Derivatives markets 2e by robert l mcdonald

Derivatives markets 2e by robert l mcdonald Derivatives markets 2e by robert l mcdonald Derivatives markets 2e by robert l mcdonald Derivatives markets 2e by robert l mcdonald Derivatives markets 2e by robert l mcdonald Derivatives markets 2e by robert l mcdonald Derivatives markets 2e by robert l mcdonald Derivatives markets 2e by robert l mcdonald

The Addison-Wesley Series in Finance Copeland/Weston Financial Themy and Cmporate Policy Dufey/Giddy Cases in International Finance Eakins, Finance: Investments, Institutions, and Management Eiteman!Stonehill!Moffett - Multinational Business Finance Gitman Principles ofManagerial Finance Gitman Principles ofManagerial Finance -Brief Edition Gitman/Joehnk Fundamentals of Investing Gitman!Madura Introduction to Finance Hughes/MacDonald International Banking: Text and Cases Madura Personal Finance Marthinsen Risk Takers: Uses and Abuses of Financial Derivatives McDonald Derivatives Markets Megginson Cmporate Finance Themy Melvin International Money and Finance Mishkin/Eakins Financial Markets and Institutions Moffett Cases in International Finance Moffett/Stonehill!Eiteman Fundamentals of Multinational Finance Rejda Principles of Risk Management and Insurance Solnik!McLeavey International Investments Derivatives Markets Second Edition R B E R T L M c D N A L D Northwestern University Kellogg School of Management Boston San Francisco New York London Toronto Sydney Tokyo Singapore Madrid Mexico City Munich Paris Cape Town Hong Kong Montreal Editor-in-Chief: Denise Clinton Senior Sponsoring Editor: Donna Battista Senior Project Manager: Mary Clare McEwing Development Editor: Marjorie Singer Anderson Senior Production Supervisor: Nancy Fenton Executive Marketing Manager: Stephen Frail Design Manager: Regina Hagen Kolenda Text Designer: Regina Hagen.Kolenda Cover Designer: Rebecca Light Co�er and Interior Image: Private Collection/Art for After Hours/SuperStock Senior Manufacturing Btt')'er: Carol Melville Supplements Editor: Marianne Groth Project Management: Elm Street Publishing Services, Inc p Co yright ©2006 Pearson Education, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher For information on obtaining permission for the use of material from this work, please submit a written request to Pearson Education, Inc., Rights and Contracts Department, 75 Arlington Street, Suite 300, Boston, MA 02116 or fax your request to (617) 848-7047 Printed in the United States of America Library of Congress Cataloging-in-Publication Data McDonald, Robert L (Robert Lynch), 1954- Derivatives markets, 2e I Robert p.cm Includes index ISBN 0-321-28030-X Derivative securities I Title HG6024.A3 M3946 2006 332.64'5-dc21 ISBN 0-321-28030-X 12345678910-HT-09 08 07 06 05 L McDonald Fo1· Irene, Claire, David, and Hemy Preface Chapter 1.1 XX1 Comparing a Forward and Outright Purchase Uses of Derivatives Credit Risk 2.2 The Role of Financial Markets Risk-Sharing How Are DerivativesUsed? Option 2.3 Short-Selling 37 38 39 Payoff and Profit for aWritten Put Option 40 The "Moneyness" of an Option 11 2.4 14 Risk and Scarcity in Short-Selling 33 Put Options Option 10 12 The Lease Rate of an Asset 32 Payoff and Profit for a Purchased Put Buying and Short-Selling Financial Assets 11 Buying anAsset 31 Payoff and Profit for aWritten Call Option Growth in DerivativesTrading 1.4 Call Options Payoff and Profit for a Purchased Call Derivatives in Practice 30 30 Option Terminology FinancialMarkets and theAverages 1.3 28 Cash Settlement Versus D� livery FinancialEngineering and Security 1.2 Diagrams Perspectives on Derivatives Design Zero-Coupon Bonds inPayoff and Profit Introduction to Derivatives What Is a Derivative? 26 LongPositions 44 15 Short Positions Chapter Sumn!al)' 16 Further Reading 16 Problems 17 43 Summary of Forward and Option Positions 43 2.5 44 Options Are Insurance 45 Homeowner'sInsuranceIs aPutOption 45 ButIThoughtInsurance Is Prudent and Put Options Are Risky 47 PART ONE Call OptionsAreAlsoInsurance INSURANCE, 2.6 Example: Equity-Linked CDs 47 48 HEDGING, AND SIMPLE STRATEGIES Graphing the Payoff on the CD 49 19 Economics of the CD 50 WhyEquity-Linked COs? Chapter and Options 2.1 An Introduction to Forwards 21 Forward Contracts 21 ThePayoff on a Forward Contract Graphing thePayoff on a Forward Contract 25 23 51 Chapter Sumn!al)' 52 Further Reading 53 Problems 54 Appendix 2.A: More on Buying a Stock Option 56 Dividends 56 vii Viii � C O N T E NTS Exercise Insurance: Guaranteeing a MaximumPrice 57 with a Call Option Margins for Written Options 57 4.3 Taxes 58 Strategies 3.1 10 Reasons Not to Hed ge 59 Basic Insurance Strategies 10 Reasons to Hed ge Insurance, Collars, and Other 59 4.4 Floors' 59 Golddiggers Revisited Other CollarStrategies Selling Insurance Paylater Strategies Synthetic Forwards 66 4.5 68 13 70 QuantityUncertainty Bull and Bear Spread s 71 Chapter Stmti11G1)' 119 Further Reading 120 Problems 120 Ratio Spread s Collars 3.4 72 73 Speculating on Volatility Strad d les 78 78 Butterfly Spread s PART 1WO 81 82 Chapter Chapter Summary 85 Further Reading 86 Problems 87 Management 4.1 Futures 5.1 5.2 92 Arbitrage 5.3 96 Basic Risk Management: The Buyer's Perspective 98 98 129 129 Pricing Prepaid Forward s with Divid end s 95 Hed ging with a Forward Contract 128 Present Value 93 Ad justing theAmount ofInsurance 127 Pricing thePrepaid Forward by Insurance: Guaranteeing a MinimumPrice 4.2 Alternative Ways to Buy a Stock Prepaid Forward Contracts on Stock 128 Pricing thePrepaidForward by Discounted Basic Risk Management: The Producer's Perspective 91 Insuring by Selling a Call Financial Forwards and 127 Analogy 91 with a Put Option 125 Pricing the Prepaid Forward by Introduction to Risk Hed gingwith a Forward Contract FORWARDS, FUTURES, AND SWAPS Example: Another Equity-Linked Note 83 Chapter 116 73 Asymmetric Butterfly Spread s 3.5 113 114 3.3- Spreads and Collars Box Spread s 10 12 Selecting the Hedge Ratio Cross-Hed ging 106 108 Selling the Gain: Collars Insuring a Short Position: Caps Put-Call Parity 106 EmpiricalEvidence onHed ging Insuring a LongPosition: 3.2 100 An ExampleWhereHed gingAd d s Value Chapter 99 Why Do Firms Manage Risk? 13 Forward Contracts on Stock 133 Creating a SyntheticForward Contract 135 Synthetic Forward s in Market-Making and Arbitrage 136 · C O N T E NTS An ApparentArbitrage and No-Arbitrage Bounds withTransaction Costs Resolution 13 Quasi-Arbitrage 140 6.5 5.4 14 Futures Contracts 142 14 Margins and Marking toMarket 144 Comparing Futures and Forward 5.5 Quanta Index Contracts 14 Uses of Index Futures 150 AssetAllocation 150 Cross-hedging with Index Futures 5.6 Currency Contracts 154 CurrencyPrepaid Forward Currency Forward Eurodollar Futures 155 Storage Costs and ForwardPrices 18 18 Gold Futures 18 184 18 BasisRisk 197 15 Weather Derivatives Futures 6.1 19 160 19 Chapter SummGI)' 200 Further Reading 201 Problems 201 Chapter Futures 7.1 Interest Rate Forwards and 205 Bond Basics 205 Zero-Coupon Bonds 20 Implied Forward Rates Chapter 18 6.8 Seasonality: The Corn Forward Market 188 6.9 Natural Gas 191 6.10 Oil 194 6.11 Commodity Spreads 195 6.12 Hedging Strategies 196 HedgingJet Fuel with Crude Oil Chapter SumnWI)' 160 Further Reading 162 Problems 162 Appendix 5.A: Taxes and the Forward Price 166 Appendix S.B: Equating Forwards and Futures 166 Coupon Bonds Commodity Forwards and 20 210 Zeros from Coupons 169 · 11 Interpreting the Coupon Rate Introduction to Commodity Forwards 169 17 Storage Costs and the Lease Rate Evaluation of Gold Production 15 Covered InterestArbitrage 5.7 15 12 Continuously Compounded Yields 6.2 Equilibrium Pricing of Commodity Forwards 171 6.3 Nonstorability: Electricity 6.4 Pricing Commodity Forwards by Arbitrage: An Example 174 · 172 17 181 Gold Investments Arbitrage in Practice: S&P 50 Index 147 Carry Markets The Convenience Yield 6.7 14 Arbitrage 17 178 Forward Prices and the Lease Rate 6.6 The S&P 50 Futures Contract Prices The Commodity Lease Rate The LeaseMarket for a Commodity An Interpretation of the Forward Pricing Formula 175 Pencils Have aPositive Lease Rate 13 Does the ForwardPricePredict the Future Price? ix � 7.2 13 Forward Rate Agreements, Eurodollars, and Hedging 214 Forward RateAgreements Synthetic FRAs 214 216 Eurodollar Futures 218 Interest Rate Strips and Stacks 223 I N D EX � three-month forward rates, 259 vs three-month T-bills, 22 -223 Long (buyer), 23 Long call, profit, 53 Long forward, profit, 53 Long forward contract, synthetic, 67 Long forward position, 44, 52 Long position, bonds, repos, and, 235 Long positions; 2, 44, 52 floors and, 59-62 profit diagrams for, 44 Long put profit, 53 Long run, portfolio insurance for, 603 Long Term Capital Management, 236 Longstaff, F , 633, 635 Lookback call, European, 739 Lookback put, European, 739 Loops, in (VBA), 90 for loop, 899 Losses capital, 490n with put and short forward, 40 Loss given default, 842 Low-coupon bonds, 233 Low discrepancy sequences, 633 Low exercise price option (LEPO), 33 Lublin, Joann S., 526 Lux, H., 709 Macaulay, Frederick, 225n Macaulay duration, 225 for zero-coupon bond, 229n MacBeth, J D., 767n Madan, D., 433 Maintenance margin, 45 Managed CDO, 853 Mandatorily convertible bond, 84 Mapping, cash flow, 829 Marcus, A J., 527n Margin, 44 maintenance, 45 marking to market and, · 44-146 for written options, 57 Marginal utility, declining, 69-370 Margin balance, in futures contracts, 146 Margin call, 45 Market(s) See also specific types in contango, 70- 95 economic derivatives, over-the-counter, for risk-sharing, Market corner, 233 Market-maker, 4, 3-4 bid price, offer price, and, delta-hedging aU-or-nothing options and, 707-708 dividend risk and, 434 exposure in currency swaps, 266 insurance and, 437-438 overnight profit of, 42 over-the-counter options and, 433n profit of, 427-429 risk of, 4-4 7, 437-438 and risk of extreme price moves, 432-433 roles of, 3-4 selling prepaid forward and, 30 Market-maker perspective, on derivatives, Market-making, 3-438 bond pricing and, 779-785 as insurance, 436-43 synthetic forwards in, 6- Market risks, value a t risk and, Market-timing, 733-734 Market value, of swaps, 253-254 Market value CDO, 853 Marking-to-market, 42, , margins and, 44- 46 proceeds and margin balance, 67 Mark-to-market proceeds, in futures contracts, 46 Married put, n Marshall & Ilsley security, 83-85 tax-deductible equity and, 495-498 Martingale, 65 "Matched book" transaction, 250 Mathematics, of delta-hedging, 422-429 Maturity default at, 843-844 effect on option price, 297-298 payoff for Marshall & Ilsley bond, 84-85 profit diagrams before, 395-399 yield to, 208 McDonald, R L., 433n, 527n, 565n, 689n McMurray, S., 49 Mean return, estimate of, 607 Mean reversion, in arithmetic B rownian process, 654-655 Measurement, of volatility, 744-757 952 � I N D EX Merger Northrop Grumman-TRW, 53 8-542 options in agreements, 538-539 price protection in, 503 Merrill Lynch, MITTS from, 48 Merton, Robert C., I, 292n, 376, 403, 639, 64 , 650n, 664n, 673, 674, 679n, 696, 697, 843 jump diffusion model, 763 jump pricing model, 697-698 Merton default model, 843-845, 846 Metallgesellschf!ft A G (MG), Mezzanine tranche, C O O s and, 854, Microsoft, compensation options and, 524, 526, 527-528 Miller, H D., 650n, 69 n Miller, Merton, 376, 473 See also Modigliani-Miller theorem Mispriced option, arbitrage for, 8-323 Mitchell, M., 54 n MITTS (Market Index Target Term Securities), 48 Mixture of normals model, 609, 647 Modeling, of discrete dividends, -362 Modified duration, 225, 237 Modigliani, Franco, 473 Modigliani-Miller theorem, 473-474, 507 Moneyness, exercise and, 304 Monotonicity, 837n Monte Carlo valuation, 528, 7-645, 4n accuracy of, 626-627 of American options, 633-636 antithetic variate method, 632 arithmetic Asian option and, 627-630 for basket options, 736 computing random numbers, 62 -623 control variate method of, 630-632 efficient, 630-633 of European call, 625-626 importance sampling and, 633 Latin hypercube sampling and, 633 low discrepancy sequences and, 633 naive, 63 , 633 for nonlinear portfolios, 822-826 stratified sampling and, 632-633 for value at risk of two or more stocks, 8 o f written straddle after days, 826 Mood, A M., 592n, 884n Moody's bond ratings, 847 Investor Services, 847n KMV model, 844n Moon, M., 563n, 565 Moore, David, 559n Moral hazard, 47n Morgan Stanley, TRACERS and, 865 Morgenson, G., 53 n Moving average, exponentially weighted, 746-747 Multi-date swap, 247 Multiple debt issues, 1 -5 Multivariate Black-Scholes analysis, 700-70 Multivariate Ito's Lemma, 665-666 Multivariate options basket options, 735-736 exchange options as, 732-733 options on best of two assets, 733-734 Myers, S., 05n Myers, S C., 0n Naik, V., 646, 696n Naive Monte Carlo valuation, 63 , 633 Naked writing, 64 Nationally Recognized Statistical Rating Organizations (NRSROs), 847 Natural gas, seasonality, storage, and, - 95 futures contract, - 94 Natural resources, commodity extraction and, 65-572 Neftci, S N., 652n, 662n, 674 Nelson, D B , 748n Net payoff, 28 Net present value (NPV) correct use of, 549-550 investment and, 548-55 static, 548-549 Netscape, 492-493, 498 Neuberger, A., 760 New York Mercantile Exchange (NYMEX) contracts traded annually at, futures contracts traded on, I gold futures contracts on, 85 light oil contracts on, 94 natural gas futures on, 92 Nikkei 225 index, 735 currency risk and, 726 futures contracts and, 49-J 50, 268 I N D EX � investing in, 8-7 9, 720-724 put warrants and, 728 No-arbitrage bounds, with transaction costs, 38- 39 No-arbitrage pricing, 70 Noise term, geometric B rownian motion and, 656-657, 658 Nonconvertible bonds, callable, 7-5 Nondiversifiable risk, Nonfinancial firms, derivatives used by, 07 Nonfinancial risk management, 05-106 Nonlinear portfolios, value at risk for, 9-826 Nonmonetary return, convenience yield as, 83 Nonrecombining tree, 325 Nonstandard option formulas, Black-Scholes equation and, 683-684 Nonstandard options, 443-46 , 703-736 Nonstorablity, of electricity, 72- 74 Normal density, 87-588 Normal distribution, 87-593 cumulative function, 589 cumulative inverse, 622-623 standard, 409-4 Normal probability plots, 609-6 2, j umps and, 642-643 Normal random variables conversion to standard normal, 590-5 sums of, -593 Northrop Grumman-TRW merger, 538-542 Notes See also specific types with embedded options, 488-489 equity-linked, 48, 483 gold-link�d 486-488 structured, 474 Treasury note futures, 230-233 Notional amount of swap, 249 NPV See Net present value (NPV) NQLX See OneChicago Numeraire, 693-696 NYMEX See New York Mercantile Exchange (NYMEX) O'Brien, J., 709 OCC See Options Clearing Corporation (OCC) Offer price, I I Offer structures, 538 953 Off-market forward, 69 Off-the-run bonds, 206, 236 Oil, 94 95 hedging jet fuel with, 99 Oil extraction, 565-572 with shut-down and restart options, 572-573 valuing infinite oil reserve, 570-572 Oil futures, 94 Oil market, 98 Oil prices See also Swap(s) derivatives markets and, producer price index for, OneChicago, 43 One-period binomial tree, 3-323 On-the-run bonds, 206, 236 On-the-run/off-the-run arbitrage, 235, 236 Open interest, 44 Open outcry, 42 Operational risk, value at risk and, Optimal investment decision, solving for, 556-558 Option(s) See also Investment; Parity; specific types ali-or-nothing, 685-686, 703-709 American-style, 32, 329, 330, 403, 404 arbitrage for mispriced, 8-323 Asian, 48, 444 449 asset-or-nothing barrier options, 5-7 on the average, 446-447 barrie� 449-453, 7-7 barrier COD, 737 basket, 735-736 on best of two assets, 733-734 Black-Scholes analysis in pricing of, 429-436 Black-Scholes equation for pricing of, 679-698 on bonds, 286-287, 335-336 bonds with embedded, 482-486 Bulow-Shoven proposal and, 529 buying, 34, 6-58 call, 1-38 capped, 7 closing prices for S&P 500 Index from CBOT, 33 on commodities, 334 commodity extraction as, 65-572 common debt and equity as 503 compensation, 503, 523-528 compound, 453-456, 467-468 in coupon bonds, 482-483 954 � I N D EX currency, 286, 290-292, 332, 38 , 727-732 debt as, 503-5 distribution o f returns i n portfolio and, 9-820 on dividend-paying stocks, 455-456 enlbedded, 488-489 equity as, 503-5 equity-linked foreign exchange, 73 -732 in equity-linked notes, 483 European-style, 32 European vs American, 293 exchange, 28 � -289, 459-46 exercise of, 57, 279, 304 exotic, 443-46 , 703-736 financial and real, 558 on futures, 332-334, 38 -382 gamma to approximate change in, 423-424 gap, 457-459, 706-707 infi nitely lived e xchange options, 468-469 as insurance, 45-48 in-the-money, 43 ladder, 740 long and short positions, 43 maximum and minimum prices of, 293-294 multi-period example, 349-350 multivariate, 732-736 one-p eriod binomial example, 348-349 outperformance, 459 - overpriced arbitrage of, path-dependent, 444 payoff and profit diagrams for, 33-43 perpetual, 403-405 power option, 690 pricing using real probabilities, 347-350 put, 8-43, 328-3 rai nbow, 734-735 real, 547-580 rebate, 6-7 reload, 532-534 repricing of, 53 -532 risk premium of, 394 Sharpe ratio of, 394-395 shout, 739 spreads of, 70-73 on stock index, 330-33 on stocks, 283-286 on stocks with discrete dividends, 380-3 style, maturity, and strike of, 292- 304 summary of, 52 synthetic, 285-286 terminology for, 32-33 underpriced, volatility of, 393-394 warrant and, written, 37-38, 40-42 Option-based model, of debt, 1 Option elasticity, 89-395, Option grants, expensing of, 528-53 Option Greeks, 382-395 formulas for, 0-4 Option overwriting, 63-64 Option premium gl-aphs for, 397, 398 Option price computation with expected value and true probabilities, 347-350, 620 computing, in one-period binomial model, 4-3 delta- and delta-gamma approximations of, 426 as discounted expected value, 347-350, 7-62 jumps and, 696-698, 764 taxes and, 341 Option pricing formula, for commodity extraction, 567-568 Option pricing model See also Black-Scholes formula; Binomial model evidence of volatility skew in, 77 1-773 Option risk, in absence of delta hedging, 4-4 Options Clearing Corporation (OCC), 6-57, 434 Option writer, 37, 38 Order statistics, Ordinary options, 706-707 Ornstein-Uhlenbeck process, 654-655 Vasicek model and, 786 Orwall, B ruce, 492n OTC See Over-the-counter market Out-of-the-money options, 43 Outperformance feature, valuing, 535-536 Outperformance option, 459 stock option (OSO), 534 Outputs, arrays as in VBA, 90 1-902 Over-the-counter contracts credit risk and, 30-3 forward contracts, 42 Over-the-counter market, Over-the-counter options, marke t-makers and, 433n I N D EX � Paddock, J L., 565n Palladium, Ford risk management and, 08 Par coupon, Parity, 28 See also Option(s) bounds for American options, 0-3 I of compound options, 454 generalized, and exchange options, 287-292 put-call, -287 Partial expectation, 603 604 Par value of bond, 496 Path-dependent option, 444 barrier options as, 449 Monte Carlo valuation and, 627-628 Payer swaption, 27 Paylater strategy, 1 3, I 4, 457n Payoff, 23 Asian option, 683n call, 35 on CD, 49, 50 combined index position and put, 59-62 comparison of long position vs forward contract, 27 distribution of, a t expiration, 36, 63, 65 on forward contract, 23-25 for future values of index, 25 graphing on forward contract, 25, 26 net, 28 for purchased and written call option, 33-37 for purchased and written put option, 39-42 supershare, 709 Payoff diagram, 28 for covered call, 66 · for covere d put, 67 for long forward contract, 29 for purchased and written call option, 33-37 for purchased and written put option, 39-40 zero-coupon bonds in, 28-29 Payoff table, for arbitrage opportunity, 8 Payout-protected option, n Peak-load electricity generation, 559-563 Peak-load manufacturing, at Intel, 559 PEPS (Premium Equity Participating Shares), 482n, 493-494 Percentage risk, of option, -393 PERCS (Preferred Equity Redeemable for Common Stock), 482n Perpetual calls, 404 955 Perpetual options, 403 Perpetual puts, 404-405 Perpetuities, 480-48 Petersen, M A., 07 Pharmaceutical investments, 563-565 Physical measure, 844 PIBOR (Paris Interbank Offer Rate), 60 Pindyck, R S., 565 Poisson distribution, 636 63 8, 639 pricing options with, 694-696 simulating j umps with, 639-643 Poisson process, 845 Portfolio elasticity of, 395, 1 -5 gold as asset in, 87 Greek measures for, 8-38 risk assessment for, risk premium of, 395 value at risk for nonlinear, 9-826 Portfolio insurance, for long run, 299, 603 Positive-definite correlations, 644 645 Positive homogeneity, 837n Positive lease rate, storability and, 76 I Power option, 690 Premium, 32 for call and put options, 39 default, 22 forward, 34- 35 future value of option premium, 43 liquidity, 222 option, 284, 300n Premium for forward contract, forward price and, 34 Prepaid forward, 727 binomial tree with, 63-365 currency prepaid, 55- Prepaid forward contract (prepay), 27, 684 pricing by analogy, 28- 29 pricing by arbitrage, 29- 30 pricing by discounted present value, 29 pricing with dividends, - 3 o n stock, 28- 33 Prepaid forward price for claim on S" , 666 667 of gold, 88 Prepaid swap, 248, 27 Enron and, 252 956 · � I N D EX Present value See also Net present value (NPV) barri er values, 403 calculations of, 684 of cap payments, 805 of future stock price, 79n pricing by discounted, 29 of project, 547 traded, 550 Price ask, 1 bid, 1 clean, 243 dirty, 243 futures and forward, 146- 47 guaranteeing with put option, 93-95 offer, 1 strike, 32, 97-98 Price bonds, denonii nated in stocks, commodities, and currencies, 47 Price limit, 42 Price options, average, 466 Price risk derivatives and, 7-8 Price vari �bility, derivatives markets and, 7-8 Probability of bankruptcy, 847-850 distri bution, to stock price, 593-603 in high and low states of economy, 372 log normal, 599-600 normal plots, 609-6 risk-neutral, 32 , in value at risk assessment, Probability calculations, for lognormal distribution, 598-605 Probability distributio n for VaR and tai l VaR, 833 Probability measure, 844 Procter & Gamble, swap with Bankers Trust, 263, 264 Producer, risk management by, -9 Producer price index, for o i l ( 947-2004), Production, seasonality in, 88- Profit, call, 35 daily calculation for market-maker, 422 of delta-hedged market-maker, 428 diagrams of, 53 at expiration, 36, 63, 65 for gold prices, I 09 hedged, 93 fro � insurance on house, 46 for long positions, 44 overnight market-maker, 42 for purchased call option, 33-37 put, 39 on short forward position, 92-93 spark spread and, 560 unhedged, 92 for written put option, 40-42 from written straddle, 80 Profit from delta hedging, interpreting, Profit diagram, 28 for bull spread, 72, 87 for butterfly, 87 for calendar spread, 399 for collar, 87 for covered call, 66 for covered put, 67 from holding call option; 398, 399 of insured house, 62 before maturity, 395-399 for no arbitrage, 70n for ratio spread (2: ), 87 for straddle, 79, 87 for strangle, 87 for unhedged buyer, long forward, and buyer hedged with long forward, 99 zero-coupon bonds in, 8-29 Pro forma arbitrage calculation, 38n Proprietary trading, 4 Psi, 383, 388, l l for call options, 392 Pulvino, T., 54 n Purchase, o f stock, 27 Purchased call, gamma for, 84 Purchased call option, 396 payoff and profit for, 33-37 profit diagram for, 44 Purchased option, Greek for, 383-3 8 Purchased put, gamma for, 84 Purchased put option, 44 45 payoff and profit for, 39 40 Purchase of shares, Purchasing Manger's Index, Put-call parity, 68-70, , 28 -287, 530 versions of, 305 I N D EX � Put option, 38 43, 328-329 adj usting insurance with, 96-98 Black-Scholes formula for, 376, 378 buying of, 69 calls as, 289-290 cash-or-nothing, 705 in CD structure, 485 collar and, 73 covered, 65-66 delta for, 85 down-and-in cash put, early exercise and, 296-297, 345-346 gamma for, 84 homeowner's insurance as, 45 47 as insurance, 59 payoff and profit for purchased, 39 40 perpetual, 404 40 premium for, 39 risk of, 47 strike price properties for, 304 summary of, 52 theta for, 390 up-and-in cash put, 4-7 up-and-out cash put, Put premium, for gold options, 09 Put sales, as hedge, for share repurchase, 522 Put strikes, profit using various, 97 Puttable bonds, 520 Put warrants, 522-523, 728 Quadratic variation, 652-653 realized, ?55-757 Quantile, 1 Quantity uncertainty, l l 6- l l 9, 694 Quanto, 1 6n, 49-1 50, 8-727, Quanta option, equity-linked foreign exchange call as, -732 Quasi-arbitrage, 39- 40 Rainbow option, 734-735 Random numbers, comput.ing, 62 -623 Random walk model, 35 -352 stock prices and, 352-353 Rate of return, Ratings transition, 848-850 Ratio, hedge, 1 3-1 957 Rational option pricing theory, 292n Ratio spread, 73 profit diagram for, 87 Real assets, 547 Realized quadratic variation, 755-757 Realized returns, Sharpe ratio and, 395n Realized volatility, 756n for IBM, 757 Real options, 547-5 80 Rebate deferred up, short Rebate option, 450, 6-7 Rebonato R., Receiver swaption, 27 Recombining tree, 324-325 Recovery rate, 842 for bonds, 850-85 Reduced form bankruptcy models, 852 Reference asset (obligation), 860 Regression(s), hedges and, 1 5n Regression beta, hedging and, 1 5n, ! 54 Regulation, financial engineering for, 490 498 Regulatory arbitrage, 2-3, Regulatory capital, value at risk and, Re-hedging, frequency of, 43 432 Reiner, E., On, 727n Reinsurance, insurance companies and, 437 Reinvestment, dividend, 32 Reload option, 532-534 Rendleman, R J , Jr., 3, 793n Rendleman-H artter model, 785-786 Rennie, A., 662n, 674 Repo rate, implied, 35 Repos (repurchase agreements), 233-235 haircuts and, 234 Long-Term Capital Management (LTCM) crisis ( 998) and, 236 Repricing, -532 Repurchases, put sales as hedge against, 522 Research and development, as capital expenditure, 563-565 Restart options, for oil production, 572-578 Return(s) continuously compounded, 353-354 standard deviation of, 354-355 variance of continuously compounded, 596 958 � I N D EX Return distributions, bootstrapping of, 83 1-832 Reverse cash-and-carry, 37 Reverse cash-and-carry arbitrage, 77 apparent, 75-176 lease rate and, 80 Reverse conversion, 285 Reverse repo, 234 Revlon stock, constructive sale of, 49 Rho, 383, 387-3 8 , l l Risk, l See also specific types basis, 1 6, 9? bond price, 828 of coupon bond, 225 credit, 1 , 15, 30-3 , , 84 1-867 diversifiable, dividend, 434 duration as measure of, 237 of extreme price moves, 432-433 in foreign stock index, 8-7 insurance purchases and, 97 jump, 764-765 market, o f market-maker, 4-4 nondiversifiable, operational, pooling o f i n insurance, 436 of put options, 47 - in short-selling, swaps and, 263 value at risk and, 3-839 volatility, 74 Risk arbitrageurs, 541 Risk-averse investor, 05 , 346 declining marginal utility and, 369-370 risk-neutral process and, 66 Risk-free bond, v aluing, 372 Risk-free rate of return, Monte Carlo v aluation and, 7-6 Risk management, , 1- 1 buyer's perspective on, 98- 00 cash-and-carry as, 37 nonfinancial, 05-1 06 producer's perspective on, 1-98 reasons for, 00- 07 for stock-pickers, 54 Risk measures, subadditive, 837-838 Risk-neutral distribution, value at risk and, 835-837 Risk-neutral investor, 346-347 Risk-neutral measure, 662-663 Risk-neutral pricing, 320-32 , 343, 346-350, 369-374, 690-693 as forward price, 553 reasons for success of, 373-374 for valuing clai m on S" , 668 Risk-neutral probability, 32 , 346, 347, , 725, 726 Risk-neutral process, 660-663 for d S" Qb, 670-672 Risk-neutral valuation, of stock, 373 Risk premium forward contract earning of, 40 forward price bias by, 40- o f option, 394 of portfolio, 395 Sharpe ratio and, 659 value at risk and, 836-837 Risk-sharing, 5-6 Risky stock, valuing with real probabilities, 372 Rogers, D A., 07 Roosevelt, D., 858n Rosansky, V I., 72n Ross, S A., 359, 555, 690, 787-788 Rouwenhorst, K G., 72n Rubinstein, M., 292n, 359, 555, 709, 0n, 724n, 727, 735n Russian doll CDOs, 854 Ryan, M D., 728 S ales, constructive, 49 S aly, P J., 532, 534n S&P 500 futures contract, 43- 44 S&P 500 index arbitrage and, 47-1 49 volatility estimates for, 745 S &P Depository Receipts (SPDRs), 148n Scarcity, in short-selling, 5- Scholes, Myron, 375, 376, 503 See also Black-Scholes formula Schwartz, E S., 6n, 563n, 565, 565n, 574n, 633, 635 Scott, L 0., 768n Seasonality corn forward market and, 88- I N D EX � in dividend payments, l 32n natural gas and, - 95 SEC See Securities and Exchange Commission (SEC) Securities See also specific types Treasury, 205n Securities and Exchange Commission (SEC), 847 derivatives reporting requirements and, Security design, financial engineering and, 473-498 Self-financing, portfolio and, 422 Seller, short as, 23 Seniorities, of debt-holders, 1 Senior tranche, 1 CDOs and, 854, 856 SFAS See Statement of Financial Accounting Standards (SFAS) Shao, J., 83 l n Shapiro, A C., 235 Share(s), convertible bond exchanged for, Share-equivalent of option, delta as , 383-384 Share repurchases, 0, 522 Sharpe, W F., 3 Sharpe ratio, 395n, 659-660, 663, 688 bond pricing model and, 782-783 of option, 394-395 Shiller, Robert, Shimko, David, 86n Short (seller), 23 Short call profit, 53 Short forward contract, collar and, 75 Short forward _position, 44-45 Short forward profit, 53 Short position, 2, 44-45, bonds, repos, and, 235 insuring with cap, 62-63 Short put profit, 53 Short rebate, Short-sale, 2- cash flows and, risk and scarcity i n , 5- o f wine, 3- Short-term interest rate, 783 Shout option, European, 739 Shoven, J B , 528, 529 Shreve, S E., 650n, 652n, 662n, 664n, 674 Shut-down, of oil production, 572-578 959 Siegel, D R., 1 , 565n, 689n Siegel, J J., 299 Simulation, of lognormal stock prices, 623-624 Single-barrel extraction of oil under certainty, 565-569 under uncertainty, 569-570 Single name credit default swaps, 860-86 , 865 Single-payment swap, 247 Single stock futures, 43 Singleton, K J., 852n Smith, C W , 03n, 07n Smith, D., 243n S mith, Randall, 492n Solnik, B , 258n Southwest Airlines, jet fuel hedging by, l 99n Spark spread, 560, SPDRs See S &P Depository Receipts (SPDRs) Special collateral repurchase agreement, 234 Speculation, financing with repos, 235 on foreign index, 728-729 short-selling and, o n volatility, using options, 78-85 Speculative grade bonds, 847 Spot price, 23 Spread, 70-73, bear, 72 bid-ask, 1- box, 72-73 bull, commodity, 95- 96 crack, 96 crush, 95 ratio, 73 vertical, Spread option, 562 Stable distribution, 592 Stack and roll, Stack hedge, 97, 98 Staged investment, 564 Standard and Poor's, 847n See also S&P 500 entries Standard deviation estimate of, 607 of returns, 354-355 Standard normal density, 87-588 Standard normal distribution, 409-4 Standard normal probability density function, 409 960 � I N D EX Standard normal variable, conversion of normal random variable to, 590-59 Statement of Financial Accounting Standards (SFAS ) l 23R, 525, 527, 532, (SFAS) 33 , 06 Static NPV, 548-549, 555 Static option replication, 433 Steiner, R., 233n Stiglitz, J E., 30n Stochastic differential equations, 649 Stochastic process, 650, 768n Stochastic vola f!lity, 744, 763, 772 Stock alternative ways to buy, 27- calls o n nondividend-paying, 294-295 cash flows for, 283 with discrete dividends, -365 forward contracts on, 33- options t o exchange, 288-289 prepaid forward contract (prepay) on, 28- 33 risk management for picking, 54 risk-neutral valuation of, 373 short-sel li ng, synthetic, 285 value at risk for, 5-8 Stock index, 22-23 forward contract vs option and, 37 option on, 330-33 Stock i ndex futures, 22 Stock options See Compensation options; Option(s) Stock prices bond valuation based on, 520 conditional expected price, 603-604 current price as present value of future price, 29, 79n jumps in, 672-674 lognormal model of, 595-598 portfolio value as function of, 827 as random walk, 352-353 simulating correlated, 643-645 simulating jumps with Poisson distribution, 639-643 simulating sequence of, 623-624 standard deviation correspondence and, 602 Stock price trees, option price trees and, 442 Stock purchase contract, 495-496 Storage as carry, of com, 89- 90 costs, forward prices, and, - 82 costs and lease rate, 82 of electricity, 72- 74 of natural gas, - 95 positive lease rate and, 76- Straddle, 78-80 at-the-money written, risk of, 822-823 profit diagram for, 87 on s ingle stock, 823-824 strangle and, 78-79 80 written, 79-80 Straddle rules, 58 Strangle, 78-79, 80, 87 Strategic options, 558 future investment options as, 558 Stratified sampling, 632 Strike foreign equity call struck in domestic currency, 729-730 pricing options for, 769 Strike price, 32, 299-304, 547, 560 average as, 446-44 convexity and, 304 effect on option price, 299-304 risk management and, 97-98 Strike price convexity, 30 Strip, Eurodollar, Strip hedge, 97 Strip, interest rate, 223 STRIPS, 206 Structured note, 474-482 Stutz, R., 4n Style, of options effect on price, 293 Subadditivity, 837-838 Subordinated tranche, COOs and, 854, 856 Subrahmanyam, M G., 258n Supershares, 709 S upply, of com, 90 Swap(s), 25, 247, 279, 826 accreting, 263 amortizing, 263 asset, 255 cash flows from, 249 collateralization and, 486n commodity, 247-254, 268-270 computing rate, 257-25 currency, 264-268 I N D EX � default, 273-274, 858-863 deferred, 26 -262 financial settlement of, 248-249 as forward rate agreements, 258n implicit loan balance of, 260-26 interest rate, 254 63 market value of, 253-254 physical settlement of, 248 prepaid, 248 total rate of return, 864 total return, 272-274 with variable quantity and price, 269-270 variance, 75 8-759 volatility, 759, 828-830 Swap counterparty, 250-25 , 255-257 Swap curves, 258-260, 270 Swap price, 250 Swap-rate calculation, 274 Swap spread, 259-260 Swap tenor, 254 Swap term, 254 Swaptions, 27 Synthetic commodity, , 72n Synthetic forwards, 66-70, 1 2, 35- 36, box spreads and, 72-73 in market-making and arbitrage, 36- 38 Synthetic FRAs, 6-2 Synthetic Nikkei investment, Synthetic options, 285-286 Synthetic stock, parity and, 285 Synthetic T-bills, 285 Tailing, 32 Tail VaR, 832, 836-837 Tax-deductible equity, 495 498 Taxes box spreads and, 74 corporate deferral, 492 495 for derivatives, o n employee options, 527n on equity-linked CD, 484n financial engineering for, 490 498 hedging and, 04, 06 individual deferral, 49 492 option prices and, 34 Taylor, H M., 69 n, 692n Taylor series expansion, of bond price, 228n 961 T-bills See Treasury bills Term repo, 234 Terrorism, futures on, 24 Theta, 383, 387, 428, 442 delta-hedging and, 425 426, 427 formula for, 4 1 hedging and, 420 for put options, 390 Thiagarajan, S R., I 07 TIBOR (Tokyo Interbank Offer Rate), 60 Times Mirror, 492 495 Time-varying volatility (ARCH), 747-75 T-note See Treasury-note futures Total rate of return swaps, 864 Total return payer, 272 Total return swap, 272-274 TRACERS, 865 TRAC-X, 865 Traded present value, 550 Trades, arbitrage and, 39 Trading of derivatives, 7-1 proprietary, 4 Tranched CDO claims, 853 Tranched CDX, 866 Tranches, 1 ratings of, 854 856 Transaction costs, in bonds, 233 future overlays and, hedging and, 06 no-arbitrage bounds with, 38- Translation invariance, 837n Treasury bill rate, monthly change in ( 947-2004), Treasury bills, 244 245 LIBOR vs 3-month T-bills, 22 1-223 quotations for, 244 stocks and, 150 synthetic, 72n, 285 yield on, 47 Treasury bond(s) See Bonds; Treasury-bond futures Treasury-bond futures, 230-233 Treasury-note futures, 230-233 Treasury securities See also Treasury bills issuance of, 205n Trottman, Melanie, 99n 962 � I N D EX True probabilities pricing options with, 369 valuation with, 9-62 Trust, tax-deductible equity and, 495-498 TRW See Northrop Grumman-TRW merger Tu, D., 83 l n Tufano, P., 07 Turnbull, S M., 852n Twin security, 550 Two-parameter distribution, 587 Two-period EuroRean call, 323-326 Uncertainty discounted cash flow and, 55 -552 investment under, 55 -558 qu antity, 1 6- 1 single-barre l extraction under, 569-570 Underlying asset, Unfunded CDs, 862 Uniformly distributed random variables, sums of, 622 U.S Tax Code, on capital income, 74 Unit of denomination, numeraire as, 693 Up-and-in cash call, Up-and-in cash put, 4-7 Up-and-in options, 450 up: and-out cash call, Up-and-out cash put, Up-and-out-currency put options, 452 Up-and-out option, 450, 452 Upper DECS, 497 Upward-sloping yield curve, 07n Utility-based valuation, 369-37 Utility weights, in high and low states of economy, 372 Valuation See also Monte Carlo valuation of American options, 633-636 bond, 520 under certainty, 679-68 of claim on S" , 666-672 of claim on sa Q11' 670-672 of compensation options, 524-525, 525-526 of derivatives on cash flow, 552-554 equation of, 680 of infinite oil reserve, 570-572 of log contract, 76 -762 Monte Carlo, 7-645 of oil producing firm, 57 of option for electricity and gas production, 560-563 of option to invest in oil, 57 -572 of project with 2-year investment horizon, 554-558 of project with infinite investment horizon, 558 with risk-neutral probabilities, 8, with true probabilities, 9-62 utility-based, 369-37 · Value at risk (VaR), 3-839 alternative risk measures and, 832-835 for bonds, 826-830 estimating volatility in, 830-83 Monte Carlo simulation for, 822-826 for nonlinear portfolios, 9-826 for one stock, 5-8 regulatory capital and, risk-neutral distribution and, 835-837 subadditive risk measures and, 837-838 for two or more stock s , 7-8 _uses of, 14-8 VaR See Value at risk (VaR) Variable prepaid forward (VPF) contract, 492 Variance, constant elasticity of, 763, 766-767 Variance estimate, variability of, 607n Variance swap, 758-759 Vasicek, 0., 779, 78 l n Vasicek model, 786-787 Cox-Ingersoll-Ross model and, 788-790 Vassalou, M., 846 VBA See Visual Basic for Applications (VBA) Vega, 82, 386, 1 for at-the-money 40-strike options, 386 Vertical spread, Visual B asic for Applications (VBA), 885-906 arrays and, 897-899 Black-Scholes formula computation with, 894-895 checking for conditions and, 896-897 creating button to invoke subroutine, 888-889 differences between functions and subroutines, 890 functions can call functions, 889 illegal function names, 889-8 90 I N D EX � iteration and, 899-90 object browser and, 895-896 storing and retrieving variables in worksheet, 890-893 subroutine in, 888 using Excel functions from within, 893-896 VIX volatility index, 743, 757, 762-763 Volatility, 74 -773 asymmetric· butterfly spread and, 82-83 averaging and, 447-448 Black-Scholes model and, 63-773 in bond pricing, 794 96 for bonds and swaps, 828-830 butterfly spreads and, 1-82 detenninistic changes over time, 772-773 early exercise of option and, 343-346 for electricity and natural gas, 560-562 equity-holders and, estimating, 360, 36 , 830-83 Health-Jarrow-Morton model and, hedging and pricing, 757-763 historical, 744 746 for IBM and S&P 500 i ndex, 745 i mplied, 400-402, 74 -744 measurement and behavior of, 744 757 of option, 393-394, 553n pricing of, 759-763 speculating on, 78-85 stochastic, 744 straddles and, 8-80 of various positions, 87 verifying for bonds, 803-804 zero, 322 Volatility clustering, 748 Volatility forecasts, i n GARCH model, 753-754 Volatility frowns, 742 Volatility skew, 402 in option pricing model, 77 -773 Volatility smile, 742 Volatility smirk, 742 Volatility surface, 742 Volatility swap, 759 Vorst, A C F., 630n Vorst, T., 863 Warrant, put, 522-523 963 Watkinson, L., 858n Weather derivatives, 99-200 Webber, N., Weston, J., 07 White, A., 768n White, Gregory L., OS Wiggins, J B., 768n Wilmott, P., 674 Writing of covered call, 64 65 selling insurance and, 63-64 Written call option, 44 45 , 96 payoff and profit for, 37-3 · with different underlying stocks, 824 826 Written options See also Written call option; Written put Greek for, 83-388 margins for, 57 Written put covered call and, 65 with different underlying stocks, 824 26 payoff and profit for, 40-42 profit diagram for, 42, 44 with same underlying stock, 823-824 Written straddle, 79-80 at-the-money, 822-823 butterfly spread and, 1-82 Wu, L., 772n Wyden, Ron, 24 Xing, Y., 846 XYZ debt issue, default swap and, 860 Yen-based investor, 9, 720-72 Yen forward contract, synthetic creation of, Yield bond, 242-244 continuously compounded, 3-2 convenience, 82-1 84 dividend, 32 effective annual rate, continuously compounded rate, and, 48n expected interest rates and, 796-797 verifying bond, 802-803 Yield curve, 208 Black-Derman-Toy model and, 798 964 � I N D EX bond pricing model and, 780-78 upward-sloping, ! 07n Vasicek and CIR models and, 789 Yield to maturity, 208, 24 -245 Yurday, E C., 858n, 864n Zero-cost collar, 76-78, I I 0- 1 , 49 1-492 financing of, 76-77 forward contract as, 1 1- 1 Zero-coupon bord, 206-208, 474-475 , 779 commodity-linked, 479 default and, 84 -843 equity-l inked, 476 inferring price of, 1 -2 Macaulay duration and, 229n movement of, 829 payoff profit, and, 28-29, price of, 684 STRIPS as, 206 valuation of, 783 value at risk for, 827-828 Zero-coupon bond prices, 794-796 Zero-coupon debt, 1 Zero premium, of forward contract, 69 Zero volatility, 322 ... obtain by entering the equations directly in a spreadsheet The displayed calculations will help you follow the logic of a calculation, but a spreadsheet will be helpful in reproducing the final result... ofNormal Random Variables The Lognormal Distribution 593 A Lognormal Model of Stock Prices 595 18.4 Lognormal Probability Calculations 598 599 624 Call 25 591 18.2 18.3 Monte Carlo Valuation... the United States of America Library of Congress Cataloging-in-Publication Data McDonald, Robert L (Robert Lynch), 1954- Derivatives markets, 2e I Robert p.cm Includes index ISBN 0-321-28030-X