305-6difference between forward contracts and, 6,19, 36-37difference between options and, 6, 151foreign exchange quotes, 37long position, 20margins and, 24—27marking to market, 24—26price quotes, 22quotations, 27—30, 53, 57, 105-6risk, 61-62short position, 20specification of, 20--23Treasury bond and Treasury note futures, 21,22, 104-10Futures interest rate, 111, 566Futures market, regulation of, 33-34Futures option, 152, 278-79, 706interest rate futures option, 279-82popularity of, 283put-call parity, 283-84quotations, 279-82Spot options compared to, 288-89valuation, using binomial trees, 284-86,399402valuation, using Biack’s model, 287-88Futures price, 20, 706convergence to spot price, 23-24cost of carry, 60expected future spot prices and, 31, 61-63expected growth rate, 286-87patterns of, 31relationship to forward prices, 51-52
G
GAP management, 116
Gamma, 312, 706cross gamma, 358estimating, using binomial tree, 398formula, 314
i 3 ivativas §21interest rate derivatives, 531
relationship with delta and theta, 315-16effect on the probability distribution of thevalue of a portfolio, 356Gamma-neutral portfolio, 313-14, 706GARCTHI, Generalized autoregressiveconditional heteroscedasticity, 376-77, 706compared with EWMA, 377-78estimating parameters, maximum likelihoodmethods, 379-82forcasting future volatility, 382-85Gaussian copula, 628-29, 632Generalized Wiener process, 218-21, 706Geometric average, 238, 706Geometric Brownian motion, 223, 706Gibson Greetings, 688, 689, 693, 694Girsanov’s theorem, 212Globex, 721Goldman Sachs Commodity Index (GSCI, 53Goldman Sachs, 53Good-till-canceled order, 33Government National Mortgage Association(GNMA), 586Greek letters, Greeks, 299, 337, 706. See alsoDelta, Theta, Gamma, Vega, and Rho.estimating using binomial tree, 398-99estimating using finite difference method, 427estimating using Monte Carlo simulation, 414interest rate derivatives, 530-31Gross basis, 26-27Gross return, stock’s, 238Growth factor, 394
HHammersmith and Fulham, 688, 613-14Hazard rate, 613-14, 706Heating degree days (HDD), 679, 707Hedge accounting, 35Hedge-and-forget strategy, 70, 303Hedger, 10, 11, 31, 61, 693-94, 707Hedging/hedge, 707
arguments for and against, 72-75
an equity portfolio, 84736
basic principles, 70-72
basis risk, 75-78
competitors and, 73-74
delta hedging, 302-9duration-based hedging strategies, 116-18effectiveness, 79
exotic options, 447
gamma, 312-15
in practice, 319
interest rate derivatives, 530-31, 565-66long hedge, 71-72
naked and covered position, 300perfect hedge, 70
performance measure, 302, 307, 308ratio, 78—79, 707
tho, 318-19
rolling forward, 86-87
shareholders and, 73
short, 71
stop-loss strategy, 300—302
theta, 309-11
using index future 82-85using incex Tuture, &—-S3
vega, 316-18Hicks, John, 31, 61Historic volatility, 239, 707Historical simulation, value at risk, 348-50, 707compared with model building approach,359-60History-dependent derivative, 461-65Holiday calendar, 707Hong Kong and Shanghai bank, 687Ilopscotch method, 426Hunt brothers, 34Hurricane Andrew, 683
IImplicit finite difference method, 418—21, 707relation to explicit finite difference method,422-23Implied volatility, 250-51, 707Implied volatility function (IVF) model, 337,460-61, 707Implied distribution, 707currency options, 331-32stock options, 334-35Implied repo rate, 707Impiied tee model, 337, 460-61, 707Importance sampling, variance reductionprocedure, 415
Subject index
Inception profit, 691, 707Index amortizing rate swap, 605, 707Index arbitrage, 54, 707Index currency option note (ICON), 14Index futures, 707hedging, using index future, 82-85portfolio insurance, using, 321—22pricing, 54quotations, 53Index options, 152, 270-76, 707portfolio insurance, 273-75quotations, 270—73valuation, binomial tree, 399-402valuation, Black-Scholes, 275-76Indexed principal swap, 605, 707Initial margin, 24-26, 158, 159, 707Inner barrier, 467Instantaneous forward rate, 707Instantaneous short rate, 537. See also Shortrate.
. Insurance derivatives, 15, 682-83
Interest only (IO), 587, 708
Interest only (10), 587Interest rate, 42-44continuous compounding, 43day count conventions, 102-3, 130forward, 98-100forward-rate agreements (FRA), 100- 101term structure theories, 102types of, 93-94zero-coupon yield curve, 97-98Interest rate cap, 515—20, 707forward risk-neutral valuation and Biack’smodel, 519-20Interest rate collar, 517, 707Interest rate derivatives, 508, 707Black’s model, 508-10bond options, 511-15convexity adjustment, 524-26embedded bond option, 511equilibrium models, 537-43European bond option, 511-15European swap option, 520-24Heath, Jarrow, Morton model, 574-77hedging, 530-31interest rate cap, 515-20LIBOR market model, 577-86natural time jag, 529-30no-arbitrage models, 543-44short rate models, 537-67Subject Index
timing adjustment, 527-29yield volatility, 513-14Interest rate floor, 517-18, 707Interest rate futuresEurodollar futures, 110-11Relation to forward interest rate, 111Treasury bond futures, 104-10Interest rate futures option, 279-82Eurodollar futures option, 279, 282Treasury bond futures option, 279, 282,Treasury note futures option, 279Interest rate modelsBGM model, 577equilibrium models, 537-43Heath, Jarrow, Morton model, 574-77LIBOR market model, 577-86no-arbitrage models, 543-44short rate models, 537-67standard market models, 508-31two-factor models, 543, 571-73Interest rate option, 707Interest rate parity, 56Interest rate swap, 707comparative-advantage argument, 131-34confirmation, 130-31day count conventions, 130financial intermediary, role of, 129-30impact of default risk, 651mechanics of, 125-31nonstandard swaps, 594-606plain vanilla interest rate swap, 125to transform an asset, 128-29to transform a liability, 127—28valuation, 136-40Interest rate trees, 550-52general tree-building procedure, 552-63trinomial trees, 551-52nonstandard branching, 552International Petroleum Exchange (IPE), 680,681International Swaps and Derivatives Association(ISDA), 130Master Agreement, 130-31In-the-money option, 153, 304, 311, 315, 707Intrinsic value, 154, 707Inverted market, 31, 708Investment asset, 41, 58, 708market price of risk, 485Investment grade, 610
737
Itd’s lemma, 216, 226-27, 487, 708It6’s process, 222, 708
J
Jett, Joseph, 686, 687, 690
J.P. Morgan, 375, 632
Jump diffusion model, 457-58, 708
K
Kappa, 708
Keynes, John Maynard, 31, 61Kidder Peabody, 686, 687, 690KMYV, 623
Knock-in and knock-out options, 439Kurtosis, 332, 708
LLambda, 708Last notice day, 32Last trading day, 32LEAPS, see Long-term equity anticipationsecuritiesLeast-squares approach, Monte Carlosimulation for American options, 474-77Leeson, Nick, 686, 687, 690Levenberg—Marquardt procedure, 565LIBOR-in-arrears swap, 526-27, 599, 708Limit move, 22, 708limit up, 22limit down, 22Limit order, 33, 157, 708Linear model, value at risk, 352-55Liquidity preference theory, shape of zero curve,102, 708Liquidity premium, 708Liquidity risk, 691-92, 708Lloyds syndicate, 683Locals, 32, 708Lock out period, callable bond, 511Lognormal property, 227-28, 234-36, 708London Interbank Bid Rate (LIBID), 93, 708London Interbank Offer Rate (LIBOR), 45,93-94, 110, 708zero curve, 111-12, 135-36, 708. See alsoSwap zero curve.London International Financial Futures andOptions Exchange (LIFFE), 19, 111,London Stock Exchange, 13, 53Long hedge, 71-72, 708738
Long position, 2, 8, 20, 708
Long-Term Capital Management (LTCM), 625,687, 692
Long Term Credit Bank of Japan, 14
Long-term equity anticipation securities(LEAPS), 153, 273, 708
Lookback option, 441-42, 461-63, 465—67, 708
Loss given default, 623-25
Low-discrepancy sequence, see Quasi-randomsequence,
MMaintenance margin, 24, 159, 708Margin account, 24, 25, 158Margin, 24-27, 158-60, 708clearing margin, 26gross margining, 27initial margin, 24-26, 158-59maintenance margin, 24, 159margin call, 24, 709net margining, 27
for stocks. 158-59TOP STOCKS, 150-37
for stock options, 159-60variation margin, 24Market-if-touched (MIT) order, 33Market maker, 130, 157, 158, 709Market model, 709Market-not-held order, 33Market order, 33, 157Market price of risk, 483, 484-86, 709multiple independent factors, 492—93Market segmentation theory, shape of zerocurve, 102, 709Marking to market, 24-26, 709Marking to model, 691Markov process, 216-17, 709Markowitz, Harry, 352Martingale, 483, 488-89, 709equivalent martingale measure result, 488-89Maturity date, 6, 709Maximum likelihood method, 378-82, 709Mean reversion, 377, 518, 539, 542, 709Measure, 483, 709Metallgesellschaft (MG), 87, 688Mid-curye Eurodollar futures option, 279Middle office, 690Midland Bank, 687Minimum variance hedge ratio, 78-82Min—max, 435
Subject index
Model building approach, value at risk, 350-52compared with historical simulation, 359-60Modified duration, 114-15, 709Moment matching, variance reductionprocedure, 416Money market account, 489, 709Monte Carlo simulation, 224, 301, 410-14, 446,459, 462, 709American options and, 474-78exercise boundary parametrization approach,477-78generating random samples, 412-13Greek letters and, 414least-squares approach, 474-77LIBOR market model of short rates, 579-81number of trials, 413quantifying seller default risk, 643 44value at risk measure, 359valuing derivatives on more than one marketvariable, 412—13valuing first-to-default basket credit defaultswaps, 643valuing mortgage-backed securities, 588valuing new business, 666-67, 671-75Moody’s, 610, 638Risk Management Services, 623Mortgage-backed security (MBS), 586-88, 709
NNaked option, 159Naked position, 300, 709Nasdaq 100 index (NDX), 53futures, 21, 53Mini Nasdaq 100 index futures, 21, 53option, 152, 270National Association of Securities DealersAutomatic Quotations Service, 53National Futures Association (NFA), 34National Westminster Bank, 687, 690Natural gas derivatives, 680-81Natural time lags, 529-30Net basis, 26-27Net present value (NPV) approach, 660Netting, 624-25, 709
_. Neutral calendar spread, 193
New York Cotton Exchange, 21
New York Federal Reserve, 687
New York Mercantile Exchange (NYMEX), 22,680, 681Subject Index
New York Stock Exchange (NYSE), 13, 52, 55,323Newton-Raphson method, 95, 251, 541, 359,709Nikkei 225 Stock Average, 52futures, 52, 55, 497No-arbitrage assumption, 709No-arbitrage interest rate model, 543-44, 709Nonstandard American options, 436Nonstationary model, 563-64, 709Nonsystematic risk, 61, 488, 709Normal backwardation, 31, 709Normal distribution, 234, 709, 722—23Normai markei, 31, 769Notice of intention to deliver, 20, 31-32Notional principal. 126, 637, 709Numeraire, 488, 709annuity factor as the numeraire, 491—92impact of a change in numeraire, 495—97interest rates when a bond price is thenumeraire, 491money market account as the numeraire,489-90numeraire ratio, 496zero-coupon bond price as the numeraire,490-9]Numerical procedure, 392, 710
oOOff-the-run bonds, 691Offer, 2, 135, 157, 710Offsetting orders, 157On-the-run bond, 691Open interest, 30, 157, 710Open order, 33Open outcry trading system, 2, 710Option-adjusted spread (OAS), 588, 710Option fence, 435Options, 6-10, 710class, 153, 702, 710difference between futures (or forward}contracts and, 6, 151exercise limits, 155exercising, 160—61exotic, 163, 435-49hedging, usitig, 11intrinsic value, 154position limits, 155positions, 8
739
regulation of, 161series, 153, 710taxation, 161-62time value, 154trading, 157types of, 6, 151-52See also: Currency options, Futures options,Index options, Stock options, Swaptions.Options Clearing Corporation (OCC), 160-61,710Options in an investment opportunity, 670-71Options on two correlated assets, 472-74Options to exchange one asset for another,445-46forward risk-neutral valuation, 494-95Options to defer, 671Options to extend, 671Orange County, 686, 688, 693, 694Order book official, see Board brokerOrder, types of, 33Out-of-the-money option, 153, 304, 311, 315,710Outer barrier, 467Outside model hedging, 565Overnight repo, 94Over-the-counter market, 1, 2, 710difference between exchange-traded marketand, 2for options, 154, 163
P
Pacific Exchange, 151
Package, 435, 710
Parallel shift, 361, 710
Par bond yield, 95-96, 710
Par value, 710
Partial simulation approach, Monte Carlo
simulation, 359
Pass-throughs, 587
Path-dependent derivative, 461-65, 710
Payoff, 3, 710
Perfect hedge, 70
Philadelphia Stock Exchange (PHLX), 151, 276
Plain vanilla product, 435, 710
Poisson process, 630, 710
Portfolio immunization, 116, 716
Portfolio insurance, 273-75, 320-23, 692, 710stock market volatility and, 323
Position limit, 23, 155, 710740
Position traders, 33Prepayment function, 587, 710Priceslifetime highs, 30lifetime lows, 30opening price, 27settlement price, 27Price sensitivity hedge ratio, 117Prime rates, 133-34Principal, 710Principal components analysis, 360-63, 530-31,584-85, 710Principal only (PO), 587, 710Probability measure, 486Probability of default, 623assuming no recovery, 612-13bond prices and, 610-19bond prices and historical probability ofdefault, 619-20estimating, using equity prices, 621-23implied from bond data, 616-17implied from CDS swaps, 641-42risk-neutral vs. real-world, 620-21Proctor and Gamble, 605, 688, 689, 693, 694Program trading, 54, 710Protective put, 185, 710Pull-to-par, 711Put—call parity, 174-75, 179, 186-87, 268,283-84, 330-31, 438, 711Put option, 6, 7~8, 151, 711Puttable bond, 511, 711Puttable swap, 711
QQuadratic model, value at risk, 356—59Quadratic resampling, variance reductionprocedure, 416Quanto, 497 99, 711adjustment, 601Quasi-random sequence, variance reductionprocedure, 416-17, 711Quotations,commodity futures, 27-30currency futures, 57currency options, 276, 277futures options, 279-82stock index futures, 53stock index options, 270-73
Subject Index
stock options, 155—57
Treasury bills, 104
Treasury bonds, 103~4
Treasury bond and note futures, 105-6Quoted price, bond and Treasury bill, 103-4,
512, 561. See also Clean price.
RRatchet cap, 581Rainbow option, 446, 472, 711Random walk, 232-33Range forward contract, 14-15, 435, 711Real option, 1, 660, 711Rebalancing, 242, 303, 711Recovery rate, 614-15, 642, 711Reference entity, 637Reference obligation, 637Reinsurance, against catastrophic risks (CATreinsurance), 682-83Repo, 94, 711Repo rate, 94, 711overnight repo, 94term repo, 94Representative sampling through a tree,variance reduction procedure, 417-18Repurchase agreement, 94Reset date, 711Retractable bond, 511Reverse calendar spreads, 194Reversion level, 711Rho, 318-19, 711estimating, using binomial tree, 398Rights issue, 155, 711Risk, see Value at riskback testing, 360hedging and basis risk, 75-78market risk, 146nonsystematic, 61, 488, 713stress testing, 360, 689swaps and credit risk, 145-46systematic, 61, 62, 488, 713Risk and return, relationship between, 61Risk-free interest rate, 45, 93, 94, 168—70, 711Risk-free zero curve, 111Risk limits, 686-89Risk-neutral valuation, 203-5, 244-45, 247,269, 678, 483, 661-65, 711Risk-neutral world, 204, 205, 711forward risk-neutral, 489Subject Index
rolling forward risk-neutral, 578traditional, 483, 486RiskMetrics, 375 ~Roll back, 711Roll-over risk, 136Rusnak, John, 686, 687,Russell 2000 index (RUT), 53, 270options, 270
Ss
Scalper, 32, 711
Scenario analysis, 319-20, 689, 692, 711
Securities and Exchange Commission (SEC), 34,
161, 711
Segmentation theory, shape of zero curve, 102
Seller default risk, 643-44
Settlement price, 27, 711
Share Price Index, 53
Shell, 686, 688
Shorting, 41-42
Short hedge, 71, 711
Short position, 2, 8, 20, 711
Short rate, 537, 711Cox, Ingersoll, Ross model, 542-43calibration, 564-65equilibrium models, 537-38general tree-building procedure, 552-63Ho—Lee model, 544-46Hull—White model, 546-49interest rate trees, 550-52no-arbitrage models, 543-44nonstationary models, 563—64one-factor equilibrium models, 538Rendleman and Bartter model, 538-39two-factor equilibrium models, 543Vasicek model, 539-42
Short selling, 41-42, 711
Short squeezed investor, 42
Short-term risk-free rate, see Short rate.
Shout option, 443, 712
Siegel’s paradox, 499-500
Sigma, see Vega.
Simulation, 712
Singapore International Monetary Exchange
(SIMEX), 19
Specialist, 712
Speculator, 10, 11-12, 32-33, 693-94, 712
Speculation,using futures, 11-12
741
using options, 12-13Spot contract, 2Spot rate, 94, 712Spot option, 288futures option compared to, 288-89Spot price, 4-5, 712convergence of futures price to, 23-24futures prices and expected future spot prices,31, 61.63Spot volatility, 518-19, 712Spread option, 712Spread trading strategy, 187-94Spread transaction, 26, 712Standard and Poor’s (S&P) Index, 52, 610, 638100 Index (OEX), 152, 270, 273500 Index (SPX), 32, 52, 55, 152, 270, 279,360500 Index futures, 32, 52, 54futures option, 279MidCap 400 Index, 52Mini S&P 500 futures, 52options, 152, 270, 273Standard Oil, 14Static hedging scheme, 303, 712Static options replication, 447-49, 712Step-up swap, 594, 712Sticky cap, 581--8