pricing. A more sophisticated measure is effective gearing, or elasticity, which is designated lambda. This is the traditional gearing multiplied by the derivative’s delta.

GOLD-LINKED NOTE

A note (or bond) with interest payments linked to the price of gold constructed by reducing the coupon (sometimes to zero) and buying (or selling) put or call options to gain exposure to an increasing (or decreasing) gold price.

GUARANTEED EXCHANGE RATE OPTION

An option (also known as a quanto option) on an asset in one currency denominated in a second currency. The exchange rate at which the purchaser converts the currency is fixed at the start. Such options are increasingly popular as investors want exposure to foreign assets without the foreign exchange risk. Most of the demand is for bond and stock index options. The extra cost of the option depends on the correlation between movements in the exchange rate and movements in the underlying. The higher (more positive) the correlation between the underlying and the exchange rate (expressed as the number of units of currency two per unit of currency one) the more expensive a call option will be and the cheaper a put option will be. Quanto options can, however, look cosmetically cheaper (or more expensive) depending on the forward interest rates in the two currencies. For example, buying a call on a US asset could be “cheaper” in euros if there is a wide interest rate differential between the euro and the dollar.

HEDGE

To hedge is to reduce risk by making transactions that reduce exposure to market fluctuations; for example, an investor with a long equity position might compensate by buying put options to protect against a fall in equity prices. A hedge is also the term for the transactions made to effect this reduction.

HIGH-LOW OPTION

A combination of two lookback options. A high-low option pays the difference between the high and low of an underlying, such as a stock index. A speculative purchaser would be taking the view that the market would be more volatile than the implied volatilities of both lookback options incorporated in the structure.

HISTORICAL VOLATILITY

Historical volatility is a measure of the volatility of an underlying instrument over a past period. Historical volatility can be used as a guide to pricing options but isn’t necessarily a good indicator of future volatility. Volatility is normally expressed as the annualized standard deviation of the log relative return.

HO-LEE MODEL

The first model that set out to model movements in the entire term structure of interest rates, not just the short rate, in a way that was consistent with the initially observed term structure. However, since the model only has a single random factor, it makes the simplifying assumption that the volatility structure remains constant along the yield curve. Heath-Jarrow-Morton later generalized this model, using a more general form of volatility and introducing continuous trading. In addition, Ho-Lee allows for the possibility of negative interest rates. The model was developed using a binomial tree, although closed-form solutions have now been found for discount bonds and discount bond options.

HULL-WHITE MODEL

An extension of the Vasicek model for interest rates, the main difference being that mean reversion is time-dependent. Both are one-factor models. The Hull-White model was developed using a trinomial lattice, although closed-form solutions for European-style options and bond prices are possible.

IMPACT FORWARD

A collared forward, such as one in which the purchaser buys a put and sells a call, both being out-of-the-money. The premiums on the two options balance out, so the strategy is zero cost. Upside and downside is limited to the gap between the strike prices.

IMPLIED DISTRIBUTION

The probability distribution of returns for an asset which is implied by options traded on that asset. The distribution is inferred by combining the variation of volatility with strike price (see volatility smile) and the assumptions made about the distribution in the option pricing model.

IMPLIED TREE

A binomial or trinomial tree, which models the distribution implied by vanilla option prices and their implied volatilities.

See also implied volatility, implied distribution, volatility smile.

IMPLIED VOLATILITY

The value of volatility embedded in an option price. All things being equal, higher implied volatility will lead to higher vanilla option prices and vice versa. The effect of changes in volatility on an option’s price is known as vega. If an option’s premium is known, its implied volatility can be derived by inputting all the known factors into an option pricing model (the current price of the underlying, interest rates, the time to maturity and the strike price). The model will then calculate the volatility assumed in the option price, which will be the market’s best estimate of the future volatility of the underlying.

See also volatility skew, volatility term structure

INDEX AMORTISING SWAP (IAS)

An interest rate swap whose principal amortizes on the back of movements in an index, such as Libor or constant maturity treasuries. The fixed-rate receiver effectively grants an option to the fixed-rate payer to amortize the swap. The option is triggered by interest rate movements after an initial lock-out period. The notional principal amortizes as rates fall or remains constant if rates remain the same. In return for granting the option, the fixed-rate receiver gets a yield above current fixed rates. IAS have been widely used by US regional banks in their asset/liability management activities. By using IAS, banks were able to obtain the negative convexity of a mortgage-backed security and avoid the risk of excessive prepayments due to changes in consumer sentiment.

But the fixed receiver is exposed to both falling and rising rates. If rates fall, there is the possibility at each interest date that some or all of the swap will be terminated, creating a reinvestment risk. If rates rise, the swap may run to maturity, providing meager income while floating rates soar.

An IAS fixed-rate receiver is selling volatility to the payer for an enhanced yield. So the lower the volatility of the index, the lower the option value and yield pick-up. A subsequent fall in volatility benefits the receiver because the likelihood that the swap will amortize decreases. IAS can be structured with negative or positive convexity and the amortization schedules and lock-out periods can be changed in order to increase or decrease yields. Also known as an Indexed Principal Swap.

INSTALLMENT OPTION

See compound option

INTEGRATED HEDGE

A hedge which combines more than one distinct price risk. For example, crude oil is usually priced in US dollars. Therefore a producer of crude oil whose home currency is not the dollar (say, the euro) is exposed to both currency risk and the price risk for crude oil. One possible integrated hedge would be a single quanto option, which would hedge the price of crude oil in euro. As such, it would depend heavily on the correlation (if any) between the two markets.

INTEREST RATE GUARANTEE

An option on a forward rate agreement (FRA), also known as a FRAtion. Purchasers have the right, but not the obligation, to purchase an FRA at a predetermined strike. Caps and floors are strips of IRGs.

INTEREST RATE SWAP

An agreement to exchange net future cashflows. Interest rate swaps most commonly change the basis on which liabilities are paid on a specified principal. They are also used to transform the interest basis of assets. In its commonest form, the fixed-floating swap, one counterparty pays a fixed rate and the other pays a floating rate based on a reference rate, such as Libor. There is no exchange of principal – the interest rate payments are made on a notional amount. In floating-floating swaps the two counterparties pay a floating rate on a different index, such as three-month Libor versus six-month Libor.

  Swaps usually extend out as far as 10 years, although 12–40 year maturities are available in some liquid currencies. However, the longer the maturity of the swap, the less liquid it becomes and credit risk increases. Credit enhancements such as mutual put options and collateral are used to ameliorate the credit risk of longer term swaps.

  Interest rate swaps provide users with a way of hedging the effects of changing interest rates. For example, a company can convert floating-rate interest payments to fixed-rate payments if it thinks interest rates will rise (which would make its liabilities more expensive). Companies can also use interest rate swaps in conjunction with new debt issuance, raising money on, say, a fixed basis and swapping it into floating-rate debt. In an interest rate swap there is a fixed-rate payer (floating-rate receiver) and a fixed-rate receiver (floating-rate payer). If there is a preponderance of fixed-rate payers (for example, when companies want to lock into low rates), the swap spread (the yield spread over equivalent maturity government bonds) increases. If there is a preponderance of fixed-rate receivers, the swap spread declines.

  Interest rate swaps were initially transacted back-to-back, with a bank acting as an intermediary. In return for putting the differing requirements together and for taking the credit risk on the interest rate payments, the bank took a fee – either fixed or a small proportion of the interest payments. Now banks run swap books and act as principals in transactions. As a result they have to hedge the swaps they put on their books. This can be done with another swap or with securities. Since US dollar and sterling interest rate swaps are priced as a spread over Treasuries, this is not too difficult, although movement in the swap spread does create basis risk.

  Most dealers use short-term interest rate futures such as Eurodollar futures or Euroyen futures to hedge swap positions. Disparities between futures and cash bonds and notes can drive swap spreads up and down. Such hedges can be imperfect when swap payments differ from the contract’s maturity.

IN-THE-MONEY

Describes an option whose strike price is advantageous compared to the current forward market price of the underlying. The more an option is in-the-money, the higher its intrinsic value and the more expensive it becomes. As an option becomes more in-the-money, its delta increases and it behaves more like the underlying in profit and loss terms; hence deep in-the-money options will have a delta of close to one.

INTRINSIC VALUE

The amount by which an option is in-the-money, that is, its value relative to the current forward market price. Option premiums comprise intrinsic value and time value.

ITO’S LEMMA

A mathematical relationship that allows the stochastic process followed by a function of a variable to be deduced. Ito’s Lemma is fundamental to the derivation of a number of options pricing models.

JOINT OPTION

An option on an underlying, often a stock index, denominated in a second currency. Unlike a guaranteed exchange rate option, in which exchange rates are fixed, the purchaser of a joint call option benefits from upside in the currency in which the asset is originally denominated, for example, S&P 500 call option struck in euro. In this case, at the inception, strike is specified in euro. At the maturity, S&P 500 level is observed and is multiplied by then current euro/US dollar rate. This converted value of S&P 500 is compared with the strike to determine the payoff in euro.

See also correlation, exchange option, quanto product

KNOCK-OUT OPTION

See barrier option

KURTOSIS

A measure of how fast the tails or wings of a probability distribution approach zero, evaluated relative to a normal distribution. The tails are either fat-tailed (leptokurtic) or thin-tailed (platykurtic). Markets are generally leptokurtic. The fatter the tails, the greater the chance a variable will reach an extreme value, implying that models such as Black-Scholes – which assume perfect normal distribution – produce pricing biases for deep in- or out-of-the-money options.

LADDER OPTION

A path-dependent option, most often based on an equity index or a foreign exchange rate. The pay-out of a ladder option increases stepwise as the underlying trades upwards (or downwards) through specified barrier levels (the “rungs” of the ladder). Each time the underlying trades through a new barrier level, the option pay-out is locked-in at the higher level.

LEVERAGE

The ability to control large amounts of an underlying variable for a small initial investment. Futures and options are regarded as leveraged products because the initial premium paid by the purchaser is generally much smaller than the nominal amount of the underlying. Leverage is usually measured as a quantity called lambda. Many structured notes are said to be leveraged because their coupon is governed by a multiple of a reference interest rate (such as Libor). It is also possible to deleverage a note by linking its coupon to a fraction of the reference rate.

LIMIT BINARY

See range binary

LISTED OPTION

See warrant, exchange traded futures, options

LITE OPTION

A European-style basket option with a payoff determined by the underlying assets that remain in the basket, after a certain number of the best and worst performing assets in the basket were removed at a specified date prior to expiry.

LONGSTAFF-SCHWARTZ MODEL

A two-factor model of the term structure of interest rates. It produces a closed-form solution for the price of zero coupon bonds and a quasi-closed-form solution for options on zero coupon bonds. The model is developed in a Cox-Ingersoll-Ross framework with short interest rates and their volatility as the two sources of uncertainty in the equation.

LOOKBACK OPTIONS

Lookback options give the holder to right at expiry to exercise the option at the most favorable rate or price reached by the underlying over the life of the option. As with average options, the strike may be either fixed or floating. With an optimal rate lookback option, the strike is fixed at the outset and the option will pay out against the highest (for a call) or lowest spot rate (for a put) reached over the life of the option, irrespective of the spot rate at expiry. The option will usually be settled in cash. Since the option is likely to have a larger pay-out than the corresponding plain vanilla option, it commands a larger premium. The strike for an optimal strike lookback option, on the other hand, is not fixed until expiry, when it is set to be the highest (for a put) or lowest spot rate (for a call) over the option’s life and exercised for cash or physical against the spot rate prevailing at expiry.

See also cliquet option, ladder option, look-forward options, shout option

LOW EXERCISE PRICE OPTION (LEPO)

A low exercise price option (Lepo) is a call option with an exercise price set deep in-the-money. The limiting case, a zero exercise price option, is when the strike price is zero. It is virtually certain to be exercised and the value and performance of its intrinsic value is effectively identical to that of the underlying equity.

These features are designed to allow participation in the performance of an equity price where there are legal or financial obstacles to purchasing the underlying directly. If the Lepo is cash-settled, the buyer profits to the same extent as with a direct holding in the underlying, but without having to transact in it. However, a Lepo holder does not earn dividends or have voting rights over the equity.

MANDARIN COLLAR

The Mandarin Collar combines a range forward with the purchase of a range binary structure, such that should the spot stay within the prescribed range, the proceeds of the range forward are enhanced by the pay-out amount of the range binary. If either of the limits trades at any time, the range binary is terminated, but the underlying exposure remains hedged by the range forward. The graph displays the payoff of a long exposure hedged using a Mandarin Collar; the choice of name should be apparent from this picture.

MARGRABE OPTION

See outperformance option

MINI-PREMIUM OPTION

The purchaser of a mini-premium option (also known as a step-payment or installment option) pays no initial premium. Instead, a fixed premium becomes payable if the market spot rate subsequently trades through each of a number of predetermined trigger levels for the spot rate. While this offers hedgers protection at zero cost, the total premium paid if all the triggers are activated will be greater than the premium for the equivalent plain vanilla option. However, in this case, the spot rate would have moved in favor of the hedger’s underlying position.

See also binary option, contingent premium option

MIN-MAX

London Metal Exchange vernacular for a collar – selling an option, in order to fund the purchase of an opposite option.

MIRAGE OPTION

A European-style option paying the compounded value of returns of an underlying asset over a specified number of time periods of specified length, where payoffs from a certain number of the best and worst performing periods are excluded from the payoff.

MONEY-BACK OPTION

An option that will repay at least the original option premium at expiry. However, the leverage of the option is greatly reduced compared with a standard option: effectively the premium is simply the interest forgone on the original principal.

MONTE CARLO SIMULATION

A method of determining the value of a derivative by simulating the evolution of the underlying variable(s) many times over. The discounted average outcome of the simulation gives an approximation of the derivative’s value. This method may be used to value complex derivatives, particularly path-dependent options, for which closed-form solutions have not been or cannot be found. Monte Carlo simulation can also be used to estimate the value-at-risk (VAR) of a portfolio. In this case, a simulation of many correlated market movements is generated for the markets to which the portfolio is exposed, and the positions in the portfolio revalued repeatedly in accordance with the simulated scenarios. The result of this calculation will be a probability distribution of portfolio gains and losses from which the VAR can be determined. The principal difficulty with Monte Carlo VAR analysis is that it can be very computationally intensive.

MOVING STRIKE OPTION

An option in which the strike is reset over time, such as an interest rate cap in which the strike is reset for the next period at the current interest rate plus a pre-agreed spread.

MULTI-FACTOR MODEL

Any model in which there are two or more uncertain parameters in the option price (one-factor models incorporate only one cause of uncertainty: the future price). Multi-factor models are useful for two main reasons. Firstly, they permit more realistic modeling, particularly of interest rates, although they are very difficult to compute. Secondly, multi-factor options (for example, spread options) have several parameters, each with independent volatilities, and also the correlation between the underlyings must be dealt with separately.

MULTI-FACTOR OPTION

Any option whose pay-out is linked to the performance of more than one asset. Such options include outside barrier options, outperformance options, portfolio options, multiple strike options and spread options. Their value is usually strongly dependent on the correlation between the underlying assets. A multi-factor option is synonymous with a multi-colored rainbow option.

MULTIPLE STRIKE OPTION

See outperformance option

NAKED OPTION

An option that is sold (bought) without an offsetting position in the underlying.

OMEGA

The currency risk that arises when the buyer or seller of an option has to account for the transaction in a different currency.

ONE-TOUCH OPTION

See binary option

OPTION

A contract that gives the purchaser the right, but not the obligation, to buy or sell an underlying at a certain price (the exercise, or strike price) on or before an agreed date (the exercise period).

  For this right, the purchaser pays a premium to the seller. The seller (writer) of an option has a duty to buy or sell at the strike price, should the purchaser exercise his right. With European-style options, purchasers may take delivery of the underlying only at the end of the option’s life. American-style options may be exercised, for immediate delivery, at any time over the life of the option. Holders of semi-American-style or Bermudan options may be exercised on specified dates – typically on a monthly or quarterly basis.

  Options can be bought on commodities, stocks, stock indexes, interest rates, bonds, currencies, etc. The trading terminology, though, may change according to the product. In most cases, the right to buy the underlying is known as a call, and the right to sell, a put.

  Options are traded on formal exchanges and in over-the-counter (OTC) markets. The exchanges, such as the Chicago Board Options Exchange, the London International Financial Futures and Options Exchange and the Philadelphia Stock Exchange, provide primarily standardized options; the OTC markets are able to provide tailored products to fit specific requirements. The choice between OTC and exchange-traded options will depend on the degree of tailoring required, the relative liquidity of both markets (this varies greatly according to the underlying) and credit concerns.

  Such credit concerns increase with the option’s maturity, since the likelihood that a counterparty will default increases with the length of time that passes between the option being bought and being exercised. Several derivatives exchanges have tried to bridge the gap between OTC and exchange-traded options by introducing flexible options that can be customized by the purchaser.

  Pricing models for simple or vanilla options have five major inputs: the option’s exercise or strike price; the time to expiration; the price of the underlying instrument; the risk-free interest rate on the underlying instrument, and the volatility of the underlying instrument (See also historical volatility, implied volatility).

  European-style options are usually priced off a closed-form analytical model first published by Fischer Black and Myron Scholes in 1973, which has subsequently been modified to fit different underlyings (see Black-Scholes model).

  At maturity, an option’s value will depend on the value of the right to buy or sell a product. If an option is purchased giving the right to buy gold at $375 an ounce and at expiration the price is $400, the option is worth $25.

  The extent to which an option is in-the-money (how far the strike price is below/above the current forward market price) is called its intrinsic value. Where the strike price is less favorable than the market price, the option is said to be out-of-the-money, and where the two prices are the same it is at-the-money.

  At any time before maturity, an option’s price will be a combination of its intrinsic value (which is always either greater than, or equal to, zero) and its time value. The latter includes the cost of carry and the probability that the price of the underlying will move into or remain in the money. Options can broadly be used in two ways – for speculation, or for insurance. Their usefulness, both from a buyer’s and a seller’s point of view, derives from their pay-outs.

  In contrast to other types of hedge, options provide insurance against unfavorable moves in a product’s price and the opportunity to take advantage of favorable moves. Forwards and futures, for example, require buyers and sellers to lock into one rate. In return for assuming this risk, sellers of options receive a premium, effectively a risk-taking fee.

  The pay-off of a purchased option means that the price risk of an option is limited to its premium – it is not as exposed to adverse movements as a position in the underlying.

  For speculators selling (writing) options, this often means taking a naked option position and therefore being exposed to adverse movements in the underlying. Hedgers may sell options to garner premium to offset any expected slight downturn in a market. Since option premiums are only a fraction of the cost of the underlying product, it is possible to achieve a much greater exposure to price changes of the underlying compared with a similar investment directly in the product – this is called leverage.

OPTION COMBINATION STRATEGIES

Options may be combined so that their pay-outs produce a desired risk profile. Some combinations are primarily trading strategies, but option combinations can be useful in, for example, allowing investors to construct a strategy to take advantage of a particular view they have of the market. Other strategies allow purchasers to reduce their premiums by giving up some of the benefits they may have received from market movements.

See also bear spread, bull spread, calendar spread, call spread, condor, cylinder, put spread, ratio spread, straddle, strangle

OPTION ON FUTURE

See futures option

OPTION REPLICATION

See replication

OPTION STYLES

The purchaser of a European-style option has the right to exercise it on a predetermined expiry date. In contrast, the holder of an American-style option has the right to exercise it at any time during its lifetime, up to and including its expiry date. This flexibility means there is a greater probability of an American-style option being exercised than the corresponding European-style option with the same strike. Hence the early exercise feature of an American option adds value and makes it the more expensive of the two. Most exchange-traded options are American-style. Further variations on these styles also exist. A Bermudan option, so called because it falls between American- and European-style options, has more than one possible exercise date. For example, the holder of a Bermudan option with a two-year maturity might have the right to exercise it every quarter or half year during the life of the contract. Bermudans are also known as limited exercise or semi-American-style options. Another twist is the deferred pay-out option, a variation on American-style options in which the option can be exercised at any time during the option’s life, but the pay-out is delayed until the expiry date. With the similar shout option, the purchaser can lock in a profit at any time, but retains the right to profit from further favorable moves.

otc derivative

Over-the-counter derivatives are privately negotiated contracts that are traded directly between two parties, rather than on a centralized exchange. Some of the most common derivatives to be traded in the OTC market include swaps, forward rate agreements, and exotic options. The self-regulatory trade organization that oversees the over-the-counter derivatives market is the International Swaps and Derivatives Association (ISDA).

OUT-OF-THE-MONEY

Describes an option for which the currency forward market price of the underlying is below the strike price in the case of a call, or above it in the case of a put. The more the option is out-of-the-money, the cheaper it is (since the chances of it being exercised get slimmer). Its delta also declines and it becomes less sensitive to movements in the underlying.

OUTPERFORMANCE OPTION

Also known as a Margrabe option. A two-factor option giving the purchaser the right to receive the outperformance of one asset over another asset. For example, a purchaser with a view that the CAC index will outperform the DAX index should buy the outperformance option which pays notional multiplied by the outperformance of the CAC index over the DAX index. In this case, the payoff is zero if CAC underperforms DAX. The value of an outperformance option will largely be dictated by the historical correlation between the underlyings.

PARISIAN OPTION

A barrier option with a barrier that is triggered only if the underlying has been beyond the barrier level for longer than a specified period of time.

PARTICIPATING FORWARD

The simultaneous purchase of a call option (put option) and sale of a put (call) at the same strike price, usually for zero cost. The option purchased must be out-of-the-money and the option sold (to finance the option purchase) is for a smaller amount and will be in-the-money.

PASSPORT OPTION

See spot trader option

PATH-DEPENDENT OPTION

A path-dependent option has a pay-out directly related to movements in the price of the underlying during the option’s life. By contrast, the pay-out of a standard European-style option is determined solely by the price at expiry.

See also average option, barrier options, cliquet option, high-low+option, lookback option and shout option

PAY-LATER OPTION

A pay-later option refers to any option for which a premium is not paid at the time the option is purchased. Payment of the premium may be deferred until expiry, when it may be deducted from any pay-out (a deferred premium option), or be contingent on the option being exercised (a contingent premium option) or passing a given barrier level (for example, a mini-premium option).

PERFECT TRADER OPTION

See spot trader option

PIN RISK

The phenomenon where a small move in the underlying can have a significant impact on the value of an at-the-money option shortly before expiration.

PORTFOLIO INSURANCE

A strategy developed in the 1980s as a way of limiting losses on risky asset portfolios. Because put options were not widely available, the strategy synthetically reproduced the pay-out of a put option by a delta-hedging program. As long as markets move continuously, transaction costs are minimal and volatility is relatively stable, option returns can be easily replicated, although one can not predetermine a maximum cost.

The effectiveness of such a strategy was thrown into doubt with the crash of 1987. The unprecedented levels of volatility and the lack of liquidity made the strategy extremely difficult to implement. Its reputation suffered and it was widely blamed for exacerbating the severity of the collapse. Portfolio insurance has not entirely disappeared, though. Some fund managers still synthetically replicate option pay-outs rather than pay option premium, especially if they think volatility will fall. However, most such strategies now involve the covering of a certain amount of volatility risk by buying out-of-the-money options.

PORTFOLIO OPTION

A portfolio option is a multi-factor option which pays out the difference between the return from a portfolio of assets and a specified strike price.

POWER OPTION

An option with a payoff dependent on the price of the underlying at expiry, raised to some power.

PREMIUM-REDUCTION DEVICE

A strategy which aims to reduce the cost of an option or other derivative. There are many ways to achieve this; three common techniques follow.

  The first is to sell a second derivative; the premium received can then be used to lower the funding requirement for the purchased derivative. This is the technique employed for reducing the cost of a collar.

  The second is to limit participation in moves in the underlying by imposing limitations on the pay-out profile of the instrument (as in a barrier option or a capped floater).

  The final way is to accept payments below market rates, with the possibility of making up the shortfall at the end of the instrument’s life (see yield adjustment).

PRINCIPAL-GUARANTEED PRODUCT

Any investment vehicle that allows investors to gain exposure to an asset while guaranteeing the return of their principal. Such products are normally constructed by buying a deep discount bond (often a zero-coupon bond) and using the rest of the money to buy embedded call or put options to gain exposure to a second asset, often a stock index.

See also guaranteed return on investment

PUT OPTION

See option

PUT SPREAD

A put spread reduces the cost of buying a put option by selling another put at a lower level. This limits the amount the purchaser can gain if the underlying goes down, but the premium received from selling an out-of-the money put partly finances the at-the-money put. A put spread may also be useful if the purchaser thinks there is only limited downside in the market.

PUT-CALL PARITY

The relationship between a European-style put option and a European-style call option on the same underlying with the same exercise price and maturity. Put-call parity states that the pay-off profile of a portfolio containing an asset plus a put option is identical to that of a portfolio containing a call option of the same strike on that same asset (with the rest of the money earning the risk-free rate of return). In practice, a put option on, say, a stock index, can be constructed by shorting the stock and buying a call option. The relationship means that traders are able to arbitrage mispriced options.

QUANTO PRODUCT

An asset or liability denominated in a currency other than that in which it is usually traded, typically equity index futures, equity index options, bond options and interest rate swaps (differential swaps). One example is the Chicago Mercantile Exchange’s Nikkei 225 stock index contract, which uses the nominal price of the yen-denominated index applied to a US dollar notional principal. Quanto products can be hedged with an offsetting position in a local currency product. Variable asset and foreign exchange exposures will arise with changes in the foreign exchange rate and in the underlying, so the structures must be continually dynamically hedged in a similar fashion to option products.

See also guaranteed exchange rate option

RAINBOW OPTION

The term “rainbow option” is synonymous with “multi-factor option”. The underlying factors are referred to as colors in the context of rainbow options. Hence a two-factor option (such as a spread option) would be a two-color rainbow option.

RANGE BINARY

The Range Binary structure has been developed primarily for trading purposes and is essentially a bet on a spot rate staying within a range. The strategy is often linked with a deposit for yield enhancement purposes.

A currency range is specified by the customer over a fixed period. A premium is paid up front and provided that the spot stays within the range (as monitored on a 24-hour basis), then a multiple of the premium invested will be payable.

A rebate range binary is one in which the premium invested is rebated if a designated boundary of the range is breached first. A similar structure, the limit binary, is also essentially for trading. This is fundamentally a bet on a spot not staying within a predetermined range. The customer specifies two spot rates, one above and one below the current spot rate. A premium is paid up front, and providing that both levels trade (as monitored on a 24-hour basis), a fixed multiple of the premium invested will be payable. A James-Bond range binary is a range binary with two lives (“You only live twice”). If the initial range is broken a new range is determined (usually centered around the breached barrier). If this second range is breached the holder receives no pay-out.

See also corridor option, trigger condition

RANGE NOTE

A range note (also known as a fairway note, an accrual note, or a corridor floater) is a structured note, which pays an above-market interest rate for each day that the underlying spot rate stays within a specified range (sometimes called the accrual corridor). If the underlying trades outside the specified range, the investor receives no interest for that day. The underlying is usually a reference interest rate, such as Libor or a Constant Maturity Treasury, but it could also be a foreign exchange rate, an equity price or the spread between two interest rates. The range is determined at the outset to suit the investor’s risk/return requirements, but might also be reset by the investor or be automatically centered on the prevailing rate at each reset date. This higher yield is achieved by the investor selling an embedded corridor option, particularly in times of high volatility. The holder of the note will therefore benefit in stable market periods when volatility is low. It is also possible for the barriers on a range note to act as knock-out levels by embedding a knock-out corridor option or a range binary. In this case the note is extinguished altogether or becomes a zero coupon note if the reference rate trades through a barrier. This is known as a barrier floater or a knock-out range note.

RATCHET OPTION

See cliquet option

RATIO SPREAD

A ratio spread involves buying different amounts of similar options with differing strike prices. The purchase of an in-the-money option is financed by the selling of more out-of-the-money options. Conversely, the out-of-the-money options are financed by selling less of an in-the-money option.

REAL OPTION

An alternative method (to cashflow models) for valuing a non-traded asset or liability whose profit and loss sensitivity to some market variable mimics that of an option. For example, consider the right to extract oil from an oilfield. Low oil prices mean that the field can be left untapped at no additional cost. However, higher oil prices may mean that the cost of extraction could be more than covered by selling oil into the bullish market. So the right to extract oil resembles an option on the oil price.

REBATE

Barrier options often have a rebate associated with the trigger level(s). A rebate is an amount paid to the holder of the derivative if the instrument is knocked out or is never activated during its lifetime as partial recompense for their initial investment. One example is the rebate range binary.

REBATE RANGE BINARY

See range binary

RELATIVE PERFORMANCE OPTION

See outperformance option

RELATIVE PERFORMANCE RISK

The risk that a fund manager’s choice of investments will fail to match the performance of the benchmark against which the fund is measured, prompting fund redemptions. A similar risk is run by corporate treasury risk managers who are measured against benchmark hedge levels. One way to address this type of risk is with outperformance options. Relative performance risk is also used to refer to the risk that an individual asset will underperform relative to its asset class. For equities, this may be measured by a stock’s beta, its standardized covariance with respect to the relevant equity index.

REPLICATION

To replicate the pay-out of an option by buying or selling other instruments. Creating a synthetic option in this way is always possible in a complete market. In the case of dynamic replication this involves dynamically buying or selling the underlying (or normally, because of cheaper transaction costs, futures) in proportion to an option’s delta. In the case of static replication the option (usually an exotic option) is hedged with a basket of standard options whose composition does not change with time – e.g., an at-expiry digital option can be replicated with a call spread.

REVERSAL

To take advantage of mispriced options by creating a synthetic long futures position and hedging it by selling futures contracts against it. A trader may buy an undervalued call, at the same time selling a fairly valued put and buying a futures contract. The same strategy could be applied if the put was undervalued. The ability to undertake this riskless arbitrage relies on put-call parity.

REVERSE BARRIER OPTION

See barrier option

REVERSE CONVERTIBLE

These are just like convertible bonds. The main difference is that rather than buying a call option on a stock, the investor sells a put on the stock or index. The investor receives higher than normal coupons but may lose some principal if the put ends up in the money.

REVERSE INDEX AMORTISING SWAP

An interest rate swap in which payments are linked to an index (e.g., Libor or constant maturity Treasuries) and increase if that index declines. The swap therefore exhibits positive convexity. Receiving fixed in a reverse index amortizing swap (reverse IAS) provides a hedge for instruments (such as mortgage swaps) that amortize as interest rates decline, although it is important to ensure that the indexes on which the amortization or accreting schedules are based are highly correlated. Unlike a conventional IAS, the fixed receiver of a reverse IAS is buying volatility (sometimes referred to as “optionality”) which offsets the short option position of a mortgage portfolio.

REVERSIBLE SWAP

An interest rate swap in which one side has an option to alter the payment basis (fixed/floating) after a certain period. This is usually achieved by the use of a swaption, allowing the purchaser the opportunity to enter a swap with payment on the opposite basis. The swaption would be for twice the principal amount, one half nullifying the original swap.

RHO

Measures an option’s sensitivity to a change in interest rates. This will have an impact on both the future price of the option and the time value of the premium. Its impact increases with the maturity of the option.

RISK REVERSAL

1) See cylinder
2) The term “risk reversal” is also used, by currency option traders, to denote the difference in implied volatility between out-of-the-money call and put options which both have a delta of 25%. The level of the risk reversal is often used as a sentiment indicator in currency markets as it indicates the relative demand for calls versus puts.

SHOUT OPTION

An option that allows a purchaser to lock in a minimum return if he thinks the market is at its high (low).

If, for example, he buys a shout call option at 100 and the market moves up to 110, he can, if he thinks it is the high, “shout” and lock in 10 points. If the market declines, he still receives 10 points. If the market finishes higher than 110, the holder receives the additional gain above 110.

With a lookback option, the holder is guaranteed to sell at the highest price the market reaches, even if it goes down again. The holder of the shout option is able to sell only at the level shouted, even if the market subsequently rises further before going down.

SKEW

A skewed distribution is one which is asymmetric. Skew is a measure of this asymmetry. A perfectly symmetrical distribution has zero skew, whereas a distribution with positive (negative) skew is one where outliers above (below) the mean are more probable. An example of an asymmetric distribution in the financial markets is the distribution implied by the presence of a volatility skew between out-of-the-money call and put options.

SPOT TRADER OPTION

A spot trader option (perfect trader option, passport option) provides the holder with the ability to trade the underlying market with limited downside in return for a fixed premium. The holder of a spot trader option enters into a number of simulated “paper” trades with the writer of the option. The holder may enter into a long, short or flat position in underlying up to a fixed notional amount. The position can be changed a fixed number of times during the lifetime of the option. At maturity, the return from these simulated trades is calculated. If this results in a profit, the holder receives this amount as a pay-out. If a loss results, the holder does not suffer this loss. The maximum loss faced by the holder is the premium paid for the option.

SPREAD OPTION

The underlying for a spread option is the price differential between two assets (a difference option) or the same asset at different times or places.

  An example of a financial difference option is the credit spread option, the underlying for which is the spread between two debt issues which derives from the relative credit rating of the issuers. Another is the cross-currency cap, where the underlying is the spread between interest rates in two different currencies. A calendar spread, a pair of options with the same strike price but different maturities, pays out the price difference for a single asset on two different dates. Spread options, including calendar spreads, are particularly popular in the commodity markets. Variations include:
    •     Location spreads, based on the price of the same commodity at two different locations. These can be used to hedge the basis risk incurred when taking delivery of a commodity at one location but required at another.
    •     Processing spreads, known as crack spreads in the crude oil market and frac spreads in the natural gas market. These are based on the price differential between a feedstock (e.g., crude oil or natural gas) and the products that can be obtained by refining or fractionating it (e.g., heating oil or propane).
    •     Quality spreads, based on the differential between different grades of the same commodity, such as “sweet” and “sour” crudes or heating oils of varying sulfur content.

STATIC REPLICATION

Static replication is a method of hedging an options position with a position in standard options whose composition does not change through time. The method attempts to replicate the pay-out of the instrument in a more manageable fashion than dynamic replication, where a position in the underlying or futures contracts must be dynamically adjusted if it is to remain effective.

Because it uses options to hedge options, a static replication portfolio is a better hedge for gamma and volatility, as well as delta, than dynamic replication. Static replication can be used for hedging a position in exotic options with vanilla options, or for replicating a long-term option with short-term options. In practice, however, it is not always possible to hedge using static replication. The number of different options and notional amounts required can quickly become unmanageable.

See also synthetic asset, replication, delta-hedging

STEALTH

Stealth measures the percentage difference between the strike and the trigger level for a barrier option. Stealth is a particularly important measure for reverse and geared barrier options, where it measures the percentage intrinsic value at the trigger level of the option.

STEP PAYMENT OPTION

See mini-premium option

STEP-UP/DOWN RANGE FORWARD

A self-adjusting range forward structure which is particularly suitable for hedging purposes. If the strike level of the long put option is breached, the strike automatically adjusts up or down (according to exposure) to a new, more favorable, level.

STOCHASTIC OPTIMISATION MODEL

A model or description of a system in which the choice of action that can be taken is dependent on the values of some random variables. For example, the value of an American-style option is such that the best choice of exercise is always made.

STOCHASTIC VOLATILITY

One of the key assumptions of the Black-Scholes model is that the stock price follows geometric Brownian motion with constant volatility and interest rates. However, in real markets, volatility is far from constant (see trading volatility). If volatility is assumed to be driven by some stochastic process, however, the Black-Scholes model no longer describes a complete market, since there is now another source of uncertainty in the option pricing model. A variety of approaches have been attempted to resolve this difficulty since the mid-1980s, most notably the Heath-Jarrow-Morton framework.

STOCK INDEX OPTION

An option, either exchange-traded or OTC, on a stock index.

STOCK OPTION

An option, either exchange-traded or OTC, on an individual equity.

STRADDLE

The sale or purchase of a put option and a call option, with the same strike price, on the same underlying and with the same expiry. The strike is normally set at-the-money. The purchaser benefits, in return for paying two premiums, if the underlying moves enough either way. It is a way of taking advantage of an expected upturn in volatility. Sellers of straddles assume unlimited risk but benefit if the underlying does not move. Straddles are primarily trading instruments.

STRANGLE

1) As with a straddle, the sale or purchase of a put option and a call option on the same instrument, with the same expiry, but at strike prices that are out-of-the-money. The strangle costs less than the straddle because both options are out-of-the-money, but profits are only generated if the underlying moves dramatically, and the break-even is worse than for a straddle. Sellers of strangles make money in the range between the two strike prices, but lose if the price moves outside the break-even range (the strike prices plus the premium received).
2) The term strangle is also used, by currency option traders, to denote the average difference in implied volatility between out-of-the-money call and put options with a 25% delta and the implied volatility of at-the-money forward options.

STRUCTURED NOTE

Structured notes are over-the-counter products, which bundle several disparate elements to create a single product, generally by embedding options in a debt instrument such as a medium-term note. They are often view-oriented and are generally tailored to be attractive to investors with highly focused risk/reward appetites and opinions on the market. For example, a structured note might embed equity or currency options or forwards in a debt issue in an effort to enhance the yield of a normal debt holding. Heavily promoted in the early 1990s, structured notes fell out of favor somewhat in 1993–94 as a sequence of surprise market moves and widely publicized losses pointed to the difficulty of pricing and trading such instruments, as well as the cost of taking the incorrect market view. During this time, the comparatively undeveloped secondary market for structured notes allowed sophisticated relative value players to buy “broken” structured notes on an asset swapped basis much more cheaply than vanilla assets from the same issuers.

STRUCTURED YIELD INVESTMENTS

Any security (normally a structured note) whose yield is conditional on certain trigger conditions being met. Such a security is normally constructed by embedding path-dependent options (such as binary options) in a vanilla debt issue. The investor’s return on the note will then vary according to the pay-out of the options.

SUBSTITUTION OPTION

A bilateral financial contract in which one party buys the right to substitute a specified asset or one of a specified group of assets for another asset at a point in time or contingent upon a credit event.

SWAPTION

An option to enter an interest rate swap. A payer swaption gives the purchaser the right to pay fixed, a receiver swaption gives the purchaser the right to receive fixed (pay floating).

Apart from those in the sterling market, many swaptions are capital-market driven. Good-quality borrowers are able to issue putable or callable bonds and use the swaptions market to reduce their financing costs. In the case of callable bonds, the issuer effectively buys an option from the investor in return for a slightly higher coupon, so that it may benefit if rates decline. Because many of these embedded options have traditionally been underpriced, good-quality borrowers have been able to monetize this anomaly by selling an equivalent swaption (a receiver swaption) to a bank at market rates.

The profit from this arbitrage lowers funding costs. If the swaption is exercised against the issuer, it calls the bonds (although the issuer would almost certainly have called the issue given the reduction in rates). In the case of putable bonds, the borrower sells a swaption to the swaption market. The premium gained lowers the funding cost at the expense of leaving the borrower unsure of the maturity of the debt.

SWING OPTION

A derivative found in energy markets allowing the purchaser to vary energy delivery in terms of quantity and timing within specified limits.

SYNTHETIC ASSET

A synthetic asset is a combination of long and short positions in financial instruments which has the same risk/reward profile as another instrument. For example, it is possible to replicate the pay-out and exposure of a short futures position by going short European-style call options and long European puts with identical strikes and expiries. Synthetic index options can be generated either through positions in the underlying and futures contracts, or with a basket of vanilla options.

SYNTHETIC OPTION

See synthetic asset, replication

TABLE TOP

Similar to a ratio spread, except that the purchase of an option is financed by sales of the same option at two different strike prices.

THETA

This measures the effect on an option’s price of a one-day decrease in the time to expiration. The more the market and strike prices diverge, the less effect theta has on a vanilla option’s price. Theta is also non-linear for vanilla options, meaning that its value decreases faster as the option is closer to maturity. Positive gamma is generally associated with negative theta and vice versa.

TIME VALUE

The value of an option, other than its intrinsic value. The time value therefore includes cost of carry and the probability that the option will be exercised (which in turn depends on its volatility).

TRIGGER CONDITION

Path-dependent derivatives such as barrier options and binary options have pay-outs which depend in some way on a market variable satisfying a specific condition during the derivative’s life. If this “trigger condition” is met, the derivative may pay out immediately (early exercise) or at some other specified time (such as expiry). Alternatively, the option may only become effective (be knocked-in) or be de-activated (knocked out) when the trigger condition is met (see barrier options).

  The most common condition is that the spot rate or price of the underlying must breach a specified level, meaning that it must trade through the barrier, either from above or below. Many other trigger conditions are possible, however. Some examples include:
    •     the spot rate must breach the trigger, and remain above/below it for a specified time (see Parisian options);
    •     the spot trades at the trigger level at a specified time (e.g., expiry) or at any time during the option’s life;
    •     the spot trades within or breaks out of a range (for example, range binaries);
    •     there is more than one trigger level, with the pay-out conditional upon or increasing with the number of triggers activated and possibly the order in which they are activated (for example, a mini-premium option);
    •     some combination of these.

TRIGGER FORWARD

The trigger forward is primarily designed for trading purposes, although it can also be used as an alternative hedge. It is usually a zero-cost structure, whereby the purchaser enters into an outright forward transaction at a rate significantly more attractive than the prevailing market rate, but where the whole structure will be knocked out if a predetermined trigger level is reached at any time before the expiry date.

  Other variations on this structure are the at-maturity trigger forward, double trigger forward and the platform trigger forward.
    •     The at-maturity trigger forward is an outright forward structure which is knocked out if a pre-determined trigger level is breached on the expiry date.
    •     The double trigger forward is a standard trigger forward with two trigger levels (one above and one below the current market level).
    •     The platform trigger forward combines a regular trigger forward with the purchase of a vanilla option struck at the trigger level with the trigger forward. This provides extra protection should the trigger level be breached.

TRIGGER OPTION

See barrier option

UNDERLYING

The variable on which a futures or option contract is based.

VANNA

The vega of an option is not constant. Vega changes as spot changes and as volatility changes. The vanna of an option measures the change in vega for a change in the underlying spot rate. As spot moves deeper out-of-the-money for a vanilla option the vega is lower. If spot and volatility movements are positively correlated the holder of an option with positive vanna will be expected to profit from this correlation.

VARIABLE NOTIONAL OPTION/SWAP

An option or swap where the notional value is linked to the underlying asset price or rate. Usually changes in the notional will be directly proportional to changes in the underlying price; i.e., they both decrease or increase together. Such derivatives have two main uses. In an equity swap, the fixed-rate receiver can opt to receive the return of either a fixed number of stocks, or the number of stocks that could be purchased for a fixed sum. The former case amounts to a variable notional amount for the swap. An example using an option is the case of a firm which sells more exports as exchange rates decline and its products therefore become cheaper abroad. Since it now has greater foreign currency revenue to hedge, it would purchase a variable notional currency option for this purpose.

VARIANCE GAMMA MODEL

A jump model that better captures the characteristics of the volatility smile for shorter-dated options than stochastic volatility models.

VASICEK MODEL

An interest rate model that incorporates mean reversion and a constant volatility for the short interest rate. It is a one-factor model from which discount bond prices and options on those bonds can be deduced. All have closed-form solutions.

VEGA

Measures the change in an option’s price caused by changes in volatility. Vega is at its highest when an option is at-the-money. It decreases the more the market and strike prices diverge. Options closer to expiration have a lower vega than those with more time to run. Positions with positive vega will generally have positive gamma. To be long vega (to have a positive vega) is achieved by purchasing either put or call options. Positions that are long vega benefit from increases in implied volatility but also from actual volatility if the option is being delta hedged. They will also lose from reductions in volatility. Spread options can be an exception: a reduction in the volatility of one of the assets may actually increase the price of the option because the correlation between the two assets decreases. Vega is sometimes known as kappa or tau.

VERTICAL SPREAD

Any option strategy that relies on the difference in premium between two options on the same underlying with the same maturity, but different strike prices. Thus put spreads and call spreads would both be vertical spreads.

VOLATILITY

A measure of the variability (but not the direction) of the price of the underlying instrument. It is defined as the annualized standard deviation of the natural log of the ratio of two successive prices. Historical volatility is a measure of the standard deviation of the underlying instrument over a past period. Implied volatility is the volatility implied in the price of an option. All things being equal, higher volatility will lead to higher vanilla option prices. In traditional Black-Scholes models, volatility is assumed to be constant over the life of an option. Since traders mainly trade volatility, this is clearly unrealistic. New techniques have been developed to cope with volatility’s variability. The best known are stochastic volatility, ARCH and GARCH.

VOLATILITY SKEW

The difference in implied volatility between out-of-the-money puts and calls. In most equity option markets out-of-the money calls have lower implied volatility than out-of-the-money puts. This is mostly ascribed to the greater supply of volatility above, rather than below, the money since fund managers are happy to write calls and not so happy to write puts. Volatility skews can be very pronounced in the currency markets although whether puts or calls are favored depends on market sentiment and demand and supply.

VOLATILITY SMILE

A graph of the implied volatility of an option versus its strike (for a given tenor) typically describes a smile-shaped curve – hence the term “volatility smile”. This can be attributed to the belief that the underlying distribution is leptokurtic, since this tends to increase the value of out-of-the-money options.

VOLATILITY TERM STRUCTURE

The term structure of volatility is the curve depicting the differing implied volatilities of options with differing maturities. Such a curve arises partly because implied volatility in short options changes much faster than for longer options. However, the volatility term structure also arises because of assumed mean reversion of volatility. The effect of changes in volatility on the option price is less the shorter the option. Most market-makers take advantage of differing volatilities to hedge their books or to trade perceived anomalies in volatility. Such strategies have to be weighted because of the differing vega effects.

VOLATILITY TRADING

A strategy based on a view that future volatility in the underlying will be more or less than the implied volatility in the option price. Option market-makers are volatility traders. The most common way to buy/sell volatility is to buy/sell options, hedging the directional risk with the underlying. Volatility buyers make money if the underlying is more volatile than the implied volatility predicted. Sellers of volatility benefit if the opposite holds. Other methods of buying/ selling volatility are to buy/sell combinations of options, the most usual being to buy/sell straddles or strangles. Other strategies take advantage of the difference between implied volatilities of differing maturity options, not between implied and actual volatility. For example, if implied volatility in short-term options is high and in longer options low, a trader can sell short-term options and buy longer ones.

VOMMA

The vega of an option is not constant. Vega changes as spot changes and as volatility changes. The vomma of an option is defined as the change in vega for a change in volatility. Vomma measure the convexity of an option price with respect to volatility. Vega is to vomma (volatility gamma) as delta is a to gamma for spot movements. Holders of options with a high vomma benefit from volatility of volatility.

See vega

WALL OPTION

See corridor option

WARRANT

(1) A certificate giving the purchaser the right, but not the obligation, to purchase a specified amount of an asset at a certain price over a specified period of time. Warrants differ from options only in that they are usually listed. Underlying assets include equity, debt, currencies and commodities.
(2) The document of title to metal stored in a London Metal Exchange-registered warehouse. The warrant is a bearer instrument and states the brand of metal, its weight, the number of pieces and the rent payable. Warrants tend to be stored and transferred electronically in the LME electronic system known as “SWORD.”

WEATHER DERIVATIVE

Typically swaps and vanilla options such as calls, puts, caps, floors and collars with payoffs linked to temperature, precipitation, humidity or wind speed. Most instruments are linked to heating degree days or cooling degree days. These two indexes measure the deviation of the average of a day’s high and low temperature from a baseline reference temperature.

WORSE-OF-TWO-ASSETS OPTION

See outperformance option

YIELD CURVE OPTION

An option that allows investors to take a view on the shape of a yield curve without taking a view on a bond market’s direction. It is normally structured as the yield of a longer maturity bond minus the yield of a shorter one. A call would therefore appreciate in value as a curve flattened. A put would decrease in value. Such options were developed in the US in 1991 in response to a steepening yield curve.

ZERO COST OPTION

Any option strategy that involves financing an option purchase by the simultaneous sale of another option so that paid and received premiums exactly offset one another.

See also collar, cylinder, participating forward, ratio spread

ZERO EXERCISE PRICe OPTION (ZEPO)

A low exercise price option whose strike price is exactly zero.

The majority of the glossary and definitions of terms are provided by Risk Magazine. © Incisive Media Ltd. 2008. Click here to download "Risk Magazine Guide to Risk Management glossary of terms 2001" in its entirety as a PDF.