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:

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.

Partial Matches:

ACCRETING

A description, applicable to a variety of instruments, denoting that the notional principal increases successively over the life of the instrument, e.g., caps, collars, swaps and swaptions. If the increase takes place in increments, the instrument may be known as a step-up.

ACCRUAL ACCOUNTING

When swaps are used for asset/liability hedging purposes, that is, to hedge specific on-balance sheet exposures, they are often accounted for on an accrual basis. Under the accrual method, the net payment or receipt each period is accrued and recorded as an adjustment of income or expense.

See also hedge accounting, mark to market

ACCRUAL CORRIDOR

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

ACCRUAL PERIOD

Period over which net payment or receipt pertaining to swaps is accrued. It is inclusive of the start date and runs to the end date without including the end date.

ADVANCE PREMIUM FORWARD

A forward contract in which the contango is partly payable in advance. This transaction is also known as a flat rate forward or stabilized contango. An advanced premium forward is particularly useful during the early years of a project when the greater contango can provide greater cash flow. The conversion of a standard forward into an advanced premium forward allows for the early realization of hedging values. In this case, the early payment of the contango is at the expense of yield in the later years in a strip of forwards.

AMORTISING

A description, applicable to a variety of instruments, denoting that the notional principal decreases successively over the life of an instrument, e.g., amortizing swap, index amortizing rate swap, amortizing cap, amortizing collar, amortizing swaption. If the decrease takes place in increments, the instrument may be known as a step-down. Mortgage-style amortization refers to an amortizing swap such that the principal amortization plus interest is the same amount in each interest period.

ANNUITY SWAP

An interest rate swap in which a series of irregular cashflows are exchanged for a stream of regular cashflows of equivalent present value.

ARS

See auction rate securities

ASSET SWAP

A package of a cash credit instrument and a corresponding swap that transforms the cash flows of the non-par instrument (bond or loan), into a par (floating interest rate) structure. Asset swaps typically transform fixed-rate bonds into par floaters, bearing a net coupon of Libor plus a spread, although cross-currency asset swaps, transforming cashflows from one currency to another are also common.

ASSET/LIABILITY MANAGEMENT

The practice of matching the term structure and cashflows of an organization’s asset and liability portfolios in order to maximize returns and minimize interest rate risk. An institutional example of this would be a bank converting a fixed-rate loan (asset) by utilizing a fixed-for-floating interest rate swap to match its floating rate funding (deposits).

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 RATE OPTION

See average option

BARRIER FLOATER

A floating-rate note in which the coupon is knocked-in or knocked-out if the reference interest rate exceeds or falls below a certain barrier level (see trigger+condition).

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.

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 SWAP

An interest rate basis swap or a cross-currency basis swap is one in which two streams of floating rate payments are exchanged. Examples of interest rate basis swaps include swapping $Libor payments for floating commercial paper, Prime, Treasury bills, or Constant Maturity Treasury rates; this is also known as a floating-floating swap. A typical cross-currency basis swap exchanges a set of Libor payments in one currency for a set of Libor payments in another currency.

BASKET CREDIT DEFAULT SWAP

A credit default swap which transfers credit risk with respect to multiple reference entities. For each reference entity, an applicable notional amount is specified, with the notional of the basket swap equal to the aggregate of the specified applicable notional amounts. Types of basket credit default swaps include linear basket credit default swaps, first-to-default basket credit default swaps, and first-loss basket credit default swaps.

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.

BID DATE

In a competitive bid transaction, the date on which swap Providers submit bids and the price/rate/agreement is established with the winning Provider.

BID PACKAGE

Documentation distributed by or on behalf of an Issuer to qualified Providers, detailing the terms, conditions and structure of the swap desired by the Issuer, which the Providers will use to formulate their bid on the scheduled bid date.

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 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.

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-DERMAN-TOY MODEL

A one-factor log-normal interest rate model where the single source of uncertainty is the short-term rate. The inputs into the model are the observed term structure of spot interest rates and their volatility term structure. The Black-Derman-Toy model, such as the Ho-Lee model, describes the evolution of the entire term structure in a discrete-time binomial tree framework. The model can be used to price bonds and interest rate-sensitive securities, though the solutions are not closed-form.

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.

BLENDED INTEREST RATE SWAP

A technique that involves combining two interest rate swaps to produce a more attractive overall rate. It involves at least two transactions. For example, if a counterparty fixes its floating rate borrowing cost at 10% and rates go down to 8%, it may do another swap with the same counterparty at 8% and combine the two to create a rate closer to the market.

bma index

Formerly the PSA Municipal Swap Index; is the principal benchmark for the floating rate interest payments for tax-exempt Issuers. The BMA Index is a national rate based on a market basket of approximately 250 high-grade, seven-day tax-exempt variable rate demand obligation issues of $10 million or more. In November 2006, the Bond Market Association (BMA) merged with the Securities Industry Association to form the Securities Industry and Financial Markets Association (SIFMA). Officially, the BMA Index is now called the SIFMA Swap Index, but it is still widely referred to by market participants as the BMA Index.

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 INDEX SWAP

A swap in which one counterparty receives the total rate of return of a bond market or segment of a bond market in exchange for paying a money market rate. Counterparties may also swap the returns of two bond markets. The two most common indexes used to measure bond market returns are the JPMorgan government bond index and the Salomon Brothers world government bond index. Bond index swaps can be an attractive way of gaining exposure to a market if the investor wants to avoid the trouble and expense of buying individual bonds, bearing in mind there are currently no government bond index futures. Bond index swaps can also be used to pass on bond market exposure when an investor does not want to sell core bond holdings, either because of wide price spreads or because they were difficult to obtain.

There can also be tax advantages in using bond swaps. For example, in Japan, banks and securities houses are exempt from withholding tax, but most foreign investors are not. Banks can therefore pass on some of those tax advantages in the swap. Also known as a total rate of return swap.

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.

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.

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.

CANCELLABLE SWAP

See callable 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.

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

CAPPED FLOATER

A floating-rate note which pays a coupon only up to a specified maximum level of the reference rate. This is done by embedding a cap in a vanilla note where the investor effectively sells the issuer a cap. A capped floater protects the debt issuer from large increases in the interest rate environment.

CAPPED SWAP

An interest rate swap with an embedded cap in which the floating payments of the swap are capped at a certain level. A floating-rate payer can thereby limit its exposure to rising interest rates.

CASH AND CARRY

When a contango exists, the premium of the forward position over the prompt generally reflects costs of storage, insurance and finance for that period. When metal is in surplus, the contango may widen to the point where an effective interest rate that is higher than market rates can be locked-in.

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.

CATASTROPHE RISK SWAP

An agreement between two parties to exchange catastrophe risk exposures. For example, in July 2001 Swiss Re and Tokio Marine arranged a $450 million deal including three risk swaps: Japan earthquake for California earthquake, Japan typhoon for France storm and Japan typhoon for Florida hurricane. Swaps increase diversification and allow each of the parties to lower the amount of capital that they need to hold.

CHange in tax law risk

The risk that there will be an unanticipated structural change to current tax laws, which would impact the spread between tax-exempt and taxable rates.

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.

COLLAR SWAP

A collar on the floating-rate leg of an interest rate swap. The transaction is zero cost – the purchase of the cap is financed by the sale of the floor. The collar constrains both the upside and the downside of a swap.

COLLARED FLOATER

A floating-rate note whose coupon payments are subject to an embedded collar. Thus the coupon is capped at a predetermined level, so the buyer forsakes some upside, but also floored, offering protection from a downturn in the reference interest rate. Also known as a mini-max floater.

COLLATERALISED BOND OBLIGATION (CBO)

A multi-tranche debt structure, similar to a collateralized mortgage obligation. But rather than mortgages, low-rated bonds serve as the collateral.

COLLATERALISED MORTGAGE OBLIGATION

A type of asset-backed security, in this case backed by mortgage payments. Typically, such securities provide a higher return than normal fixed-rate securities but purchasers suffer prepayment risk if mortgage holders redeem their mortgages. Because the right to redeem the mortgage is effectively an embedded call, such securities have negative convexity.

See also collateralized bond obligation, collateralized debt obligation, collateralized loan obligation.

COllateralization risk

Risk that the circumstances under which an Issuer would have to post collateral pursuant to certain swap agreement provisions will arise in the future.

COMMODITY SWAP

A swap in which one of the payment streams for a commodity is fixed and the other is floating. Usually only the payment streams, not the principal, are exchanged, although physical delivery is becoming increasingly common. Commodity swaps have been in existence since the mid-1980s and enable producers and consumers to hedge commodity prices. The consumer is usually a fixed payer and the producer a floating payer (receiving fixed), thereby hedging against falls in the price of the commodity. If the floating-rate price of the commodity is higher than the fixed price, the difference is paid by the floating payer, and vice versa.

Swaps are done in oil, natural gas, metals and some agricultural products, although futures are more common in agricultural markets. Swaps allow users to hedge risks which cannot be offset by the use of futures contracts. This could be a geographical or quality basis risk, or it could arise from the maturity of a transaction. Liquidity in commodity swap markets varies greatly – from the very liquid, equivalent to an active futures market (e.g., European jet fuel) to the relatively illiquid, where the swaps provider is assuming an unusual or unique risk.

COMpetitive bid

Process of entering into a swap agreement where interested swap Providers submit bids to the Issuer on a specified date, and the swap is entered into with the winning Provider offering the interest rate, terms and conditions most favorable to the Issuer.

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 SWAP DERIVATIVE

See Constant Maturity Treasury (CMT) derivative

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 SWAP

The generic term for a swap activated when rates reach a certain level or a specific event occurs. Swaptions are often considered to be contingent swaps. Other types of swaps, for example, drop-lock swaps, are activated only if rates drop to a certain level or if a specified level over a benchmark is achieved.

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.

CORRELATION SWAP

Often used in currency markets, an instrument that allows an investor to take three volatility swaps and bet on how much one currency will move compared to the two others.

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 CARRY

The cost of financing an asset. If the cost is lower than the interest received, the asset has a positive cost of carry; if higher, the cost of carry is negative. The cost of carry is determined by the opportunities for lending the asset and the shape of the yield curve. So a bond, for example, would have a positive cost of carry if short-term rates (financing rates) were lower than the bond’s yield or (and) if the cost could be mitigated by lending out the securities.

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.

COUNTERPARTY

A party in a swap transaction. From an Issuer’s perspective, this is synonymous with Provider.

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 DEFAULT SWAP

A bilateral financial contract in which one counterparty (the protection buyer or buyer) pays a periodic fee, typically expressed in basis points per annum on the notional amount, in return for a contingent payment by the other counterparty (the protection seller or seller) upon the occurrence of a credit event with respect to a specified reference entity. The contingent payment is designed to mirror the loss incurred by creditors of the reference entity in the event of its default. The settlement mechanism may be cash or physical.

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 EVENT

Any one of a specified set of events, which, if occurring with respect to an obligation of the reference entity specified in a credit default swap, will trigger contingent payments. Applicable events, which generally include bankruptcy, repudiation/moratorium, restructuring, failure to pay, and cross-acceleration (as each is defined by ISDA) are determined by negotiation between the parties at the outset of a credit default swap.

CREDIT INTERMEDIATION SWAP

A credit swap with a dynamic notional that for a fixed fee provides the protection buyer with a contingent payment that matches the mark-to-market on any given day of a specified derivative (or other market-sensitive instrument). Also known as a dynamic credit swap

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 PENALTY

The additional requirements (e.g., a higher interest rate, additional insurance, etc.) of a party to a swap imposed due to that party’s lower credit rating.

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.

CREDIT SPREAD

A credit spread is the difference in yield between two debt issues of similar maturity and duration. The credit spread is often quoted as a spread to a benchmark floating-rate index such as Libor, or alternatively as a spread to a highly rated reference security such as a government security. The credit spread is often used as a measure of relative creditworthiness, with reduction in the credit spread reflecting an improvement in the borrower’s perceived creditworthiness.

CREDIT SUpport

Collateral that can be in the form of cash and/or marketable securities posted by one party to a swap agreement to reduce the credit exposure of its counterparty.

CREDIT-LINKED NOTE

A security with redemption and/or coupon payments linked to the occurrence of a credit event with respect to a specified reference entity. In effect, a credit-linked note embeds a credit default swap into a funded asset to create a synthetic investment that replicates the credit risk associated with a bond or loan of the reference entity. Credit-linked notes are typically issued on an unsecured basis directly by a corporation or financial institution (e.g., an MTN or Certificates of Deposit issued by JPMorgan Chase Bank). Credit-linked notes may also be issued from a collateralized Special Purpose Vehicle (SPV).

CROSS-CURRENCY CAP

A cap in which the vendor will pay the purchaser the spread between interest rates (usually Libor-based) in different currencies minus a strike spread, where this exceeds zero, in return for a premium. It has the same relationship to a differential swap as a cap has to an interest rate swap.

CROSS-CURRENCY SWAP

A cross-currency swap involves the exchange of cashflows in one currency for those in another. Unlike single-currency swaps, cross-currency swaps often require an exchange of principal. Typically the notional principal is exchanged at inception at the prevailing spot rate. Interest rate payments are then passed back on a fixed, floating or zero basis. The principal is then re-exchanged at maturity at the initial spot rate.

Cross-default termination

The ability of one party to terminate the swap at its market value if the other party defaults on other obligations of particular types.

CUMULATIVE CAP

A cumulative interest rate cap protects against increases in total interest expense over a specified period of time. This period of time will incorporate several rate settings in determining the final interest expense (for example, four three-month Libor settings for an annual interest expense amount). This differs from a standard cap, which caps an absolute rate of interest in each calculation period. Because a cumulative cap does not provide the period-to-period protection of a standard cap, it is generally cheaper than the corresponding standard cap.

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.

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.

DEBT-EQUITY SWAP

This is not a swap in the usual sense. It is a one-off transaction of physical instruments without any exchange of future cashflows. It involves substituting equity for debt, either bonds or loans, usually when the debt becomes unserviceable. They are used by heavily indebted companies and countries.

DEFAULT SWAP

See credit default swap

DEFERRED SWAP

A swap in which the payments are deferred for a specified period, usually for tax or accounting reasons. Unlike a forward swap, where the entire swap is delayed, in a deferred swap only the payments are deferred. For example, a company wanting to enter a swap, but not wanting cashflows until a future period, might want to defer payment.

DELAYED RESET SWAP

Also known as an in-arrears swap. A swap in which floating payment is based on the future, rather than present, value of the reference rate. For six-month delayed Libor reset swaps, for example, instead of fixing Libor six months and two days before the payment date, the floating-rate borrower delays fixing until two days before payment. Such swaps are popular in a steep yield curve environment, when a fixed-rate receiver may think rates will not rise as fast as the yield curve predicts.

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.

DIFFERENTIAL SWAP

A quanto product, typically involving the combination of a simple interest rate swap in the denominating currency, and a quantized swap denominated in the same currency but referenced to a different currency. For example, a counterparty receives euro six-month Libor, denominated in euros, and pays US dollar six-month Libor, denominated in euros plus a spread approximately equal to the difference between the fixed rates of the simple swap and the quantized swap as quoted on the same basis, e.g., semi-annual 360.

DIFFUSION PROCESS

A continuous-time model of the behavior of a random variable. An example of such a model is Generalized Brownian Motion (GBM) which is often used to model the behavior of spot rates.

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.

DISCOUNT SWAP

An off-market swap in which the fixed payments are below the market rate. At the end of the swap the shortfall is made up by one payment. Construct-ion and project finance companies use this type of structure to reduce interest rate payments before start-up and during completion of a project. The more interest rate payments are discounted, the more credit risk is taken by the counterparty.

DOwngrade termination

Provision in some swap agreements allowing one party to terminate the swap at its market value if the other party’s long-term, unsecured debt rating falls below a given level.

DROP-LOCK SWAP

A swap in which, if the rate on the index initially used to set the fixed-rate payments differs from that prevailing at the outset of the swap by a specified amount and for a specified amount of time, the fixed rate is reset.

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.

DURATION

Duration is the average life of the present values of all future cashflows from a bond. For a given maturity, the higher the coupon, the more it (rather than the redemption payment) contributes to yield. So the higher the coupon, the shorter the duration. Although the duration of a bond increases monotonically as the maturity increases, it is non-linear (except for zero-coupon bonds), because the coupon payments are increasingly important to the yield. Duration usually refers to what technically should be described as modified duration. This measures the effect on a bond’s price of a unit change in yield. So if a bond has a duration of two, a yield change of 1% will produce a price change of 2% in the other direction. The higher the modified duration, the more sensitive the bond is to interest rate changes.

DYNAMIC CREDIT SWAP

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.

Effective date

The first date on which payment obligations begin to accrue, including the date any upfront payment is exchanged. In the case of a forward swap, payment accruals may not begin for months or even years into the future. When a swap is entered into in connection with an issue of bonds, the Effective Date is often set to coincide with the issue date of the bonds.

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 (INDEX) SWAP

A swap in which the total or price return on an equity index, equity basket or single equity is exchanged for a stream of cashflows based on a short-term interest rate index (or another index).

Equity swaps are a convenient structure for switching into or out of equity markets, particularly for those that prefer to avoid, or are not allowed to use stock index futures. Like futures, the price of the swap is directly related to the cost of carry, although there may also be tax considerations.

EQUITY INDEX PARTICIPATION NOTE

A note (bond) in which interest paid is tied to the movement of an equity index or single stock.

See also guaranteed products, embedded option

EQUITY KNOCKOUT SWAP

An interest rate or cross-currency swap that gets terminated (knocked-out) if a given stock or equity-index reaches a specified trigger level between inception and expiry. The knockout can be un-conditional once the pre-determined equity level is reached, or the client can be given the choice to cancel the swap should the trigger level be reached.

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.

ESCALATING PRINCIPAL SWAP

See accreting swap

ESCALATING RATE SWAP

Also known as a step-up coupon swap. A swap in which the fixed-rate payments increase over time. For example, a company that expects its income to increase can pay a fixed rate that increases incrementally.

EXCHANGE RATE AGREEMENT (ERA)

A synthetic agreement for forward exchange (SAFE) that changes in value as the spread between two forward currency exchange rates (for example, the three-month and six-month forward) changes. Unlike a forward exchange rate agreement, the ERA is settled with reference to two forward rates rather than a forward and the spot rate on settlement.

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.

EXPOSURE

A firm’s exposure is its vulnerability to loss from unanticipated events. These events might include movement in financial market variables, such as foreign exchange rates, interest rates, commodity prices or volatilities. Alternatively, a firm could be exposed to credit risk, operational risk, or legal risk. Recognizing and minimizing – or optimizing – exposure is the function of risk management.

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.

FIRST-LOSS BASKET SWAP

A basket credit default swap in which the seller of protection agrees to make contingent payments to the buyer of protection upon the occurrence of a credit event with respect to one or more reference entities. The contingent payment amount for each credit event equals the loss incurred with respect to the liquidation value of an obligation of the impaired reference entity, with the aggregate amount of contingent payments due by the seller of protection capped by the swap notional amount. Through this type of structure, the seller of protection obtains levered exposure to a portfolio of credits.

FIRST-TO-DEFAULT BASKET SWAP

A specialized type of basket credit default swap in which the protection seller is exposed to the first reference entity in the basket of reference entities for which a credit event occurs. The applicable notional amount for each reference entity in the basket is typically equal to the notional of the first-to-default swap. Losses are capped at the notional amount and the protection seller does not have exposure to subsequent credit events.

FIXED leg

In a swap transaction, the payments made by one party to another based on a pre-determined fixed interest rate.

FIXED-FLOATING SWAP

See interest rate swap

FLEXIBLE FREQUENCY DIGITAL SWAP

See digital swap

FLOATING leG

In a swap transaction, the payments made by one party to another based upon a pre-determined floating (variable) rate index.

FLOATING-FLOATING SWAP

See basis swap, interest rate swap

FLOOR

A contract whereby the seller agrees to pay to the purchaser, in return for upfront premium, the difference between a reference rate and an agreed strike rate should the strike rate exceed the reference rate. Interest rate floors, such as caps, are effectively a string of interest rate guarantees.

FLOORED FLOATER

A floating-rate note that guarantees a minimum coupon even if the reference rate drops below the minimum rate. This is achieved by embedding a floor in a vanilla note. A floored floater protects the buyer from large decreases in the reference interest rate.

FORWARD EXCHANGE RATE AGREEMENT (FXA)

A synthetic agreement for forward exchange (SAFE) developed by Midland Montague. Essentially a cash-settled forward. The counterparties agree on a forward exchange rate for a chosen delivery date, and at the maturity of the contract the two counterparties make mark-to-market payments based on the prevailing spot rates.

See also synthetic agreement for exchange

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 purchase AGREEMENT

Forward Purchase Agreements/Float Contracts can be structured to offer a municipal debt issuer a yield over time in exchange for a commitment by an issuer to direct the monthly debt service principal and interest payments to a counterparty for their use prior to semi-annual debt service payments. This contract provides long term yields on short term cash flows. The contract is also very effective in reducing negative arbitrage in escrow portfolios.

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.

FORWARD rate curve

The yield curve, as of a future (or forward) date, constructed using currently prevailing rates on instruments settling in the future; commonly used to price many interest rate derivative instruments.

FORWARD SPREAD AGREEMENT

A contract in which counterparties contract into a spread between two variable rates, usually Libors, applied to a nominal amount of one currency. The settlement amount will be the spread between prevailing Libor minus the contracted spread. Differential swaps are therefore a string of forward spread agreements.

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.

FORWARD SWAP

A swap in which rates are fixed before the start date. If a company expects rates to rise soon but only needs funds later, it may enter into a forward swap.

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.

FUTURE RATE AGREEMENT

See forward rate agreement

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.

GAO REPORT

The colloquial name for the May 1994 report “Financial Derivatives: Actions Needed to Protect the Financial System” published by the US General Accounting Office, the investigative arm of Congress. The report made six key points:
    •     Derivatives perform a valuable function by enabling end-users to manage the financial risks associated with their business
    •     The concentration of over-the-counter (OTC) derivatives activity among 15 extensively linked major US dealers opens up the possibility of liquidity problems and systemic risk should any of these dealers fail
    •     There are no comprehensive or federal regulatory requirements to ensure that major OTC players in the US follow good practice in risk management, so newcomers could increase the systemic risk by taking on unnecessary risk
    •     Significant gaps exist in the regulation of many major OTC derivatives, most notably affiliates of securities firms and insurance companies
    •     Insufficient precision in accounting for and financial reporting of derivatives compound the difficulties faced by interested parties when trying to assess their impact
    •     Innovation and creativity are strengths of the US financial services industry which should not be shackled by over-regulation.

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

GOLD FORWARD OFFERED RATE

The rates at which dealers will lend gold on swap against US dollars.

GOLD LEASE RATE

The gold lease rate is the cost to borrow gold. Similar to other commodities it is a function of supply and demand. The rate (non-credit adjusted) is determined by the difference between Libor and the gold forward rate for the specified period. Credit adjustments are subsequent to the calculation.

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.

GUARANTEED investment contract (GIC)

A Guaranteed Investment Contract ("GIC") is a contract between a municipal entity or 501(c)(3) organization and a financial institution (the "Provider") in which the Provider guarantees a rate of return on bond proceeds deposited under the investment contract. Guaranteed Investment Contracts have proven to satisfy the unique economic, tax and legal requirements associated with the investment of tax-exempt bond proceeds and have been used with increasing frequency among tax-exempt issuers.

  A GIC offers the preservation of principal, earns a fixed yield, and allows for access to funds with no market risk. A GIC is particularly well suited for construction funds because it allows for full flexibility of draws, thus eliminating any market and/or reinvestment risk if construction draws fluctuate for any reason. GICs can also be used for debt service reserve funds, bond funds, and escrow funds, with draws occurring semi-annually on bond payments dates or as required by the Indenture. The yield on an investment contract will generally exceed the yield on a repurchase agreement by approximately 30 basis points.

  Guaranteed investment contracts can be structured with varying degrees of security. Typically, the security is provided by requiring the Provider of the GIC to maintain a certain level of long-term credit rating by one or more of the recognized Rating Agencies. The rating requirement for the Provider is often determined by the Indenture or other bond documents. In the event the Provider is downgraded below a certain level (e.g. below the "A" category from Moody's or Standard & Poor's) while the GIC is in place, then the Provider is required to provide additional security such as posting collateral with an independent third-party or assigning the contract to a new provider that both meets the rating requirement and is acceptable to the Issuer.

  Documentation for a GIC is usually a straight forward contract between the Provider of the GIC and the Trustee and/or the Issuer.

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.

HIGH-COUPON SWAP

A swap in which the fixed-rate payments are above market rates. (Also known as a premium swap.)

HISTORIC RATE ROLLOVER

A historic rate rollover allows an existing currency forward or spot position to be rolled forward without generating any intermediate cash flows. Effectively the position is reinstated for a new settlement date using a new off-market forward rate based on the historic rate.

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.

IMPLIED FORWARD CURVE

The forward curve implied by forward rate agreements (derived from the par curve) of various maturities. It is usually steeper than the normal yield curve.

IMPLIED REPO RATE

The return earned by buying a cheapest-to-deliver bond for a bond futures contract and selling it forward via the futures contract.

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

Refers to a party’s financial position if it would be owed a payment by the other party if a swap were terminated at the prevailing market price.

IN-ARREARS SWAP

See delayed reset swap

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.

INDEXED STRIKE CAP

A cap for which the pay-out level is indexed to the level of the reference rate. For example, such a cap might be struck at 7.5% as long as the reference rate remained below 9%, but rise to 8.5% if the reference rate exceeded 9%. An indexed strike cap is cheaper than a conventional cap.

INTEREST RATE CORRIDOR

An interest rate corridor is composed of a long interest rate cap position and a short interest rate cap position. The buyer of the corridor purchases a cap with a lower strike while selling a second cap with a higher strike. The premium earned on the second cap then reduces the cost of the structure as a whole. The buyer of the corridor is then protected from rates rising above the first cap’s strike, but exposed again if they rise past the second cap’s strike. It is possible to limit this liability by selling a knock-out cap rather than a conventional cap. The structure is then known as a knock-out interest rate corridor.

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 risk

The risks associated with changes in interest rates (i.e., the risk that changes in interest rates will adversely affect an Issuer’s position with respect to borrowing costs, re-investment opportunities, at-market investment termination, etc.)

INTEREST-RATE CAP

See cap

INTernational swaps and derivatives association

See ISDA

INVERSE FLOATER

The payments made on an inverse floating rate note (“floater”) decrease as the reference interest rate increases, the reverse of the typical case where the payments rise with the reference rate.

The purchaser of an inverse floating rate note is in effect selling interest rate caps – this will increase the coupon payments in a stable or lower interest rate environment, but reduce them should interest rates rise. Typically, the payment rate is found by multiplying the market rate at the outset by two and subtracting the reference rate from this figure. The floater can be leveraged by using a larger multiplier than two.

Isda

International Swaps and Derivatives Association – Represents participants in the privately negotiated derivatives industry; is the largest global financial trade association, by number of member firms. ISDA was chartered in 1985, and today has more than 840 member institutions from 56 countries on six continents. These members include most of the world's major institutions that deal in derivatives, as well as many of the businesses, governmental entities and other end users that rely on over-the-counter derivatives to manage the financial market risks inherent in their core economic activities.

See also ISDA Master Agreement, OTC derivatives

Isda master agreement

The standardized master legal agreement for all derivative transactions between an Issuer and a Provider that states standardized definitions, terms, and representations governing the swap transactions.

Jj kenny index

JJ Kenny Index is now called the S&P Weekly High Grade Index, established in 1982 at the inception of the variable rate demand bond market, the JJ Kenny index represents the current rate that 7 day variable rate demand bonds will clear the market at par. The index is comprised of over 250 high grade short term variable rate municipal bonds.

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

JUMP DIFFUSION

One of the key assumptions of the Black-Scholes model is that the asset price follows geometric Brownian motion with constant volatility and interest rates. In a jump diffusion model, it is assumed that in addition to this regular diffusion, there are jumps in the market. This type of model is sometimes used for modeling equities and emerging market currencies.

KNOCK-IN FLOOR, ONE TOUCH

A floor which will be entered into at any reset date if the reference interest rate rises beyond a trigger level on or before that date. For example, a three-year floor struck at 5% for three-month Libor might have a knock-in level of 4%. If Libor was below 4% on one of the floor’s quarterly reset dates, the floor would be entered into, leaving the seller exposed to the lower rates.

KNOCK-OUT CAP, ONE TOUCH

A cap which can be cancelled at any reset date if the reference interest rate rises beyond a trigger level on or before that date. For example, a three-year cap struck at 5% for three-month Libor might have a knock-out level of 7%. If Libor was above 7% on one of the cap’s quarterly reset dates, the cap would be cancelled, leaving the holder exposed to the higher rates. This extinguishing feature of knock-out caps means they can be considerably cheaper than conventional caps. This makes them more useful in creating structures offering cheap protection than their vanilla analogues (for example, knock-out interest rate corridor).

KNOCK-OUT INTEREST RATE CORRIDOR

A corridor in which a client purchases a standard cap with a lower strike and sells a knock-out cap with a higher strike (rather than selling a conventional cap). This means that the client is protected from an increase in interest rates up to the strike level for the knock-out cap, but exposed if rates rise beyond that level. However, the client is protected once again if the rates rise above the knock-out level, as the short knock-out cap will then be extinguished.

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.

LEASE RATE SWAP

Similar to an interest rate swap, a lease rate swap is a fixed-for-floating agreement in which gold is borrowed/lent at a “fixed” rate. The floating leg is re-priced at incremental time periods over the maturity of the swap. At the end of each floating period the agreed upon benchmark lease rate is compared to the contract rate and the party in debit pays the differential. The floating component is then rolled out for a further period.

LEGAL RISK

The risk that a counterparty to a transaction will not be liable to meet its obligations under law. This may be the case for a variety of reasons. Most fundamentally, the transaction may not be sufficiently well documented to be enforceable under law.

  A counterparty may argue that it was not sufficiently well advised of the nature and risks of a transaction prior to entering into it. This may be exacerbated if it can be demonstrated that a dealer was previously acting in a fiduciary (advisory) role, or if the dealer is found guilty of professional misconduct when making the deal. Alternatively, the transaction itself may not comply with the relevant law. For example, it is illegal to trade futures outside a regulated exchange under the terms of the US Commodity Exchange Act.

  A contract may also be may deemed unenforceable if the agent acting on behalf of the counterparty was not authorized to do so. A counterparty may in fact be legally constrained from entering certain types of transaction.

  For example, the London Borough of Hammersmith and Fulham, a British local authority, had extensive involvement in the sterling swaps market between 1986 and 1989. These deals, which far exceeded the council’s debt, were judged in 1989 to be speculative and beyond the council’s powers, leaving those dealers who stood to gain from the council’s losses unable legally to seek redress.

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.

LIBOR-IN-ARREARS SWAP

See delayed reset swap

LINEAR BASKET CREDIT DEFAULT SWAP

A basket credit default swap, where investors are exposed to multiple reference entities as if they had entered into a separate credit default swap contract with respect to each reference entity.

LINEAR FX-LINKED SWAP

An interest rate swap with a quasi-fixed coupon that varies with the movement of a chosen spot foreign exchange rate over the life of the deal. These swaps can be structured to pay a higher (or lower) coupon if a given currency weakens (or strengthens) after the outset of the deal. The observation dates for the FX component coincide with the Libor reset dates for coupon calculation. These swaps can be structured with a leveraged FX exposure.

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

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 MODEL OF INTEREST RATES

A special case of the Heath-Jarrow-Morton model due to Brace, Gatarek and Musiela in which the term structure of interest rates is modeled in terms of simple Libor rates (which are lognormally distributed with respect to forward measure) rather than instantaneous forward rates. This allows the modeler to exclude the possibility of negative interest rates from the model and obtain prices for caps, floors and swaptions consistent with the Black-Scholes framework. The model can be calibrated using readily available market data: forward or swap rates volatilities and correlations, and is particularly suited to path-dependent instruments.

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.

MEAN REVERSION

The phenomenon by which interest rates and volatility appear to move back to a long-run average level. Interest rates’ mean-reverting tendency is one explanation for the behavior of the term structure of volatility. Some interest rate models incorporate mean reversion, such as Vasicek and Cox-Ingersoll-Ross, in which high interest rat