THE OF EQUITY DERIVATIVES AND STRUCTURED PRODUCTS

Transcription

1 THE OF EQUITY DERIVATIVES AND STRUCTURED PRODUCTS 2007

2 A A ACCRETING A description, applicable to a variety of instruments, denoting that the notional principal increases successively over the life of the instrument, eg, caps, collars, swaps and swaptions. If the increase takes place in increments, the instrument may be known as a step-up. See also amortising 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 NOTE See range note 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. ALL-OR-NOTHING OPTION See binary option ALPHA Alpha is used to measure the performance of a fund in relation to its benchmark. An alpha hat measures 2.0 indicates a fund has achieved a return 2% better than could have been expected from its benchmark. Alternative risk transfer An approach to risk management combining capital markets, reinsurance and investment banking techniques that allows a party to either free itself from risks not easily transferred via traditional insurance, or alternatively cover such risks in a nontraditional way by using the capital markets for example. ALTIPLANO An Altiplano is a type of mountain range structure, which offers investors a fixed payout at the end of the product s life on the condition that none of the assets that make up the underlying basket have decreased below a given level. If the level is breached, the product pays a capital guarantee plus participation in the growth of the total underlying basket. AMERICAN-STYLE OPTION The holder of an American-style option has the right to exercise the option at any time during he life of the option, up to and including the expiry date. See also option styles AMORTISING A description, applicable to a variety of instruments, denoting that the notional principal decreases successively over the life of an instrument, eg, amortising swap, index amortising rate swap, amortising cap, amortising collar, amortising swaption. If the decrease takes place in increments, the instrument may be known as a step-down. Mortgage-style amortisation refers to an amortising swap such that the principal amortisation plus interest is the same amount in each interest period. See also accreting ANNAPURNA An Annapurna is a kind of mountain range product, which offers a return equal to the greater of a capital guarantee plus a fixed coupon and a participation in the performance of the underlying basket. The level of the fixed coupon and of the participation rate in the performance depend on if and when the worst-performing stock breaches a downside barrier. The later the breach, the higher the fixed coupon and equity participation rate. 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. 1 Equity Derivatives Glossary

3 A ARBITRAGE A guaranteed or riskless profit from simultaneously buying and selling instruments that are perfect equivalents, the first being cheaper than the second. ARBITRAGE-FREE MODEL Any model that does not allow arbitrage on the underlying variable. Some simple early models assumed parallel shifts in the yield curve, but the varying yields of different duration bonds could be arbitraged using butterfly strategies. AUTOREGRESSIVE CONDITIONAL heteroscedasticity (Arch) A discrete time model for a random variable. It assumes that variance is stochastic and is a function of the variance of previous time steps and the level of the underlying. ASIAN OPTION See average option ASSET ALLOCATION The distribution of investment funds within a single asset class or across a number of asset classes (such as equities, bonds and commodities) with the aim of diversifying risk or adding value to a portfolio. See also overlay ASSET BACKED SECURITY An asset backed security is a security collateralised by assets such as bonds, credit card repayments, loan repayments or real estate. ASSET SWAP A package of a cash credit instrument and a corresponding swap that transforms the cash lows 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 organisation s asset and liability portfolios in order to maximise returns and minimise risk. An institutional example of this would be a bank converting a fixed-rate loan (asset) by utilising a fixed-for-floating interest rate swap to match its floating rate funding (deposits). AT-THE-MONEY 1.At-the-money forward: An option whose strike is set at the same level as the prevailing market price of the underlying forward contract. With a Black-Scholes model, the delta of a European-style, at-themoney forward option will be close to 50%. 2.At-the-money spot: An option whose strike is set the same as the prevailing market price of the underlying. Because forwards commonly trade at a premium or discount to the spot, the delta may not be close to 50%. See also in-the-money, out-of-the-money 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. An average rate (or average price) option is a cashsettled option with a predetermined (ie fixed) strike which is exercised at expiry against the average value of the underlying over the specified dates. In general, hedging with an average option is cheaper than using a portfolio of vanilla options, since the averaging process offsets high values with 2 Equity Derivatives Glossary

4 A/B low ones and therefore lowers volatility and premium. Average options, also known as Asian options, are particularly popular in the equity, 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 payout is determined by comparing the ratio of settlement price to strike and a fixed percent strike. AVERAGE PRICE OPTION See average option AVERAGE RATE OPTION See average option AVERAGE STRIKE OPTION See average option B Barrier options, also known as knock-out, knock-in or trigger options, are pathdependent 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 downand-in for the knock-in barrier option. 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. See also discrete barrier option, double barrier option, Parisian barrier option, pathdependent option, trigger, trigger condition BACK-TESTING The validation of a model by feeding it historical data and comparing the model s results with the historical reality. The reliability of this technique generally increases with the amount of historical data used. BASIS 1.The difference between the price of a futures contract and its theoretical value. 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. BARRIER OPTION BASIS RISK In a futures market, the basis risk is the risk that the value of a futures contract does not 3 Equity Derivatives Glossary

5 B 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. Types of basket credit default swaps include linear basket credit default swaps, first-todefault basket credit default swaps, and firstloss basket credit default swaps. See also credit default swap BASKET OPTION An option that enables a purchaser to buy or sell a basket of currencies, equities or bonds. BASKET SWAP A swap in which a floating leg is based on the returns on a basket of underlying assets, such as equities, commodities, bonds, or swaps. The other leg is usually (but not always) a reference interest rate such as Libor, plus or minus a spread. BASIS SWAP An interest rate basis swap or a crosscurrency 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 crosscurrency basis swap exchanges a set of Libor payments in one currency for a set of Libor payments in another currency. BASIS TRADING To basis trade is to deal simultaneously in a derivative contract, normally a future, and the underlying asset. The purpose of such a trade is either to cover derivatives sold, or to attempt an arbitrage strategy. This arbitrage can either take advantage of an existing mispricing (in cash-andcarry arbitrage) or be based on speculation that the basis will change. See also cash-and-carry arbitrage 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. BASKET TRADING See program trading BEAR SPREAD An option spread trade that reflects a bearish view on the market. It is usually understood as the purchase of a put spread. See also bull spread, call spread BERMUDAN OPTION The holder of a Bermudan option, also known as a mid-atlantic option, has the right to exercise it on one or more possible dates prior to its expiry. See also option styles BEST-OF OPTION A best-of option pays out on the best performing of a number of underlying assets over an agreed period of time. For instance, if a basket contains stock A, stock B and stock C and stock B gains in value by the larger amount during the products term, then the payout would be based on the increase in value of Stock B. BETA 1. The beta of an instrument is its standardised covariance with its class of instruments as a whole. Thus the beta of a stock is the extent to which that stock follows movements in the overall market. 2. Beta trading is used by currency traders if they take the volatility risk of one currency in 4 Equity Derivatives Glossary

6 B another. For example, rather than hedge a sterling/yen option with another sterling/yen option, a trader, either because of liquidity constraints or because of lower volatility, might hedge with euro/yen options. The beta risk indicates the likelihood of the two currencies volatilities diverging. BETTER-OF-TWO-ASSETS OPTION See best-of option BILATERAL NETTING Agreement between two counterparties whereby the value of all in-the-money contracts is offset by the value of all outof-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. BINOMIAL MODEL Any model that incorporates a binomial tree. 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 ratesensitive 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 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 5 Equity Derivatives Glossary

7 B/C 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 (ie have lognormal prices), that there are no transaction costs, that volatility and interest rates remain constant throughout the life of the option, and that the market follows a diffusion process. The model has five major inputs: the risk-free interest rate, the option s strike price, the price of the underlying, the option s maturity, and the volatility assumed. Since the first four are usually determined by the market, options traders tend to trade the implied volatility of the option. BOND Companies or governments issue bonds as a means of raising capital. The bond purchaser is in effect making a loan to the issuer, and unlike with shares investors at no point hold a stake in the company. 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. BOX To buy/sell mispriced options and hedge the market risk using only options, unlike the conversion or the reversal, which use futures contracts. If a certain strike put is underpriced, the trader buys the put and sells a call at the same strike, creating a synthetic short futures position. To get rid of the market risk, he sells another put and buys another call, but at different strike prices. See also convergence trade BRACE-GATAREK-MUSIELA (BGM) MODEL See market model of interest rates. understood as the purchase of a call spread. See also bear spread, call spread BUTTERFLY SPREAD The simultaneous sale of a straddle and purchase of a money strangle. The structure profits if the underlying remains stable, and has limited risk in the event of a large move in either direction. As a trading strategy to capitalise upon a range trading environment it is usually executed in equal notional amounts. Alternatively, such trades are often applied to benefit from changes in volatility. In such circumstances the butterfly spread is traded on a vega-neutral basis (ie the volatility sensitivity of the long position is initially offset by the volatility sensitivity of the short position). As the holder of an initially vega-neutral spread, the trader will benefit from changes in volatility since the strangle position profits more from an increase in volatility than the straddle and loses less than the straddle in a decline in volatility (this is due to the fact that the vomma of the strangle is higher than that of the straddle). C CALENDAR SPREAD A strategy that involves buying and selling options or futures with the same (strike) price but different maturities. Such a strategy is used in futures when one contract month is theoretically cheap and another is expensive. With options, the strategy is often used to play the shape of or expected changes in, the volatility term structure. For example, if onemonth volatility is high and one-year volatility low, arbitrageurs might buy one-year straddles and sell short-term straddles, thereby selling short-term volatility and buying long-term volatility. If, all else being equal, short-term volatility declines relative to long-term volatility, the strategy makes money. BULL SPREAD An option spread trade that reflects a bullish view on the market. It is usually 6 Equity Derivatives Glossary

8 C CALL OPTION See option CALL SPREAD A strategy that reduces the cost of buying a call option by selling another call at a higher strike price (Bull call spread). This limits potential gain if the underlying goes up, but the premium received from selling the out-of-the-money call partly finances the at-the-money call. A call spread may be advantageous if the purchaser thinks there is only limited upside in the underlying. Alternatively a Bear call spread can be constructed by selling a call option and buying another at a higher strike price. See also bear spread, bull spread, put spread CALLABLE SWAP An interest rate swap in which the fixedrate 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. See also collar CAPITAL-PROTECTED A structured product that provides capital protection offers an amount that at least matches a given proportion of the investor s original capital input at maturity. Can also be referred to as principal-protected. Capitalprotected credit-linked note A credit-linked note where the principal is partly or fully guaranteed to be repaid at maturity. In a 100% principal-guaranteed credit-linked note, only the coupons paid under the note bear credit risk. Such a structure can be analysed as (i) a Treasury strip and (ii) a stream of risky annuities representing the coupon, purchased from the note proceeds minus the cost of the Treasury strip. See also creditlinked note 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. CAPTION An option on a cap. A type of compound option in which the purchaser has the right, but not the obligation, to buy or sell a cap at a predetermined price on a predetermined date. Captions can be a cheap way of leveraging into the more expensive option. See also floortion CASH AND CARRY When a contango exists, the premium of the forward position over the spot generally reflects costs of buying and holding (eg financing, transaction costs, insurance, 7 Equity Derivatives Glossary

9 C custody) for that period. See also cash and carry arbitrage CASH MARKET The physical market for buying and selling an underlying (eg equities, bonds), as opposed to a futures market. CHOOSER OPTION A chooser option offers purchasers the choice, after a predetermined period, between a put and a call option. The pay-outs are similar to those of a straddle but chooser options are cheaper because purchasers must choose before expiry whether they want the put or the call. 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. Cash-and-carry arbitrage and reverse cash-and-carry arbitrage typically keep the futures and underlying markets closely aligned. See also basis trading, reverse cash-and-carry arbitrage CATASTROPHE BOND A bond that pays a coupon that decreases only after a catastrophe such as a hurricane or earthquake with a specified magnitude in a specified region and period of time. CATASTROPHE OPTION These options can be American-style or European-style, either paying out if a single specified catastrophe such as a hurricane or earthquake occurs, or alternatively, having a pay-out dependent on an index. For example, the index may represent the number of claims received by property insurance companies. CATASTROPHE RISK SWAP An agreement between two parties to exchange catastrophe risk exposures. For example, in July 2001 Swiss Re and Tokyo 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. CLIQUET Cliquet structures, which can also be called ratchet structures, periodically settle and reset their strike prices, allowing users to lock-in potential profits on the underlying. With a cliquet the payout is worked out from the performance of the underlying asset in a number of set periods during the product s life. See also ladder options CLIQUET OPTION Also known as a ratchet or reset option. A path-dependent option that allows buyers to lock-in gains on the underlying security during chosen intervals over the life time of the option.the option s strike price is effectively reset on predetermined dates. Gains, if any, are locked in. So if an underlying rises from 100 to 110 in year one, the buyer locks in 10 points and the strike price is reset at 110. If it falls to 97 in the next year the strike price is reset at that lower level, no further profits are locked in, but the accrued profit is kept. See also ladder option, lookback option, moving strike option, path dependent option CLOSED-FORM SOLUTION Also called an analytical solution. An explicit solution of, for example, an option pricing problem by the use of formulae involving only simple mathematical functions, such as Black-Scholes or Vasicek models. Closedform models can usually be evaluated much more quickly than numerical models, which are sometimes far more computationally intensive. COLLAR The simultaneous sale of an out-of-themoney call and purchase of an out-of-themoney put (or cap and floor in the case of interest rate options).the premium from selling the call reduces the cost of purchasing 8 Equity Derivatives Glossary

10 C the put. The amount saved depends on the strike rate of the two options. If the premium raised by the sale of the call exactly matches the cost of the put, the strategy is known as a zero cost collar. The combination of purchasing the put and selling the call while holding the underlying protects the holder from losses if the underlying falls in price, at the expense of giving away potential upside. See also cap, equity collar, impact forward, risk reversal, zero cost option 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. so reduce its required capital reserves, while retaining contact with the borrowers and fees from servicing the loans. See also collateralised mortgage obligation 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 collateralised bond obligation, collateralised debt obligation, collateralised loan obligation COMBO See risk reversal 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 collateralised mortgage obligation. But rather than mortgages, low-rated bonds serve as the collateral. See also collateralised mortgage obligation COLLATERALISED DEBT OBLIGATION (CDO) Generic name for collateralised bond obligations, collateralised loan obligations, and collateralised mortgage obligations. See also collateralised mortgage obligation, synthetic collateralised debt obligation COLLATERALISED LOAN OBLIGATION (CLO) A structured bond backed by the loan repayments from a portfolio of pooled personal or commercial loans, excluding mortgages. The structure allows a bank to remove loans from its balance sheet and COMPOUND OPTION A compound option is an option on an option. The tool allows the user to buy or sell an option at a fixed price during a set period. They are often used to hedge against increase in option prices during volatile periods. Examples include captions and floortions. CONDOR The simultaneous purchase (sale) of an outof-the-money strangle and sale (purchase) of an even further out-of-the-money strangle. The strategy limits the profit or loss of the pay-out and is directionally neutral. CONSTANT MATURITY SWAP This is an interest rate swap where the floating interest arm is reset periodically with reference to longer duration treasury-based instruments rather than a market index such as LIBOR. 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. 9 Equity Derivatives Glossary

11 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. CONSTANT PROPORTION PORTFOLIO INSURANCE (CPPI) A fund management technique that aims to provide maximum exposure to risky assets while still protecting investors capital. The technique requires the manager to dynamically rebalance the portfolio between risky assets (such as equities) and safe assets (such as bonds) according to a quantitative model. The level of risky assets is managed such that at all times, in the event of a market crash, the remaining NAV of the fund is still sufficient to meet the stated protection level. Generally the proportion of Risky Assets in the fund is increased when these perform well and decreased when these perform poorly. The capital protection level may be fixed, or rachet up (reset) according to a certain percentage of the fund NAV achieved during the fund term. 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. CONTRACT FOR DIFFERENCE (CFD) A Contract for Difference is typically an agreement made between two parties to exchange (at the closing of the contract) a cashflow equivalent to the difference between the opening and closing prices, multiplied by the number of shares detailed in the contract. CFDs are traded on margin, do not incur stamp duty and can have individual stocks or indexes as the underlying. CONVERGENCE TRADE Trading strategy where similar securities are bought and sold simultaneously in the expectation that prices will converge in an orderly fashion. 1.A way of taking advantage of mispriced options by creating a synthetic short futures position and hedging market risk by buying a futures contract against it. Thus if a put is undervalued, a trader buys it, at the same time selling a fairly valued call and buying a futures contract. The same strategy can be applied if the call is mispriced. If the option is truly undervalued, the trader earns a riskless profit. The whole exercise relies on put-call parity 2.The act of converting a convertible bond into equity. See also box, reversal CONVERTIBLE BOND A bond issued by a company that may be exchanged by the holder for a number of that company s shares at a predetermined ratio, or at a discount to the share price at maturity. Because the convertible embeds a call option on the company s equity, convertibles carry 10 Equity Derivatives Glossary

12 C 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. See also equity warrant, resettable convertible bond 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, eg collateralised 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 crosscurrency 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 realised correlations. See also joint option CORRELATION SWAP An instrument that allows an investor to take financial exposure on a set of correlations. CORRIDOR FLOATER See range note 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 behaviour 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. 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 bing 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 11 Equity Derivatives Glossary

13 C 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. increase the yield of the asset. Investors also sell covered puts if markets have fallen rapidly but seem to have bottomed, because of the high volatility typically received on the option. See also covered call 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 assets s yield or (and) if the cost could be mitigated by lending out the securities. See also future COUNTERPARTY CREDIT RISK See credit risk COVERED CALL To sell a call option while owning the underlying security on which the option is written. The technique is used by fund managers to increase income by receiving option premium. It would be used for securities they are willing to sell, only if the underlying went up sufficiently for the option to be exercised. Generally, covered call writers would undertake the strategy only if they thought volatility was overpriced in the market. The lower the volatility, the less the covered call writer gains in return for giving up upside in the underlying. It provides downside protection only to the extent that the option premium offsets a market downturn. See also covered put COVERED PUT To sell a put option while holding cash. This technique is used to increase income by receiving option premium. If the market goes down and the option is exercised, the cash can be used to buy the underlying to cover. Covered put writing is often used as a way of target buying: if an investor has a target price at which he wants to buy, he can set the strike price of the option at that level and receive option premium to COVERED WARRANT See warrant COX-INGERSOLL-ROSS MODEL In its simplest form this is a lognormal onefactor 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. See also basket credit default swap 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. 12 Equity Derivatives Glossary

14 C 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 are determined by negotiation between the parties at the outset of a credit default 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 RISK Also known as default risk. In broad terms, the risk that a loss will be incurred if a counterparty to a (derivatives) transaction does not fulfil its financial obligations in a timely manner. The term is sometimes loosely used as shorthand for the likelihood or probability of default, irrespective of the value of any position exposed to this risk. More precisely, credit risk is the risk of financial loss arising out of holding a particular contract or portfolio. 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 SPREAD FORWARD A cash-settled forward contract with settlement amounts based on the credit spread between two predetermined debt issues on the maturity date. See also credit spread option CREDIT SPREAD OPTION An option on the credit spread between two debt issues. The option will pay out the difference between the credit spread at maturity and a strike spread determined at the outset. See also credit spread forward 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. Credit-linked notes may also be issued from a collateralised Special Purpose Vehicle (SPV). See also capital-protected credit-linked note 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. See also crosscurrency floor CROSS-CURRENCY FLOOR This is an option setting a cap on the spread between two index interest rates in different currencies. See also cross-currency cap 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, 13 Equity Derivatives Glossary

15 floating or zero basis. The principal is then re-exchanged at maturity at the initial spot rate. CURRENCY OVERLAY See overlay C/D 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 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 unfavourable exchange rates. Unlike options, forwards do not enable companies to take advantage of favourable 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 or quanto option. CURRENCY RISK Currency risk arises from changes in the value of currencies. For example, if a company receives a portion of its income in a foreign currency, it is exposed to changes in the value of that currency. Risk management and derivatives can be used to minimise this risk. CURRENCY STRUCK OPTION This is the same as joint option. CURRENT EXPOSURE Another name for replacement cost. CYLINDER See risk reversal D DEFERRED PAYOUT OPTION A deferred payout option is a variation on American-style options similar to a shout option. The holder of the option may exercise it at any time, for the value taken by the underlying at that time, but the payout is delayed until the expiry date. This term is also applied to certain digital options whose payout is not paid when triggered, but deferred until the final maturity. See also option styles DEFERRED START OPTION See forward start option 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 14 Equity Derivatives Glossary

16 D 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. 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. See also static replication 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. DIFFERENCE OPTION See spread option DIFFUSION PROCESS A continuous-time model of the behaviour of a random variable. An example of such a model is Generalised Brownian Motion (GBM), which is often used to model the behaviour of spot rates. DIGITAL OPTION Digital options pay a set amount if the underlying asset is above, or sometimes below, a certain level on a specific date. These options have only two possible outcomes: a set payout, or nothing at all. Thus, they are also known as binary or all-ornothing options. 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 amortised over the maturity of the swap and an instalment paid at each payment date. DISCRETE BARRIER OPTION Barrier options where the trigger level is only active for part of the option s lifetime. This includes barrier options where the trigger is only valid on certain fixing dates, as well as cases where the trigger is valid for subintervals of the option s lifetime. See also barrier option DISTRIBUTION The probability distribution of a variable describes the probability of the variable attaining a certain value. Assumptions about the distribution of the underlying are crucial to option models because the distribution determines how likely it is that the option will be exercised. Many models assume the logarithm of the relative return has a normal distribution, which can be described by two 15 Equity Derivatives Glossary

17 D/E parameters. The first is the distribution s mean; the second its standard deviation (equivalent, if annualised, to volatility). In practice, most empirically observed asset distributions depart from normality. This departure can be described in terms of the skew (how much it tilts to one side or the other) and kurtosis, which describes how fat or thin are the tails at either side. Most markets tend to have fat tails (to be leptokurtic) rather than thin tails (platykurtic). This pushes up the price of out-of-the-money options. DOUBLE BARRIER OPTION This is an option with two barriers; one setting the upper limit of the price of the underlying and one setting the lower limit. If the underlying crosses either of these barriers the option is either activated (knock-in) or deactivated (knock-out). See also barrier option. DOUBLE NO-TOUCH A double no-touch option pays a set amount as long as one of two specified barrier levels are not broken during the life of the option. This tool is popular for usage in relatively stable markets. DOWNSIDE RISK The risk the investor is exposed to if there is a fall in the value of the underlying. 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. DYNAMIC HEDGING See delta hedging E EMBEDDED OPTION An option, often an interest rate option, embedded in a debt instrument that affects its redemption. Examples include mortgagebacked securities and callable and puttable 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 zerocoupon bonds and call options. EQUILIBRIUM MODEL A model that specifies processes for the underlying economic variables and the extra risk premium investors require for risky assets. The evolution of asset prices and their risk derived from the model thus specified. 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 COLLAR Equity collars are used by investors keen to reduce their downside risk. An equity collar is formed by buying an equity put option with a strike price below the current value of the equity, at the same time as selling an equity call option with a strike above the current equity price. Thus a collar is imposed around the investor s equity position. If the value of the underlying equity falls through the strike of the bought put, it can be exercised to limit losses. However, if the underlying stock rises 16 Equity Derivatives Glossary

18 E through the strike of the sold call, the investor may have to deliver the equity at the strike, thus foregoing potential additional upside. See also collar EQUITY KNOCK-OUT 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 knock-out can be unconditional 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 LINKED NOTE An equity linked note is a tool that is linked to a single equity, equity index or basket of equities. They may or may not be principal protected. EQUITY WARRANT A warrant is a financial instrument issued by a bank or other financial institutions, which is traded on a stock exchange s equity market. Warrants may be issued over securities such as shares in a company, a currency, an index or a commodity. A call warrant gives the holder the right (but not the obligation) to buy a given security at a given price known as the exercise price, on a given date, known as the expiry date. Conversely a put warrant gives the holder the right to sell the security at the exercise price on the expiry date. These instruments are sometimes known as covered warrants or derivative warrants. See also convertible bond, warrant EUROPEAN-STYLE OPTION European-style options can only be exercised on their expiry date. They stand in contrast to American-style options, which can be exercised at any time until maturity. EVEREST STRUCTURE A capital guaranteed structure generally offering the investor the sum invested at maturity and potential upside linked to the performance of the least-performing asset in a predefined basket. The Everest structure may also pay coupons over its life. EXCHANGEABLE BOND These are just like convertible bonds. The main difference is that these are typically issued on stock, which is not the stock of the issuing firm. EXCHANGE-TRADED OPTION See option EXERCISE See option EXOTIC OPTION Any option with a more complicated payout structure than a plain vanilla put or call option. The payout 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 payout can differ from that of a plain vanilla. The payout 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 payout options, shout options, lookback options, cliquet options, ladder options) a fixed amount (binary options) Alternatively, or additionally, a payout 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 in the case of corridor or mini-premium options). 17 Equity Derivatives Glossary

19 E/F 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 modelling interest rate options. EXTREME VALUE THEORY An area of statistical research that focuses on modelling the extreme values of return distributions. This is important in finance because many models (for example the Black-Scholes Model) assume that the distribution of returns is log-normal. However, real-world distributions are found to have fat-tails implying that rare events such as crashes are more likely than the traditional theories suggest. F FAT TAILS See kurtosis FINANCIAL ENGINEERING The design and construction of investment products to achieve specified goals. FLEXIBLE OPTION A flexible option (also known as a flexible exchange or flex option) is a customisable exchange-traded option, which allows the buyer to customise contract terms such as expiry date and contract size in addition to the strike price. Flexible options with single stock, index, or even currency underlyings are traded on several major exchanges. FLOOR FUND Also known as a ratchet fund. A particular type of structured product that aims to deliver minimum returns, which usually are at least equal to the sum invested, plus some additional upside based on the performance of the stock market. However, unlike guaranteed funds, very few floor funds come with a contractual guarantee. Many floor funds are managed using the technique of constant proportion portfolio insurance (CPPI). FLOORTION An option on a floor. The purchaser has the right, but not the obligation, to buy or sell a floor at a predetermined price on a predetermined date. See also caption FORWARD See future 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 offbalance 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 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. 18 Equity Derivatives Glossary

20 F/G 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. FRATION See interest rate guarantee 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 and stock indexes. 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. See also cost of carry, implied repo rate FUTURE RATE AGREEMENT See forward rate agreement FUTURES OPTION An option, either a put or a call, on any futures contract. Also known as an option on a future. G 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 atthe-money and decreases as the price of the underlying moves further away from the strike price in either direction. 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. See also vega 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. GEARED BARRIER OPTION A type of in-the-money barrier option where the barrier is in-the-money and lies between the strike and the underlying spot rate. GEARING Gearing refers to the degree of exposure of a product to movements in the underlying index. A product with 100% gearing would have returns exactly equal to any rise in the index. A product s gearing is also called participation. GEOMETRIC BROWNIAN MOTION Geometric Brownian motion is a model frequently used for the diffusion process followed by asset prices. Standard Brownian motion is a random walk process with Gaussian increments; that is, changes in the asset price are normally distributed. The term geometric means it is the proportional change in the asset price (as opposed to the absolute level) that is normally distributed. This gives the model useful properties, in that the asset price cannot be negative, and that the 19 Equity Derivatives Glossary