similar problems to LTCM and trying todo similar trades. This exacerbated the situation, causing liquidity spreads to be even higher thanthey would otherwise have been and reinforcing the flight to quality. Consider, for example,LTCM’s position in U.S. Treasury bonds. It was long the illiquid off-the-run bonds and short theliquid on-the-run bonds. When a flight to quality caused spreads between yields on the two types ofbonds to widen, LTCM had to liquidate its positions by selling off-the-run bonds and buying on-the-run bonds. Other large hedge funds were doing the same. As a result, the price of on-the-runDerivatives Mishaps and What We Can Learn from Them 693
bonds rose relative to off-the-run bonds and the spread between the two yields widened even morethan it had done already.
A further example is provided by the activities of British insurance companies in the late 1990s.These insurance companies had entered into many contracts promising that the rate of interestapplicable to an annuity received by an individual on retirement would be the greater of the marketrate and a guaranteed rate. At about the same time, all insurance companies decided to hedge partof their risks on these contracts by buying long-dated swap options from financial institutions. Thefinancial institutions they dealt with hedged their risks by buying huge numbers of long-datedsterling bonds. As a result, bond prices rose and long sterling rates declined. More bonds had to bebought to maintain the dynamic hedge, long sterling rates declined further, and so on. Financialinstitutions lost money and, because Jong rates declined, insurance companies found themselves ina worse position on the risks they had chosen not to hedge.
The chief lesson to be learned from these stories is that it is important to see the big picture ofwhat is going on in financial markets and to understand the risks inherent in situations wheremany market participants are following the same trading strategy.
30.3. LESSONS FOR NONFINANCIAL CORPORATIONS
 
We now consider lessons primarily applicable to nonfinancial corporations.
Make Sure You Fully Understand the Trades You Are Doing
Corporations should never undertake a trade or a trading strategy that they do not fully under-stand. This is a somewhat obvious point, but is surprising how often a trader working for anonfinancial corporation will, after a big loss, admit to not knowing what was really going on andclaim to have been misled by investment bankers. Robert Citron, the treasurer of Orange Countydid this. So did the traders working for Hammersmith and Fulham, who in spite of their hugepositions were surprisingly uninformed about how the swaps and other interest rate derivativesthey traded really worked.
If a senior manager in a corporation does not understand a trade proposed by a subordinate, thetrade should not be approved. A simple rule of thumb is that if a trade and the rationale forentering into it are so complicated that they cannot be understood by the manager, it is almostcertainly inappropriate for the corporation. The trades undertaken by Procter and Gamble andGibson Greetings would have been vetoed using this criterion.
One way of ensuring that you fully understand a financial instrument is to value it. If acorporation does not have the in-house capability to value an instrument, it should not trade it.In practice, corporations often rely on their investment bankers for valuation advice. This isdangerous, as Proctcr and Gamble and Gibson Grectings found out when they wanted to unwindtheir deals. They were facing prices produced by Bankers Trust’s proprietary models, which theyhad no way of checking.
Make Sure a Hedger Does Not Become a Speculator
One of the unfortunate facts of life is that hedging is relatively dull, whereas speculation isexciting. When a company hires a trader to manage foreign exchange risk or interest rate riskthere is a danger that the following happens. At first, the trader does the job diligently and earns694 CHAPTER 30
the confidence of top management. He or she assesses the company’s exposures and hedges them.As time gocs by, the trader becomes convinced that he or she can outguess the market. Slowlythe trader becomes a speculator. At first things go well, but then a loss is made. To recover theloss the trader doubles up the bets. Further losses are made and so on. The result is likely to be adisaster.
As mentioned earlier, clear limits to the risks that can be taken should be set by seniormanagement. Controls should be set in place to ensure that the limits are obeyed. The tradingstrategy for a corporation should start with an analysis of the risks facing the corporation inforcign exchange, interest rate, commodity markets, and so on. A decision should then be taken onhow the risks are to be reduced to acceptable levels. It is a clear sign that something is wrongwithin a corporation if the trading strategy is not derived in a very direct way from the company’sexposures.
Be Cautious about Making the Treasury Department a Profit Center
In the last 20 years there has been a tendency to make the treasury department within a corporation aprofit center. This appears to have much to recommend it. The treasurer is motivated to reducefinancing costs and manage risks as profitably as possible. The problem is that the potential for thetreasurer to make profits is limited. When raising funds and investing surplus cash, the treasurer isfacing an efficient market. The treasurer can usually improve the bottom line only by takingadditional risks. The company’s hedging program gives the treasurer some scope for making shrewddecisions that increase profits. But it should be remembered that the goal of a hedging program is toreduce risks, not to increase expected profits. As pointed out in Chapter 4, the decision to hedge willlead to a worse outcome than the decision not to hedge roughly 50% of the time. The danger ofmaking the treasury department a profit center is that the treasurer is motivated to become aspeculator, An Orange County, Procter and Gamble, or Gibson Greetings type of outcome is thenliable to occur.
 
The huge losses experienced from the use of derivatives have made many treasurers very wary.Since the spate of mishaps in 1994 and 1995, some nonfinancial corporations have announcedplans to reduce or even eliminate their use of derivatives. This is unfortunate because derivativesprovide treasurers with very efficient ways to manage risks.
The stories behind the losses emphasize the point, made as early as Chapter 1, that derivativescan be used for either hedging or speculation; that is, they can be used either to reduce risks or totake risks. Most losses occurred because derivatives were used inappropriately. Employeeswho had an implicit or explicit mandate to hedge their company’s risks decided instead tospeculate.
The key lesson to be learned from the losses is the importance of internal controls. Seniormanagement within a company should issue a clear and unambiguous policy statement about howderivatives are to be used and the extent to which it is permissible for employees to take positionson movements in market variables. Management should then institute controls to ensure that thepolicy is carried out. It is a recipe for disaster to give individuals authority to trade derivativeswithout a close monitoring of the risks bcing taken.Derivatives Mishaps and What We Can Learn from Them 695
SUGGESTIONS OR FURTHER READING
 
Dunbar, N., Inventing Money: The Story of Long-Term Capital Management and the Legends Behind It,Wiley, Chichester, 2000.
Jorion, P., Big Bets Gone Bad: Derivatives and Bankruptcy in Orange County, Academic Press, NewYork, 1995.
Jorion, P., ‘““How Long-Term Lost Its Capital,” R/SK, September 1999.
Ju, X., and N. Pearson, “Using Value at Risk to Control! Risk Taking: How Wrong Can You Be?”Journal of Risk, 1, no. 2 (Winter, 1998/9), 5-36.
Thomson, R., Apocalypse Roulette: The Lethal World of Derivatives, Macmillan, London, 1998.Zhang, P. G., Barings Bankruptcy and Financial Derivatives, World Scientific, Singapore, 1995.GLOSSARY OF NOTATION
 
The following is a guide to the ways that symbols are used in this book. Symbols that appear in onesmall part of the book may not be listed here, but are always defined at the place when they are first
used.
a: Growth factor per step of an underlyingvariable in a risk-neutral world in a bino-mial model during time 6t. For example,when the underlying variable is a non-
dividend-paying stock a = e"*:; when it is a
currency, a = e"—’?*; and so on. The vari-able a is also used in Chapter 11 as the driftrate in a generalized Wiener process. InChapter 23, it is the reversion rate in an
interest rate process,
b: In Chapter 11, 5’ is the variance rate in ageneralized Wiener process. In Chapter 23, bis the reversion level in an interest rateprocess.
B: Coupon-bearing bond price.c: Price of a European call option. It is also
used in Chapter 5 to denote a bond’scoupon.
C: Price of an American call option. It is alsoused in Chapter 5 to denote convexity.
d\, d): Parameters in option pricing formulas.See, for example, equations (12.20), (13.4),and (13.17).
d: Proportional down movement in a binomialmodel. If d = 0.9, value of variable moves to90% of its previous value when there is adown movement.
dz: Wiener process.
D: In Chapters 8 and 12, D is the presentvalue of dividends on a stock. In Chapter5, D is used to denote duration.
D;: The ith cash dividend payment.E(-): Expected value of a variable.
E(-): Expected value of a variable in a risk-neutral world. (This is the traditional risk-neutral world where the numeraire is themoney market account.)
E7(-): Expected value of a variable in a worldwhcre numeraire is a zero-coupon bondmaturing at time T.
E,(-): Expected value of a variable in a worldwhere numeraire is the value of an annuity
f: Value of a derivative. f; is the value of aderivative at time T and fp is the value of aderivative at time zero. f; is used on occa-sion to denote the value of the ith derivative.
Jui Value of derivative if an up movementoccurs.
fa; Value of derivative if a down movementoccurs.
F: Forward or futures price at a general time t.Fy: Forward or futures price at time zero.F;: Forward or futures price at time T.
h: Hedge ratio in Chapter 4. The variable, h*,is the optimal hedge ratio.
H: Barrier level in a barrier option.T: Present value of income on a security.
K: Strike price of an option. Also the deliveryprice in a forward contract.
L: Principal amount in a derivatives contract.
697698
M(a, y, p): Cumulative probability in a bivari-ate normal distribution that the first variableis less than x and the second variable is lessthan y when the coefficient of correlationbetween the variables is p.
N(x): Cumulative probability that a variablewith a standardized normal distribution isless than x. A standardized normal distribu-tion is a normal distribution has a mean ofzero and standard deviation of 1.0. Tablesfor N(x) are at the end of this book.
p: This is used in two important ways. Thefirst is as the value of a European put option(e.g., in Chapter 12). The second is as theprobability of an up movement in binomialmodels (e.g., in Chapter 18),
P: Value of an American put option. InChapters 4 and 16, P denotes a portfoliovalue.
P(t, T): The price at time t of a zero-couponbond maturing at time 7.
q. Dividend yield rate. In Chapter 10, ¢ de-notes the probability of an up movement inthe real world. (This can be contrasted withp which is the probability of an up move-ment in the risk-neutral world.)
~
: Risk-free interest rate. Sometimes (e.g,Chapters 3 and 8) it is the rate applicablebetween times 0 and T and sometimes (e.g.,Chapter 23) it is the instantaneous (i.e., veryshort term) risk-free interest rate.
ry: Risk-free interest rate in a foreign country.
r Average instantaneous risk-free rate of inter-est during the life of a derivative.
R: In Chapter 23, this is the dt-period rate andshould be distinguished from r, which is theinstantaneous risk-free rate. In Chapters 26and 27, it is the recovery rate with R definedas the expected recovery rate.
R,: In Chapter 3, this is an interest rateexpressed with continuous compounding
Glossary of Notation
R,,: In Chapter 3, this is an interest rateexpressed with compounding m times peryear
S: Price of asset underlying a derivative at ageneral time ¢. In different parts of thebook, S is used to refer to the price of acurrency, the price of a stock, the price of astock index, and the price of a commodity.
Sp: Value of S$ at time T.So: Value of S at time zero.t: A future point in time.
T: Time to end of life of option or otherderivative.
u: Proportional up movement in a binomialmodel. For example, u = |.2 indicates thatthe variable increases by 20% when an upmovement occurs. In Chapter 3, u is used todenote the storage costs per unit time as aproportion of the price of an asset.
u;: In Chapters 12 and 17, this denotes thereturn provided on an asset between obser-vation i— ! and observation i.
Vv: Vega of a derivative or a portfolio ofderivatives.
y: Usually denotes a bond’s yield. In Chapter 3,it denotes the convenience yield.
y(T): yield on a risk-free bond maturingtime T in Chapters 26 and 27; y(T) is thecorporate bond yield.
fB: In Chapters 4 and 13, this denotes thecapital asset pricing model’s beta parameter.
atat
Pr: Gamma of a derivative or a portfolio ofderivatives.
A: Delta of a derivative or a portfolio ofderivatives.
5x: Small change in x for any variable x.
e. Random sample from a standardized nor-«mal distribution.
yn: Continuously compounded return on stock.
yw: Expected return on an asset.Glossary of Notation
6: In Chapters 21 and 28, this is the value of avariable that is not necessarily the price of atraded security. ~
©: Theta of a derivative or portfolio of deri-vatives.
Tl: Value of a portfolio of derivatives.
p: Coefficient of correlation.
o: Usually this is the volatility of an asset (i.e.,o/5t is the standard deviation of the percen-tage change in the asset’s price in time 6ét).Note that, in Chapter 4, of and og are thestandard deviations of § and F at hedge
699
maturity. Also, in the Hull White and Ho
Lee models (Chapter 23), o is the instanta-neous standard deviation (not the volatility)of the short rate.
o,: In Chapter 16, this is the volatility of thenth asset. In Chapter 17, it is the volatility ofa particular asset on day n, estimated at theend of day n — 1.
op: Standard deviation (not volatility) of aportfolio in Chapter 16.
o(m, sy: Normal distribution with mean mand standard deviation s.GLOSSARY OF TERMS
 
Accrual Swap An interest rate swap whereinterest on one side accrues only when acertain condition is met.
Accrued Interest The interest earned on abond since the last coupon payment date.
Adaptive Mesh Model A model developed byFiglewski and Gao that grafts a high-resolu-tion tree on to a low-resolution tree so thatthere is more detailed modeling of the assetprice in critical regions.
American Option An option that can beexercised at any time during its life.
Amortizing Swap A swap where the notionalprincipal decreases in a predetermined wayas time passes.
Analytic Result Result where answer is in theform of an equation.
Arbitrage A trading strategy that takes ad-vantage of two or more securities beingmispriced relative to each other.
Arbitrageur An individual engaging in arbit-rage.
Asian Option An option with a payoff depen-dent on the average price of the underlyingasset during a specified period.
Ask PriceAsked Price See Offer price.
See Offer price
Asset-or-Nothing Call Option An option that ~
provides a payoff equal to the asset price ifthe asset price is above the strike price andzero otherwise.
700
Asset-or-Nothing Put Option An option thatprovides a payoff equal to the asset price ifthe asset price is below the strike price andzero otherwise.
Asset Swap Exchanges the coupon on a bondfor LIBOR plus a spread.
As-You-Like-It Option See Chooser option.
At-the-Money Option An option in which thestrike price equals the price of the under-lying asset.
Average Price Call Option An option giving apayoff equal to the greater of zero and theamount by which the average price of theasset exceeds the strike price.
Average Price Put Option An option giving apayoff equal to the greater of zero and theamount by which the strike price exceeds theaverage price of the asset.
Average Strike Option An option that pro-vides a payoff dependent on the differencebetween the final asset price and the averageasset price.
Back Testing Testing a value-at-risk or othermodel using historical data.
Backwards Induction A procedure for work-ing from the end of a tree to its beginning inorder to value an option.
Barrier Option An option whose payoff de-pends on whether the path of the underlyingasset has reached a barrier (ie., a certainpredetermined level).
Basis The difference between the spot priceand the futures price of a commodity.Glossary of Terms
701
 
Basis Point When used to describe an interestrate, a basis point is one hundredth of onepercent (= 0.01 percent)
Basis Risk The risk to a hedger arising fromuncertainty about the basis at a future time.
Basket Option An option that provides apayoff dependent on the value of a portfolioof assets.
Basket Credit Default Swap Credit defaultswap where there are several reference enti-ties.
Bear Spread A short position in a put optionwith strike price K, combined with a longposition in a put option with strike price K,where K, > K,. (A bear spread can also becreated with call options.)
Bermudan Option An option that can beexercised on specified dates during its life.
Beta A measure of the systematic risk of anasset.
Bid—Ask Spread See Bid-offer spread.
Bid-Offer Spread The amount by which theoffer price exceeds the bid price.
Bid Price The price that a dealer is preparedto pay for an asset.
Binary Option Option with a discontinuouspayoff; for example, a cash-or-nothing op-tion or an asset-or-nothing option.
Binomial Model A model where the price ofan asset is monitored over successive shortperiods of time. In each short period it isassumed that only two price movements arepossible.
Binomial Tree A tree that represents how anasset price can evolve under the binomialmodel.
Bivariate Normal Distribution A distributionfor two correlated variables, each of which isnormal.
Black’s Approximation An approximate pro-cedure developed by Fischer Black for valu-ing a call option on a dividend-paying stock.
Black’s Model An extension of the Black-Scholes model for valuing European optionson futures contracts. As described in Chap-ter 22, it is used extensively in practice tovalue European options when the distribu-tion of the asset price at maturity is assumedto be lognormal. :
Black-Scholes Model A model for pricingEuropean options on stocks, developed byFischer Black, Myron Scholes, and RobertMerton.
Board Broker The individual who handleslimit orders in some exchanges. The boardbroker makes information on outstandinglimit orders available to other traders.
Bond Option An option where a bond is theunderlying asset.
Bond Yield Discount rate which, when ap-plied to all the cash flows of a bond, causesthe present value of the cash flows to equalthe bond’s market price.
Bootstrap Method A procedure for calculat-ing the zero-coupon yield curve from marketdata.
Boston Option See Deferred payment option.
Break Forward See Deferred payment op-tion.
Bull Spread A long position in a call withstrike price K,; combined with a short posi-tion in a call with strike price K», whereK, > K,. (A bull spread can also be createdwith put options.)
Butterfly Spread A position that is created bytaking a long position in a call with strikeprice K, a long position in a call with strikeprice K3, and a short position in two callswith strike price Ky, where K; > K, > K;and K, = 0.5(K, + K;). (A butterfly spreadcan also be created with put options.)
Calendar Spread A position that is created bytaking a long position in a call option thatmatures at one time and a short position inasimilar call option that matures at a different702
time. (A calendar spread can also be createdusing put options.)
Calibration Method for implying a model’sparameters from the prices of actively tradedoptions.
Callable bond =A bond containing provisionsthat allow the issuer to buy it back at apredetermined price at certain times duringits life:
Call Option An option to buy an asset at acertain price by a certain date.
Cancelable Swap Swap that can be canceledby one side on prespecified dates.
Capital Asset Pricing Model A model relatingthe expected return on an asset to its beta.
Cap See Interest rate cap.
Caplet One component of an interest ratecap.
Cap Rate The rate determining payoffs in aninterest rate cap.
Cash-Flow Mapping A procedure for repre-senting an instrument as a portfolio of zero-coupon bonds for the purpose of calculatingvalue at risk.
Cash-or-Nothing Call Option An option thatprovides a fixed predetermined payoff if thefinal asset price is above the strike price andzero otherwise.
Cash-or-Nothing Put Option An option thatprovides a fixed predetermined payoff if thefinal asset price is below the strike price anzero otherwise.
Cash Settlement Procedure for settling a fu-
tures contract
ing the underlying asset.
CAT Bond Bond where the interest and,possibly, the principal paid are reduced if aparticular category of “‘catastrophic” insur-ance claims exceed a certain amount.
 
cash rather than by deliver-
CDD Cooling degree days. The maximum ofzero and the amount by which the dailyaverage temperature is greater than 65°Fahrenheit. The average temperature is the
Glossary of Terms
average of the highest and lowest tempera-tures (midnight to midnight),
Cheapest-to-Deliver Bond The bond that ischeapest to deliver in the Chicago Boardof Trade bond futures contract.
Method of sam
Cholesky Deeomngsition plingWacthiogd of: sampung
TMGesny --CCOMposiion
from a multivariate normal distribution.
Chooser Option An option where the holderhas the right to choose whether it is a call ora put at some point during its life.
Class of Options See Option class.
Clean Price of Bond The quoted price of abond. The cash price paid for the bond (ordirty price) is calculated by adding theaccrued interest to the clean price.
Clearinghouse A firm that guarantees theperformance of the parties in an exchange-traded derivatives transaction. (Also referredto as a clearing corporation.)
Clearing margin A margin posted by a mem-ber of a clearinghouse.
Collar See Interest rate collar
Collateralized Debt Obligation A way ofpackaging credit risk. Several classes ofsecurities are created from a portfolio ofbonds and there are rules for determininghow defaults are allocated to classes.
Collateralized Mortgage Obligation(CMO) Amortgage-backed security where investorsare divided into classes and there are rulesfor determining how principal repaymentsare channeled to the classes.
Combination A position involving both callsand puts on the same underlying asset.
Commission Brokers Individuals who executetrades for other people and charge a com-mission for doing so.
Commodity Futures Trading Commission A
~ body that regulates trading in futures con-
tracts in the United States.
Commodity Swap A swap where cash flowsdepend on the price of a commodity.Glossary of Terms
Compounding Frequency This defines how aninterest rate is measured.
Compound Option An option on an option.
Compounding Swap Swap where interest
compounds instead of being paid.
Conditional Value at Risk (C-VaR) Expectedloss during N days conditional on being inthe (100-X)% tail of the distribution ofprofits/losses. The variable N is the timehorizon and X% is the confidence level.
Confirmation Contract confirming verbalagreement between two parties to a tradein the over-the-counter market
Constant Maturity Swap A swap where aswap rate is exchanged for either a fixed rateor a floating rate on each payment date.
Constant Maturity Treasury Swap A swapwhere the yield on a Treasury bond is ex-changed for either a fixed rate or a floatingrate on each payment date.
Consumption Asset An asset held for con-sumption rather than investment.
Contango A situation where the futures priceis above the expected future spot price.
Continuous Compounding A way of quotinginterest rates. It is the limit as the assumedcompounding interval is made smaller andsmaller.
Control Variate Technique A technique thatcan sometimes be used for improving theaccuracy of a numerical procedure.
Convenience Yield A measure of the benefitsfrom ownership of an asset that are notobtained by the holder of a long futurescontract on the asset.
Conversion Factor A factor used to determinethe number of bonds that must be deliveredin the Chicago Board of Trade bond futurescontract.
Convertible Bond A corporate bond that canbe converted into a predetermined amountof the company’s equity at certain timesduring its life.
703
Conyexity A measure of the curvature in therelationship between bond prices and bondyields.
Convexity Adjustment An overworked term.For example, it can refer to the adjustmentnecessary to convert a futures interest rate toa forward interest rate. It can also refer tothe adjustment to a forward rate that issometimes necessary when Black’s model isused.
Copula A way of defining the correlationbetween variables with known distributions.
Counterparty ‘The opposite side in a financialtransaction.
Cornish-Fisher Expansion An approximaterelationship between the fractiles of a prob-ability distribution and its moments.
Cost of Carry The storage costs plus the costof financing an asset minus the incomeearned on the asset.
Coupon Interest payment made on a bond.
Covered Call A short position in a call optionon an asset combined with a long position inthe asset.
Credit Default Swap An instrument that givesthe holder the right to sell a bond for its facevalue in the event of a default by the issuer.
Credit Derivative A derivative whose payoffdepends on the creditworthiness of one ormore entities.
Credit Rating A measure of the creditworthi-ness of a bond issue.
Credit Ratings Transition Matrix A_ tableshowing the probability that a company willmove from one credit rating to anotherduring a certain period of time.
Credit Risk The risk that a loss will beexperienced because of a default by thecounterparty in a derivatives transaction.
Credit Spread Option Option whose payoff
depends on the spread between the yieldsearned on two assets.704
Credit Value at Risk The credit loss that willnot be exceeded at some specified confidencelevel.
Cumulative Distribution Function The prob-ability that a variable will be less than x asa function of x.
Currency Swap A swap where interest andprincipal in one currency are exchanged forinterest and principal in another currency.
Day Count A convention for quoting interestrates.
Day Trade A trade that is entered into andclosed out on the same day.
Default Correlation Measures the tendency oftwo companies to default at about the sametime.
Defauit Probability Density Measures the un-conditional probability of default in a futureshort period of time.
Deferred Payment Option An option wherethe price paid is deferred until the end of theoption’s life.
Deferred Swap An agreement to enter into aswap at some time in the future. Also calleda forward swap.
Delivery Price Price agreed to (possibly sometime in the past) in a forward contract.
Delta The rate of change of the price of aderivative with the price of the underlyingasset.
Delta Hedging A hedging scheme that isdesigned to make the price of a portfolioof derivatives insensitive to small changes inthe price of the underlying asset.
Delta-neutral Portfolio A portfolio with adelta of zero so that there is no sensitivityto small changes in the price of the under-lying asset.
DerivaGem The software accompanying thisbook.
Derivative An instrument whose price de-
pends on, or is derived from, the price ofanother asset.
Glossary of Terms
Diagonal Spread A position in two callswhere both the strike prices and times tomaturity are different. (A diagonal spreadcan also be created with put options.)
Differential Swap A swap where a floatingrate in one currency is exchanged for afloating rate in another currency and bothrates are applied to the same principal.
Diffusion Process Model where value of assetchanges continuously (no jumps).
Discount Bond See Zero-coupon bond.
Discount Instrument An instrument, such as aTreasury bill, that provides no coupons.
Discount Rate The annualized dollar returnon a Treasury bill or similar instrumentexpressed as a percentage of the final face
value,
Dividend A cash payment made to the ownerof a stock.
Dividend Yield The dividend as a percentageof the stock price.
Down-and-In Option An option that comesinto existence when the price of the under-lying asset declines to a prespecified level.
Down-and-Out Option An option that ceasesto exist when the price of the underlyingasset declines to a prespecified level.
Downgrade Trigger A clause in a contractthat states that the contract will be termi-nated with a cash settlement if the creditrating of one side falls below a certain level.
Drift rate The average increase per unit oftime in a stochastic variable.
Duration A measure of the average life abond. It is also an approximation to theratio of the proportional change in the bondprice to the absolute change in its yield.
Duration Matching A procedure for matchingthe durations of assets and liabilities in a“financial institution.
Dynamic Hedging A procedure for hedgingan option position by periodically changingthe position held in the underlying assets.Glossary of Terms
The objective is usually to maintain a delta-neutral position.
Early Exercise Exercise prior to the maturitydate.
Efficient Market Hypothesis A hypothesis thatasset prices reflect relevant information.
Electronic Trading System of trading where acomputer is used to match buyers and sell-ers.
Embedded Option An option that is an in-separable part of another instrument.
Empirical Research Research based on histor-ical market data.
Equilibrium Model A model for the behaviorof interest rates derived from a model of theeconomy.
Equity Swap A swap where the return on anequity portfolio is exchanged for either afixed or a floating rate of interest.
Eurodollar A dollar held in a bank outsidethe United States
Eurodollar Futures Contract A futures con-tract written on a Eurodollar deposit.
Euro