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:

UNDERLYING

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

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.

ARBITRAGE-FREE MODEL

Any model that does not allow arbitrage on the underlying variable. Some simple early models assumed parallel shifts in the yield curve, but the varying yields of different duration bonds could be arbitraged using butterfly strategies.

ARCH

(AutoRegressive Conditional Heteroscedasticity.) A discrete time model for a random variable. It assumes that variance is stochastic and is a function of the variance of previous time steps and the level of the underlying.

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%.

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.

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.

BASIS

1. The difference between the prices of a futures contract and the underlying.
2. The convention for calculating interest rates. A bond can be 30/360 or actual/365 in the US, or 360/360 in Europe. Money market instruments can be actual/360 in the US or actual/365 in the UK and Japan.

BASIS RISK

In a futures market, the basis risk is the risk that the value of a futures contract does not move in line with the underlying exposure. Because a futures contract is a forward agreement, many factors can affect the basis. These include shifts in the yield curve, which affect the cost of carry; a change in the cheapest-to-deliver bond; supply and demand; and changing expectations in the futures market about the market’s direction.

Generally, basis risk is the risk of a hedge’s price not moving in line with the price of the hedged position. For example, hedging swap positions with bonds incurs basis risk because changes in the swap spread would result in the hedge being imperfectly correlated. Basis risk increases the more the instrument to be hedged and the underlying are imperfect substitutes.

BASIS TRADING

To basis trade is to deal simultaneously in a derivative contract, normally a future, and the underlying asset. The purpose of such a trade is either to cover derivatives sold, or to attempt an arbitrage strategy. This arbitrage can either take advantage of an existing mispricing (in cash-and-carry arbitrage) or be based on speculation that the basis risk will change.

BASKET SWAP

A swap in which the floating leg is based on the returns on a basket of underlying assets, such as equities, commodities, bonds, or swaps. The fixed leg is usually (but not always) a reference interest rate such as Libor, plus or minus a spread.

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.

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.

BUTTERFLY SPREAD

The simultaneous sale of an at-the-money straddle and purchase of an out-of-the-money strangle. The structure profits if the underlying remains stable, and has limited risk in the event of a large move in either direction. As a trading strategy to capitalize upon a range trading environment it is usually executed in equal notional amounts.

Alternatively, such trades are often applied to benefit from changes in volatility. In such circumstances the butterfly spread is traded on a “vega-neutral” basis (i.e., the volatility sensitivity of the long position is initially offset by the volatility sensitivity of the short position). As the holder of an initially vega-neutral spread, the trader will benefit from changes in volatility since the strangle position profits more from an increase in volatility than the straddle and loses less than the straddle in a decline in volatility (this is due to the fact that the vomma of the strangle is higher than that of the straddle).

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

CAPITAL ADEQUACY DIRECTIVE

First mooted in 1990 and issued in 1993, the European Union’s Capital Adequacy Directive (often shortened to CAD) became law across the European Union on January 1, 1996. The CAD requires banks to separate trading book from more generalized banking book, and to apply the building block approach to interest rate and equity risk in the trading book, as well as foreign exchange risk across both books. In general, the CAD requires banks to apply capital equal to 8% of net positions for general market risk and an additional capital amount to cover specific risk.

  In November 1999, the European Union issued proposals for new capital adequacy rules. In parallel with the Basel Committee’s proposals, the proposals sought to align regulatory capital requirements more closely with underlying risks and to provide institutions with incentives to move to higher standards of risk management.

  In February 2001, the European Union released a second consultation paper for the new capital adequacy framework for banks and investment firms. The Capital Adequacy Directive generally applies to investment firms, including some managers of pension funds. The consultative paper discussed many of the same issues and methodologies as Basel II, including the internal ratings-based and revised standardized approaches, credit risk mitigation, consolidated capital requirements, interest rate and operational risks, the supervisory review process, and disclosure requirements.

  A further consultation period will run in parallel with the further Basel consultation, in the first few months of 2002. Features that have caused most discussion include the impact of the proposed operational risk charge on investment firms and smaller credit institutions and the potential implications of the proposed new regime for lending to small- and medium-sized enterprises.

See also Basel Capital Accord, comprehensive approach

CASH MARKET

An underlying, as opposed to a futures market.

CASH-AND-CARRY ARBITRAGE

A strategy used in bond or stock index futures in which a trader sells a futures contract and buys the underlying to deliver into it, to generate a riskless profit. For the strategy to work, the futures contract must be theoretically expensive relative to cash. The value of a futures contract is assessed by looking at the implied repo rate. If the implied repo rate is greater than the market repo rate, then futures are said to be cheap.

Cash-and-carry arbitrage and reverse cash-and-carry arbitrage typically keep the futures and underlying markets closely aligned.

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.

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.

CONTANGO

Situation when a commodity’s future price is higher than its spot price. Whereas financial futures and forwards are invariably priced off the cost of carry of the underlying, the forward or spot prices of commodities are heavily influenced by supply and demand. Contango arises where there is sufficient supply in the spot market or where future supply is thought to be tight.

See also advance premium forward, backwardation

CONTRACT FOR DIFFERENCE (CFD)

A Contract for Difference is typically an agreement made between two parties to exchange (at the closing of the contract) a cashflow equivalent to the difference between the opening and closing prices, multiplied by the number of shares detailed in the contract. CFDs are traded on margin, do not incur stamp duty and can have individual stocks or indexes as the underlying.

Alternatively, in the currency markets, the term CFD can refer to an OTC currency forward contract that settles for a cash amount (maybe in a third currency) without requiring the exchange of the two underlying currencies. It is often used instead of a traditional forward because it mitigates settlement risk.

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.

COST OF FUNDS

Refers to an Issuer’s actual interest rate cost on its debt obligations, which may or may not include carrying costs such as remarketing fees, liquidity fees, letter of credit fees, etc., that is sometimes used as the underlying in a swap transaction.

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.

COVERED WARRANT

A warrant issued by a third party, often a bank or securities house, which entitles the holder to buy existing shares in a company at a fixed price for a given period. The term is also more generically applied to any covered warrant issued by a third party on any underlying.

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 RISK MODELS

The success of VAR-based models of market risk and the ongoing development of the Basel Committee's regulatory framework has sparked a wave of interest in credit risk modeling since the 1990s. But default probabilities cannot be observed, and correlations between defaults are difficult to measure – so it's difficult to aggregate credit risk. For these kinds of reasons, the robust modeling of credit risk is a more difficult task than for market risk.

Despite such difficulties, a number of commercial models of portfolio credit risk are available, but they are all broadly based on one of two fundamental models: equity-based and ratings-based. Merton-type models treat the value of a credit exposure as a derivative written on the firm's underlying assets. Volatility and correlation structures are then deduced from changes in the equity's value. Ratings-based models assume that credit risk exposures are defined by credit ratings. Transitions between different ratings and correlations between ratings transitions for pairs of exposures are then modeled.

Despite such difficulties, a number of commercial models of portfolio credit risk are available, but they are all broadly based on one of two fundamental models: equity-based and ratings-based. Merton-type models treat the value of a credit exposure as a derivative written on the firm's underlying assets. Volatility and correlation structures are then deduced from changes in the equity's value. Ratings-based models assume that credit risk exposures are defined by credit ratings. Transitions between different ratings and correlations between ratings transitions for pairs of exposures are then modeled.

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.

DELEVERAGED FLOATING-RATE NOTE

An instrument developed in the US on the back of a positive yield curve to increase the yield of floating-rate assets by indexing them to higher-yielding long-term fixed-rate bonds. The underlyings are normally constant maturity Treasuries. The rates are called deleveraged FRNs because the investor receives a portion (usually 50%) of the reference rate of those securities plus a fixed spread (which increases the longer the FRNs maturity).

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.

DIGITAL SWAP

A swap in which the fixed leg is only paid on each swap settlement date if the underlying has met certain trigger conditions over the period since the previous payment date. Nothing is paid if this is not the case. The premium for such a swap is amortized over the maturity of the swap and an installment paid at each payment date.

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.

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.

EQUILIBRIUM MODEL

A model that specifies processes for the underlying economic variables and the extra risk premium investors require for risky assets. The evolution of asset prices and their risk premiums can then be derived from the model thus specified.

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).

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.

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 RATE AGREEMENT

A forward rate agreement (FRA) allows purchasers/sellers to fix the interest rate for a specified period in advance. One party pays fixed, the other an agreed variable rate. Maturities are generally out to two years and are priced off the underlying yield curve. The transaction is done on a nominal amount and only the difference between contracted and actual rates is paid. If rates have risen by the time of the agreement’s maturity, the purchaser receives the difference in rates from the seller and vice versa. A swap is therefore a strip of FRAs. FRAs are off-balance sheet – there are no up-front or margin payments and the credit risk is limited to the mark-to-market value of the transactions. Unlike interest rate swaps, FRAs settle at the beginning of the interest period, two business days after the calculation date.

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.

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.

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.

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.

HEATH-JARROW-MORTON MODEL

A multi-factor interest rate model which describes the dynamic of forward rate evolution. An extension of the Ho-Lee model, the underlying is the entire term structure of interest rates. The approach is very similar to the original Black-Scholes Model: it does not model qualities such as the “price for risk.”

The model requires two inputs: the initial yield curve and a volatility structure for the forward. The volatility is only specified in a very general form. By choosing an appropriate volatility function, it is possible to reduce HJM to simpler models such as Ho-Lee, Vasicek, and Cox-Ingersoll-Ross.

The practical importance of the HJM model is that it provides a single coherent framework for pricing and hedging an entire book of instruments (including instruments like caps and swaptions) and is not excessively computationally intensive. Research building on HJM (such as the market model) has concentrated on widening its scope to remove the possibility of negative interest rates, include more than one interest rate curve and incorporate default risk.

HEDGE ACCOUNTING

The practice of deferring accounting recognition of gains and losses on financial market hedges until the corresponding gain or loss of the underlying exposure is recognized. Companies favor hedge accounting because it enables them to incorporate costs of hedges into the cost basis of the exposure. This matches gains against offsetting losses, reducing earnings volatility in a manner consistent with the purpose of the hedge. At this writing, the US Federal Accounting Standards Board was in the midst of a long-term project to codify accounting for derivatives transactions which will address the circumstances under which hedge accounting is permitted.

See also FAS 133 and IAS 39; accrual accounting, mark to market

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.

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

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.

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

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.

LAMBDA

A measure of the effective leverage of an instrument. It is defined as the percentage change in the market value of a derivative for a one-percent move in the underlying. Unlike gearing, the lambda value captures the instrument’s delta.

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.

LIBOR

London Inter-Bank Offered Rate is the interest rate banks charge each other for short-term money, up to a 12-month term. LIBOR is commonly used as the underlying for the floating leg of a Swap. The British Bankers’ Association (BBA) sets the rates daily.

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.

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.

MARK to market

To mark-to-market is to calculate the value of a financial instrument (or portfolio of such instruments) based on the current market rates or prices of the underlying. Marking-to-market on a daily (or more frequent) basis is often recommended in risk management guidelines.

See also accrual accounting, hedge accounting

MARKET RISK

Exposure to a change in the value of some market variable, such as interest rates or foreign exchange rates, equity or commodity prices. For holders of a derivatives position, market risk may be passed through from a change in the value of the underlying to the price of the derivative, or may arise from other sources, such as implied volatility or time decay.

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

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.

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.

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.

NAKED OPTION

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

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.

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.

OVERLAY

A strategy to change the exposure of a portfolio using derivatives, while leaving the securities in the underlying portfolio unchanged. This has the advantage of cost and flexibility, as portfolio managers can adjust portfolio risk more quickly and cheaply with derivatives than by liquidating portfolio holdings. Another reason might be tactical – the adjustment may only be desired for a brief period of perceived market threat. A third reason might be to transform a portfolio risk; an international fund manager may wish to segregate the currency aspect of a portfolio and can do so with a currency overlay program.

See also asset allocation, portfolio insurance

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.

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

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.

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).

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.

RANDOM WALK

The series of values taken by a random variable with the progress of some parameter such as time. Each new value (each new step in the walk) is selected randomly and describes the path taken by the underlying variable.

See also geometric Brownian motion, stochastic process

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.

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.

RESETTABLE CONVERTIBLE BOND

It is a convertible bond where the conversion ratio can reset to a new value depending on the average price of the underlying stock on pre-specified dates.

REVERSE CASH-AND-CARRY ARBITRAGE

A technique, used mainly in bond futures and stock index futures, that involves buying a futures contract and selling the underlying. It is used when a futures contract is theoretically cheap, such as when the implied repo rate is less than the market repo rate.

RISK MANAGEMENT

Control and limitation of the risks faced by an organization due to its exposure to changes in financial market variables, such as foreign exchange and interest rates, equity and commodity prices or counterparty creditworthiness. This may be because of the financial impact of an adverse move in the market variable (market risk), because the organization is ill-prepared to respond to such a move (operational risk), because a counterparty defaults (credit risk), or because a specific contract is not enforceable (legal risk).

Market risks are usually managed by hedging with financial instruments, although a firm may also reduce risk by adjusting its business practices (see natural hedge). While financial derivatives lend themselves to this purpose, risk can also be reduced through judicious use of the underlying assets (for example, by diversifying portfolios).

SECURITISATION

The conversion of assets (usually forms of debt) into securities which can be traded more freely and cheaply than the underlying assets and generate better returns than if the assets were used as collateral for a loan. One example is the mortgage-backed security, which pools illiquid individual mortgages into a single tradable asset.

SETTLEMENT RISK

Settlement risk (delivery risk), as a particular form of counterparty credit risk, arises from a non-simultaneous exchange of payments. For example, a bank that makes a payment to a counterparty, but will not be recompensed until a later date, is exposed to the risk that the counterparty may default before making the counter-payment. Settlement risk is distinct from market risk because it relates to exposure to a counterparty rather than exposure to the underlying risk related to the reference entity of the derivative contract.

Settlement risk is most pronounced in the foreign exchange markets, where payments in different currencies take place during the normal business hours in their respective countries and can therefore be made up to eighteen hours apart, and where the volume of payments makes it impossible to monitor receipts except on a delayed basis. This type of risk afflicted counterparties of Bank Herstatt in 1974, which closed its doors after receipt but before payment on foreign exchange contracts. As a result, settlement risk is sometimes called Herstatt risk. There are now a number of settlement processing organizations for foreign exchange, such as Multinet and Echo, which aim to reduce settlement risk by centralizing the settlement process.

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

STOCK INDEX ARBITRAGE

The technique of selling a futures contract on a stock index and buying the underlying stocks, via program trading, or vice versa when the price of the futures contract is above or below its theoretical value. The ability to conduct such strategies depends on the efficiency of the futures and cash markets.

STOCK INDEX FUTURE

A futures contract on a stock index. Most are cash-settled. The theoretical price of a stock index future equals the cost of carrying the underlying stock for that period: the opportunity cost of the funds invested minus any dividends. If the cost of buying and holding the underlying stocks is less than the futures price, an arbitrageur can sell futures and buy the underlying stocks.

The higher interest rates are (compared with the dividend yield), the greater the opportunity cost of holding the stocks, hence the futures price should be higher than the current index price. If interest rates are less than the dividend yield, the opportunity cost of holding stocks is less and the futures price should fall below the current index price. There is usually a so-called arbitrage band in which, although the futures and underlying prices diverge, it is not worthwhile arbitraging the two. This arises as a result of transaction costs from bid-ask spreads, the market impact of buying and selling stock, and execution risks.

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.

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 COLLATERALISED DEBT OBLIGATION

A synthetic collateralized debt obligation (CDO) uses credit derivatives to transfer credit risk in a portfolio. This is in contrast to a traditional CDO which is typically structured as a securitization with ownership of the assets transferred to a separate special purpose vehicle (SPV). The assets are funded with the proceeds of debt and equity issued by the vehicle. In a synthetic CDO, an institution transfers the total return or default risk of a reference portfolio via a credit default swap, a total return swap, or a credit-linked note. The SPV then issues securities with repayment contingent upon the loss on the portfolio. Proceeds are either held by the vehicle and invested in highly rated, liquid collateral, or passed-on to the institution as an investment in a credit-linked note.

Balance sheet synthetic CDOs are typically used by banks to manage risk capital and are easier to execute than traditional CDOs. Arbitrage synthetic CDOs are often used by insurance companies and asset managers and exploit the spread between the yield on the underlying assets and the reduced expense of servicing a CDO structure.

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.

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.

VARIABLE rate demand obligation (VRDO)

A debt security with an interest rate that can change over time. The variable (floating) rate is usually tied to an underlying index. Also called a variable rate demand bond (VRDB), or a variable rate demand note (VRDN).

VARIANCE SWAP

The cash pay-out of a variance swap is equal to notional multiplied by the difference between the realized variance of the underlying index over the life of the swap and the strike variance.

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 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 SWAP

The cash pay-out of a volatility swap is equal to notional multiplied by the difference between the realized volatility of the underlying index over the life of the swap and the strike volatility.

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.

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.”