introduction to derivatives - gbv · introduction to derivatives options, futures, and swaps r....
TRANSCRIPT
INTRODUCTIONTO DERIVATIVESOptions, Futures, and Swaps
R. Stafford JohnsonXavier University
New York OxfordOXFORD UNIVERSITY PRESS2009
CONTENTS
Exhibits, Figures, and Tables xxvii
Preface xxxv
PART I OPTION STRATEGIES AND MARKETS
1 Option Concepts and Fundamental Strategies1.1 Short History of the Derivative Market 1
1.1.1 Futures Market 11.1.2 Options Market 31.1.3 Overview 3
1.2 Option Terminology 41.3 Fundamental Option Strategies 5
1.3.1 Call Purchase 51.3.2 Naked Call Write 61.3.3 Covered Call Write 81.3.4 Put Purchase 81.3.5 Naked Put Write 91.3.6 Covered Put Write 10
1.4 Other Option Strategies 101.4.1 Straddle 111.4.2 Spread 12
1.5 Option Price Relationships 131.5.1 Call Price Relationships 131.5.2 Call Price Curve 151.5.3 Variability 161.5.4 Put Price Relationships 171.5.5 Put Price Curve 171.5.6 Variability 18
1.6 Put-Call Parity 181.7 Conclusion 20
Key Terms 20Selected References 20Problems and Questions 20Web Exercise 22
2 The Option Market 232.1 Introduction 232.2 Option Exchanges 23
2.2.1 Structure 24
VI
CONTENTS vii
2.2.2' Market Makers and Specialists 252.2.3 Standardization 26
2.2.3.1 Listing 262.2.3.2 Exercise Dates 262.2.3.3 Exercise Price 272.2.3.4 Contract Size 272.2.3.5 Limits 272.2.3.6 Flex Options 282.2.3.7 Option Quotation 28
2.2.4 Option Clearing Corporation 282.2.5 Summary 31
2.3 Types of Trades and Orders 322.3.1 Opening Transactions 322.3.2 Expiring Transactions 322.3.3 Exercising Transactions 332.3.4 Closing Transactions 33
2.4 Margins, Transaction Costs, and Taxes 342.4.1 Margins 34
2.4.1.1 Naked Short Positions 342.4.1.2 Covered Short Positions 352.4.1.3 Spreads 362.4.1.4 Summary 36
2.4.2 Cost of Trading 362.4.2.1 Commissions 372.4.2.2 Fees 382.4.2.3 Bid-Ask Spread 382.4.2.4 Taxes 39
2.5 Non-Stock Options 402.5.1 Stock Index Options 402.5.2 Foreign Currency Options 432.5.3 Futures Options 432.5.4 Interest Rate Options 43
2.6 OTC Options 452.6.1 OTC Currency Options 452.6.2 OTC Interest Rate Options 46
2.7 Conclusion 46Key Terms 47Selected References 47Problems and Questions 48Web Exercises 49
3 Option Strategies 503.1 Introduction 503.2 Call Purchase 50
3.2.1 Follow-up Strategies 503.2.2 Call Purchases in Conjunction With Other Positions 54
viii CONTENTS
3.2.2.1 Simulated Put 543.2.2.2 Simulated Straddle 55
3.3 Naked Call Write 553.3.1 Foliow-Up Strategies: Rolling Credit 56
3.4 Covered Call Write 573.4.1 Types of Covered Call Writes 573.4.2 Follow-up Strategies 58
3.5 Ratio Call Write 593.6 Put Purchase 60
3.6.1 Put Selection 613.6.2 Follow-Up Strategies 623.6.3 Put Purchase in Conjunction With a Long
Stock Position 633.6.3.1 Simulated Call 633.6.3.2 Portfolio Insurance 65
3.7 Naked Put Write 663.8 Covered Put Write 663.9 Ratio Put Write 673.10 Call Spreads 67
3.10.1 Vertical (Money) Spreads 673.10.1.1 Bull and Bear Call Spreads 673.10.1.2 Ratio Money Spread 683.10.1.3 Butterfly Money Spread 69
3.10.2 Horizontal (Time) Spreads 713.11 Put Spreads 723.12 Straddle, Strip, and Strap Positions 73
3.12.1 Straddle Purchase 733.12.2 Straddle Write 743.12.3 Strips and Straps 75
3.13 Combinations 783.14 Condors 793.15 Simulated Stock Positions 79
3.15.1 Simulated Long Position 803.15.2 Simulated Short Position 803.15.3 Splitting the Strikes 81
3.16 Hedging Stock Portfolio, Bond, andCurrency Positions 843.16.1 Hedging Portfolio Positions Using Index Options 843.16.2 Hedging Currency Positions With Currency
Options 873.16.2.1 Hedging Future T-Bond Sales With an OTC
T-Bond Put 893.17 Conclusion 91
Key Terms 92Selected References 92Problems and Questions 92Web Exercises 97
CONTENTS ix
PART II OPTION PRICING
4 Fundamental Option Price Relations 984.1 Introduction 984.2 Minimum and maximum call prices 98
4.2.1 Maximum American and European Call Prices 984.2.2 Minimum Price of an American Call 994.2.3 Formal Proof of the Boundary Condition 1004.2.4 Minimum Price of a European Call 1024.2.5 Boundary and Minimum Price Conditions for Calls on
Dividend-Paying Stocks 1024.3 Option prices With different exercise prices 103
4.3.1 Price Relation of Calls With Different Exercise Prices 1034.3.2 Price Limits on Calls With Different Exercise Prices 106
4.4 Call Price and Time to Expiration Relations 1084.5 Call Price Relations With Stock Prices, Volatility, and
Interest Rates 1094.5.1 Call Price and Stock Price Relation 1094.5.2 Call Price and Volatility Relation 1094.5.3 Call Price and Interest Rate Relation 110
4.6 Early Exercise of an American Call..." 1104.7 Minimum and Maximum Put Prices 112
; 4.7.1 Maximum American and European Put Prices 1124.7.2 Minimum Price of an American Put 1124.7.3 Minimum Price of a European Put 1134.7.4 Boundary Conditions 1154.7.5 Minimum Price Conditions for Puts on
Dividend-Paying Stocks 1154.8 Put Prices with Different Exercise Prices 116
4.8.1 Price Relation of Puts With Different ExercisePrices 116
4.8.2 Price Limits on Puts With Different Exercise Prices 1194.9 Put Price and Time to Expiration Relation 1204.10 Put Price Relations with Stock Prices, Volatility, and Interest
Rates 1214.10.1 Put Price Relations With the Stock's Price and
Volatility 1214.10.2 Put Price and Interest Rate Relation 121
4.11 Put and Call Relationships 1224.11.1 Put-Call Parity for Options on a Stock Paying
No Dividends 1224.11.2 The Price of a European Call and Put on a Stock
Paying No Dividends 1244.11.3 Put-Call Parity for European Options on a Stock
With a Dividend 1254.11.4 Put-Call Parity Prices for American Calls and Puts 1254.11.5 Box Spread 125
CONTENTS
4.12 Boundary Conditions Governing Index Options 1274.12.1 Cash Settlement 1284.12.2 Spot Portfolio 1284.12.3 Dividend Adjustments 130
4.13 Boundary Conditions Governing Currency Options 1324.13.1 Minimum Values of Currency Options 1324.13.2 Put-Call Parity Model 134
4.14 Conclusion 134Key Terms 136Selected References 137Problems and Questions 137Web Exercise 141
Appendix 4A Boundary and Minimum Price Conditions forCalls on Dividend-Paying Stocks 141
Boundary Condition 141Minimum Price on a European Call 142Minimum Price on an American Call 142
$3-Dividend Case 142$1-Dividend Case 143Threshold Dividend 144
Summary 145Problems and Questions 145
Appendix 4B Minimum Price Conditions for Puts onDividend-Paying Stocks 145
Minimum Price of a European Put 145Minimum Price of an American Put 146
Problem 147
5 The Binomial Option Pricing Model 1485.1 Introduction 1485.2 Single-Period BOPM 149
5.2.1 Valuing Call Options Through a ReplicatingPortfolio 149
5.2.2 Single-Period Arbitrage Call Strategy 151 . -5.2.3 Rewriting the Equilibrium Call Price Equation 152
5.3 Single-Period BOPM for Put Options 1535.3.1 Valuing Put Options Through a Replicating
Portfolio 153 .5.3.2 Single-Period Arbitrage Strategy 1565.3.3 Rewriting the Equilibrium Put Price Equation 1565.3.4 Put-Call Parity Model 158
5.4 The Multiple-Period BOPM for Calls 1585.4.1 Two-Period BOPM 1585.4.2 Equation for the Two-Period BOPM 1615.4.3 n-PeriodBOPM 1615.4.4 Multiple-Period Arbitrage Strategy 163
5.4.4.1 Overpriced Arbitrage Strategy 164
CONTENTS xi
5.4.4.2 Underpriced Arbitrage Strategy 1645.4.5 Pricing American Call Options on Nondividend-Paying
Stock 1645.5 The Multiple-Period BOPM for Puts 165
5.5.1 Two-Period Case 1655.5.2 Equation for the Multiple-Period Put Model 1675.5.3 Multiple-Period Arbitrage Strategies for Puts 1675.5.4 Put-Call Parity Model: Multiple-Period Case 1675.5.5 Pricing American Put Options 167
5.6 Estimating the BOPM 1685.6.1 Probability Distribution Resulting from a
Binomial Process 1695.6.2 Solving for u and d 1715.6.3 Annualized Mean and Variance 1735.6.4 u and d Formulas for Large n 1745.6.5 Estimating | i^ and V^ Using Historical
Data 1755.6.6 Note on the Risk-Free Rate 1765.6.7 BOPM Excel Programs 1765.6.8 Example 177
5.7 Features of the BOPM 1775.7.1 Risk-Neutral Probability Pricing 180
5.8 Conclusion 183Key Terms 184Selected References 184Problems and Questions 184Web Exercise 188
Appendix 5A Examples of Multiple-PeriodArbitrage Strategies 189
5A.I Initially Overpriced Call 1895A.2 Initially Underpriced Call 1915A.3 Initially Overpriced Put 192
Problems and Questions 192Appendix 5B Risk-Neutral Probability Pricing—Multiple-Period
Case 194
The Binomial Pricing of Options on Dividend-paying Stocks andStock Indices 196
6.1 Introduction 1966.2 Pricing Options on Dividend-Paying Stocks—Single-Period
Case 1966.2.1 European Call Option 1966.2.2 American Call Option 1996.2.3 European Put Option 2006.2.4 American Put Option 2026.2.5 Put-Call Parity Model With Dividends 202
xii CONTENTS
6.3 Pricing Options on Dividend-Paying Stocks—Multiple-PeriodCase 2036.3.1 Known Dividend-Payment Approach 2046.3.2 Merton's Continuous Dividend-Yield Approach 207
6.4 Binomial Pricing of Stock Index Options 2096.4.1 Proxy Portfolio 2096.4.2 Dividend Adjustments 211
6.4.2.1 Merton Approach 2136.4.2.2 Known Dividend-Payment
Approach 2156.5 Conclusion 217
Key Terms 217Selected References 218Problems and Questions 218Web Exercises 220
7 The Binomial Pricing of Options on Currencies and Bonds 2227.1 Introduction 2227.2 Binomial Pricing of Foreign Currency Options 222
7.2.1 Single-Period Foreign Currency BOPM 2227.2.2 Multiple-Period Foreign Currency BOPM 2257.2.3 Example of Pricing FC Options 225
7.3 Pricing OTC Treasury-Bond Options 2287.3.1 Spot Rates and Equilibrium Bond Prices 2287.3.2 Binomial Interest Rate Model 2297.3.3 Valuing T-Bond Options With a Binomial Tree 2307.3.4 Estimating the Binomial Interest Rate Tree 232
7.3.4.1 Subdividing the Tree 2327.3.4.2 Estimating the u and d Parameters 2337.3.4.3 Calibration Model 2347.3.4.4 Variability Condition 2347.3.4.5 Price Condition 235
7.4 Conclusion 238Key Terms 238Selected References 238Problems and Questions 239Web Exercises 241
8 The Black-Scholes Option Pricing Model 2428.1 Introduction 2428.2 The Black-Scholes Call Option Model 242
8.2.1 The Nature of the B-S OPM 2428.2.2 B-S OPM Formula 242
Example 2438.2.3 Comparative Analysis 2448.2.4 Black-Scholes OPM Excel Programs 246
8.3 Black-Scholes Arbitrage Portfolio 246
CONTENTS xiii
8.4 Dividend Adjustments for the Black-Scholes Call Model 2478.4.1 Black's Pseudo-American Call Model 247
Example 2488.4.2 Merton's Continuous Dividend-Adjustment Model 249
8.5 B-S OPM for Puts 2508.5.1 B-S Put Model 250
Example 2518.5.2 Comparative Analysis 2518.5.3 B-S Arbitrage Put Portfolio 2528.5.4 Dividend Adjustments for the B-S Put Model 2538.5.5 The Value of an American Put Given an
Ex-Dividend Date 2548.5.6 The Value of an American Put Without Dividends 255
8.6 Estimating the B-S OPM 2558.6.1 Interest Rates 2568.6.2 Volatility 2568.6.3 Volatility Smiles and Term Structure 258
8.7 Pricing Index Options with the B-S OPM 2598.7.1 European Stock Index Options 2598.7.2 American Index Options 260
8.8 Pricing Currency Options with the B-S OPM 2618.9 Pricing Bond Options with the B-S OPM 262
• 8.10 Other Option Pricing Models 2638.11 Conclusion 264
Key Terms 265Selected References 265Problems and Questions 267Web Exercises 271
Appendix 8A Mathematical Foundation of the BlackSchole OPM 272
Appendix 8B Black-Scholes Arbitrage/Hedging Portfolio 274B-S Hedged Portfolio for Calls 274B-S Arbitrage Strategy 275 - .B-S Arbitrage Portfolio for Puts 275Arbitrage Put Portfolio 276
Appendix 8C Empirical Tests of the B-S OPM 276Efficient Market Tests 276Price Comparisons 277Estimating Errors 278
Questions 279
Applications of the Option Pricing Model, the Greeks, andExotic Options 280
9.1 Introduction 2809.2 Applications of the OPM 280
9.2.1 Option Positions With Different Holding Periods 280
xiv CONTENTS
9.2.2 Option Return-Risk Characteristics 2839.3 Greeks: Delta, Gamma, and Theta 286
9.3.1 Delta 2869.3.2 Theta 2879.3.3 Gamma 2899.3.4 Position Delta, Gamma, and Theta Values 2909.3.5 Neutral Ratio Spread 292
9.4 Exotic Options 2939.4.1 Forward-Start Option 2939.4.2 Compound Options 2959.4.3 Chooser Options 2959.4.4 Binary Options 296
9.4.4.1 Cash-Or-Nothing Options 2969.4.4.2 Asset-Or-Nothing Options 2989.4.4.3 Supershares 300
9.4.5 Path-Dependent Options 3019.4.5.1 Lookback Options 3019.4.5.2 Asian Options 3029.4.5.3 Shout Option 302
9.4.6 Barrier Options 3039.4.7 Other Exotic Options 303
9.4.7.19.4.7.29.4.7.39.4.7.49.4.7.59.4.7.6
9.5 Admonishment:
Exchange Option 303Rainbow Option 304Basket Options 304Burmudan Option 304PRIMES and SCORESPERCS 305
Derivative Abuses 3059.6 Conclusion 306
Key Terms 307Selected References 307Problems and QuestionsWeb Exercises 312
308
304
PART III FUTURES AND FUTURES OPTION CONTRACTS
10 Futures and Forward Contracts 31310.1 Introduction 313
10.1.1 Definition 31410.2 The Nature of Futures Trading and the Role
of the Clearinghouse 31410.2.1 Futures Positions 31410.2.2 Clearinghouse 315
103 Futures Hedging 31810.3.1 Long Hedge Example 31810.3.2 Short Hedge Example 31910.3.3 Hedging Risk 319
CONTENTS xv
10.3.4 Hedging Models 32110.4 Speculating with Futures 321
10.4.1 Intracommodity Spread 32110.4.2 Intercommodity Spread 322
10.5 The Market and Characteristics of Futures 32210.5.1 Microstructure 32210.5.2 Standardization 32310.5.3 Continuous Trading 32310.5.4 Price and Position Limits 32310.5.5 Delivery Procedures 32410.5.6 Alliances and 24-hour Trading 324
10.6 Margins Requirements, TransactionCosts, and Taxes 32410.6.1 Margin Requirements 32410.6.2 Points on Margin Requirements 32510.6.3 Transaction Costs 32610.6.4 Note on Taxes 326
10.7 Types of Futures and Forward Contracts 32710.7.1 Physical Commodities 32710.7.2 Energy Contracts 32710.7.3 Indices 32910.7.4 Stocks 33010.7.5 Foreign Currency Futures and Forward Contracts 331
; 10.7.5.1 Currency Futures 33110.7.5.2 Interbank Forward Market 331
10.7.6 Interest Rate Futures 33310.7.6.1 T-Bill Futures 33410.7.6.2 Eurodollar Futures Contract 33510.7.6.3 T-Bond Futures Contracts 33610.7.6.4 T-Note Futures Contracts 336
10.8 T-Bond and T-Note Delivery Procedures 33610.8.1 Cheapest-to-Deliver Bond 33610.8.2 Delivery Process 338
10.9 Conclusion 338Key Terms 339Selected References 339Problems and Questions 340Web Exercises 343
11 Pricing Futures and Forward Contracts 34411.1 Introduction 34411.2 Basis 34411.3 Carrying-Cost Model 344
11.3.1 Pricing a T-Bill Futures Contract 34511.3.1.1 Equivalent Spot and Synthetic T-Bill
Rates 34711.3.1.2 Implied and Actual Repo Rates 348
xvi CONTENTS
11.3.2 Pricing a Forward Contract on a Stock Portfolio 34811.3.3 Pricing an Index Futures Contract 349
11.3.3.1 Pricing Forward Exchange Rates 34911.3.4 Equilibrium T-Bond Futures Price 350
Example 35111.3.5 Arbitrage 35211.3.6 Pricing a Futures Contract on a Commodity 35211.3.7 Normal and Inverted Markets 353
11.4 Price Relationship Between Futures Contracts WithDifferent Expirations 353
Example 35411.5 Relation Between the Futures Price and the Expected Spot
Price 35511.6 The Values of Futures and Forward Contracts 35611.7 Relation between Futures and Forward Prices 35711.8 Relation between Futures and Options 357
11.8.1 Put-Call-Futures Parity 35711.8.1.1 Equivalence Between Put-Call-Spot and
Put-Call-Futures Parity Models 35811.8.2 BOPM in Terms of Futures Positions 358
11.9 Conclusion 359Key Terms 359Selected References 359Problems and Questions 360
Appendix 11A Formal Relation between Futures andForward Prices 364
Problems and Questions 365Appendix 1 IB BOPM in Terms of Futures Positions 365
Single-Period BOPM for Index Option in Terms ofIndex Futures 365
BOPM Arbitrage Strategy Using Index Futures 367Single-Period Foreign Currency BOPM Priced in Terms of
Currency Futures 368BOPM Arbitrage Strategy Using Currency Futures 370
Problems and Questions 371
12 Options on Futures Contracts 37212.1 Introduction 37212.2 Characteristics 37212.3 Market for Futures Options 373
12.3.1 Interest Rate Options 37312.4 Differences in Futures and Spot Options 37312.5 Fundamental Futures Options Strategies 374
12.5.1 Stock Index Futures Options 37412.5.2 Treasury-Bill Futures Options 376
CONTENTS xvii
12.5.3 Hedging With Futures Options 37612.5.3.1 Long Hedge Example 37712.5.3.2 Short Hedge Example 378
12.6 Futures options pricing relations 37912.6.1 Arbitrage Relations 37912.6.2 Put-Call Parity Model for Futures Options 379
12.7 Single-period BOPM for Futures Options 38012.7.1 Points on BOPM for Futures Options 38312.7.2 BOPM Defined in Terms of the Futures Prices' Up
and Down Parameters 38412.7.3 Single-Period BOPM Example: Pricing a Call on a
Stock Index Futures Given a ContinuousDividend Yield 386
12.8 Multiple-period BOPM for Futures Options 38812.8.1 Pricing S&P 500 Index Futures Call and
Put Options 38812.8.2 Pricing Foreign Currency Futures Call and
Put Options 39112.9 Valuing interest rate futures options with a binomial
interest rate tree 39412.9.1 Valuing T-Bill Futures and Spot Options With a
Binomial Tree 39412.9.1.1 Spot T-Bill Call 39512.9.1.2 T-Bill Futures Call 39612.9.1.3 T-Bill Futures Put 397
12.9.2 Valuing T-Bond Futures Call Options 39812.10 Black Model for Pricing Futures Options 398
12.10.1 Example: Pricing S&P 500 Futures Options 40012.11 Conclusion 401
Key Terms 401Selected References 401Problems and Questions 402Web Exercises 409
Appendix 12A Algebraic Derivations 410Derivation of Equation (12.7-10): C^ = ±[pCu + ( l -p)C d] and
PQ = 7 tPpu + ( l - p ) P d ] 410Derivation of Risk-Neutral Probability (p) for Currency
Futures Option 412Algebraic Derivation of p f , uf, and df 413
Appendix 12B Single-Period BOPM PricingExamples 414
Pricing Call and Put Options on a Currency FuturesContract 414
Pricing a Call on a Commodity Futures Contract 417
xviii CONTENTS
Appendix 12C Examples of Pricing Futures Options Using the BlackFutures Option Model 420
Pricing British Pound Futures Options 420Pricing Crude Oil Futures Options 420T-Bond Futures Put 421
PART IV MANAGING EQUITY, CURRENCY, AND DEBT POSITIONSWITH DERIVATIVES
13 Managing Equity Positions with Stock IndexDerivatives 422
13.1 Introduction 42213.2 Speculative Strategies 42213.3 Hedging with Stock Index Derivatives 423
13.3.1 Naive Hedging Model 42313.3.2 Stock Index Price-Sensitivity Model 42313.3.3 Short Index Hedging Example 42413.3.4 Long Index Hedging Example 425
13.4 Market Timing 42713.4.1 Market-Timing Example 427
13.5 Speculating on Unsystematic Risk 42813.5.1 Speculating on Unsystematic Risk: Example 429
13.6 Stock Index Futures Pricing:CARRYING-COST MODEL 430
13.7 Index Arbitrage and Program Trading 43113.7.1 Program Trading 43113.7.2 Index Arbitrage 43113.7.3 Stock Volatility and the Triple Witching Hour 433 •*,-
13.8 Dynamic Portfolio Insurance 43313.8.1 A Dynamic Portfolio Insurance Strategy Using
Index Puts 43313.8.2 A Dynamic Portfolio Insurance Strategy Using Bonds 43613.8.3 Constructing Stock-Bond Portfolios for n-Period Case 437
13.9 Dynamic Portfolio Insurance Using Stock Index Futures 43813.9.1 Dynamic Futures-Insured Portfolio: Two-Period
Example 43913.10 Conclusion 442
Key Terms 442Selected References 443Problems and Questions 443Web Exercises 447
Appendix 13 A Derivation of The Stock PortfolioPrice-Sensitivity Hedging Model 447
Appendix 13B Examples of Dynamic Portfolio InsuranceStrategy Using Bonds 448
Three-Period Example 448Ten-Period Example 456
CONTENTS xix
Problems and Questions 462Appendix 13C Derivation of The Dynamic Hedge Ratio 462
14 Managing Foreign Currency Positions with Derivatives 46514.1 Introduction 46514.2 Interest Rate Parity Theorem 466
14.2.1 Hedging Interbank Forward Contracts 46614.2.2 Currency Futures Prices 46714.2.3 Investment Uses of Interest Rate Parity Theorem 467
14.3 Currency Speculation 46814.3.1 Pure Speculative Positions With Futures 46814.3.2 Speculating With Equivalent Money Market Positions 46914.3.3 Speculating With Options 46914.3.4 Currency Futures Spreads 47114.3.5 Cross-Exchange Rate Relations 471
14.4 Hedging with Currency Derivatives 47214.4.1 Hedging Future Currency Cash Inflow 47214.4.2 Hedging Currency Positions Using the
Money Market 47414.4.3 Hedging International Investments 476
14.5 Conclusion 477Key Terms 477Selected References 477Problems and Questions 478Web Exercises 481
15 Managing Fixed-Income Positions with Interest-RateDerivatives 483
15.1 Introduction 48315.2 Hedging Fixed-Income Positions 483
15.2.1 Naive Hedging Model 48415.2.2 Long Hedge—Future 91-Day T-Bill Investment 484
15.2.2.1 Hedging With a Long T-Bill FuturesContract 484
15.2.2.2 Hedging With a T-Bill Futures Call 48615.2.3 Hedging a Future 182-Day T-Bill Investment 48615.2.4 Managing the Maturity Gap 488
15.2.4.1 Hedging With a Short EurodollarFutures Contract 488
15.2.4.2 Hedging With a Eurodollar Futures Put 48915.3 Cross Hedging 490
15.3.1 Price-Sensitivity Model 49015.3.2 Hedging a Commercial Paper Issue With a T-Bill
Futures Contract 49115.3.3 Hedging a Bond Portfolio With T-Bond Futures Puts 492
15.4 Speculating With Interest Rate Derivatives 49415.4.1 Intracommodity Spread 494
xx CONTENTS
15.4.2 Intercommodity Spread 49415.4.3 Speculating With Interest Rate Options 49515.4.4 Managing Asset and Liability Positions 495
15.5 Syntheitc Debt and Investment Positions 49615.5.1 Synthetic Fixed-Rate Loan 49715.5.2 Synthetic Floating-Rate Loan 49815.5.3 Synthetic Investments 499
15.6 Using Options To Set A Cap or Floor On A Cash Flow 49915.6.1 Setting a Cap on a Floating-Rate Loan With a
Series of Eurodollar Puts 49915.6.2 Setting a Floor on a Floating-Rate Investment With a
Series of Eurodollar Calls 50015.7 Conclusion 501
Key Terms 502Selected References 502Problems and Questions 502Web Exercises 507
Appendix 15A Derivation of the Kolb-Chiang Price-Sensitivity HedgingModel 508
16 Managing Fixed-Income Positions with OTC Derivatives 51016.1 Introduction 51016.2 Types of OTC Derivatives 510
16.2.1 Forward Rate Agreements 510Example: Hedging the Rate on a Future CD InvestmentWithaFRA 511
16.2.2 Interest Rate Call 512Example: Hedging a Future Loan Rate With an OTCInterest Rate Call 513
16.2.3 Interest Rate Put 514Example: Hedging a CD Rate With an OTC InterestRate Put 515
16.2.4 Cap 51616.2.5 Floor 517
16.3 Hedging a Series of Cash Flows—OTC Capsand Floors 517
Example: A Floating Rate Loan Hedged With anOTC Cap 517Example: A Floating Rate Asset Hedged With anOTC Floor 519
16.4 Financing Caps and Floors: Collarsand Corridors 519
16.5 Other Interest Rate Products 52216.5.1 Barrier Options 52216.5.2 Path-Dependent Options 523
16.6 Pricing Interest Rate Options With A BinomialInterest Tree 525
CONTENTS xxi
16.6.1 Valuing a Caplet and Floorlet With aBinomial Tree 525
16.7 Pricing Caplets and Floorlets With The BlackFutures Option Model 526
Example: Pricing a Caplet 527Example: Pricing a Cap 528
16.8 Conclusion 528Key Terms 528Selected References 529Problems and Questions 529Web Exercise 535
17 Interest Rate Swaps 53617.1 Introduction 53617.2 Generic Interest Rate Swaps 537
17.2.1 Features 53717.2.2 Interest Rate Swap: Example 53717.2.3 Synthetic Loans 53817.2.4 Similarities Between Swaps and Bond Positions
and Eurodollar Futures Strips 54017.2.4.1 Bond Positions 54017.2.4.2 Eurodollar Futures Strip 540
17.3 Swap Market 54117.3.1 Structure 54117.3.2 Swap Market Price Quotes 54217.3.3 Opening Swap Positions 54317.3.4 Closing Swap Positions 544
17.4 Swap Valuation 54517.5 Comparative Advantage and
The Hidden Option 54717.5.1 Comparative Advantage 54717.5.2 Hidden Option 548
17.6 Swaps Applications 54917.6.1 Arbitrage Applications—Synthetic Positions 549
17.6.1.1 Synthetic Fixed-Rate Loan 54917.6.1.2 Synthetic Floating-Rate Loan 55017.6.1.3 Synthetic Fixed-Rate Investment 550
, 17.6.1.4 Synthetic Floating-Rate Investment 55117.6.2 Hedging 55217.6.3 Speculation 552
17.7 Credit Risk 55317.8 Conclusion 554
Key Terms 554Selected References 554Problems and Questions 555Web Exercises 559
xxii CONTENTS
PARTV SWAPS
18 Swap Derivatives: Forward Swaps and Swaptions 56018.1 Introduction 56018.2 Forward Swaps 560
18.2.1 Hedging a Future Loan With a Forward Swap 56018.2.2 Hedging a Future Investment 56118.2.3 Other Uses of Forward Swaps 562
18.3 Swaptions 56218.3.1 Speculation 56318.3.2 Hedging 566
18.3.2.1 Caps and Floors on Future Debt andInvestment Positions 566
18.3.2.2 Investor Hedging the Risk of an EmbeddedCall Option 567
18.3.2.3 Borrower Hedging the Risk of an EmbeddedPut Option 567
18.3.2.4 Arbitrage—Synthetic Positions 56818.4 Cancelable and Extendable Swaps 568
18.4.1 Cancelable Swap 56818.4.2 Extendable Swaps 569(
18.4.3 Synthetic Positions 569"18.5 Nongeneric Swaps 56918.6 Conclusion 570
Key Terms 571Selected References 571Problems and Exercises 571
19 Swap Valuation 57519.1 Introduction 57519.2 Swap Valuation 575
19.2.1 Valuation of Off-Market Swaps 57519.2.2 Equilibrium Value of a Swap—Zero-Coupon
Approach 57819.2.3 Zero-Coupon Swap Yield Curve—Bootstrapping 578
19.2.3.1 Valuation 57919.3 Break-Even Swap Rate 581
19.3.1 Implied Forward Rates 58119.3.2 Forecasting Future Interest Rates With Implied
Forward Rates 58219.3.3 Implied Forward Swap Rates 58319.3.4 Break-Even Swap Rate 584
19.4 Break-Even Forward Swap Rates and the Valuation of A ForwardSwap 584
19.5 The Valuation of a Swaption 58619.5.1 Intrinsic Value 58619.5.2 Time Value Premium 588
CONTENTS xxiii
19.5.3 Black Futures Option Model 58819.5.4 Put-Call-Futures Parity 592
19.6 Valuation of Cancelable and Extendable Swaps 59219.6.1 Valuing Cancelable Swaps 59219.6.2 Valuing Extendable Swaps 593
19.7 Conclusion 593Key Terms 594Selected References 594Problems and Questions 594Web Exercise 598
20 Currency and Credit Swaps 59920.1 Introduction 59920.2 Currency Swaps 599
20.2.1 Valuation 60020.2.1.1 Equivalent Bond Positions 60020.2.1.2 Equivalent Forward Exchange
Positions 60320.2.2 Comparative Advantage 60520.2.3 Nongeneric Currency Swaps 608
20.3 Credit Default Swaps 60820.3.1 Generic Credit Default Swap 60920.3.2 Terms 60920.3.3 Uses 61020.3.4 The Equilibrium CDS Spread 61020.3.5 CDS Valuation 61220.3.6 Alternative CDS Valuation Approach 61320.3.7 Estimating Default Rates and Valuing CDSs Based
on Estimated Default Intensities 61420.3.7.1 Estimating Probability Intensities From Historical
Default Rates 61520.3.7.2 Estimating Expected Default Rates—Implied
Default Rates 61720.3.8 Summary of the Two Valuation Approaches 61820.3.9 The Value of an Off-Market CDS Swap 61820.3.10 Other Credit Derivatives 620
20.3.10.1 Binary CDS 62020.3.10.2 Basket CDS 62020.3.10.3 CDS Forward Contracts 62020.3.10.4 CDS Option Contracts 62020.3.10.5 Contingent CDSs 62120.3.10.6 Total Return Swaps 621
20.3.11 CAT Bond 62120.4 Conclusion 621
Key Terms 621Selected References 622Problems and Questions 622
xxiv CONTENTS
Web Exercises 627
PART VI EMBEDDED OPTIONS AND ASSET-BACKED SECURITIES
21 Embedded Options 62821.1 Introduction 62821.2 Corporate Stock and Debt as Options 628
21.2.1 Equity and Debt as Call Option Positions 62821.2.2 Valuing Equity as a Call Option With the B-S OPM 63121.2.3 Subordinated Debt 631
21.3 Option Features of Bonds 63221.3.1 Coupon Bonds 63221.3.2 Callable Bonds 634
21.3.2.1 Valuing a Three-Period Callable Bond With aBinomial Tree 634
21.3.3 PutableBond 63821.3.4 Sinking Fund Bonds 63921.3.5 Pricing Callable and Putable Bonds With
a-Multiple-Period Tree 64021.3.6 Using the B-S OPM to Price Embedded Call and
Put Options 64221.4 Convertible Securities 643
21.4.1 Warrants 64321.4.2 Rights 64521.4.3 Convertible Bonds 64621.4.4 Convertible Bond Terms 64721.4.5 Minimum and Maximum Convertible Bond Prices 64721.4.6 Valuation of Convertibles Using Binomial Trees 648 ».
21.5 Using Options as A Capital Budgeting Tool 65121.6 Conclusion 653
Key Terms 654Selected References 654Problems and Questions 655Web Exercises 658
Appendix 21A Equity and Debt as Put Options 65821 A. 1 Valuing Equity as a Put Option With the
B-S OPM 65921 A. 2 Put-Call Parity Model 659Problems and Questions 660
22 Mortgage- and Asset-Backed Securities andTheir Derivatives 661
22.1 Introduction 66122.2 Prepayment 662
22.2.1 Prepayment Models 66222.2.2 Estimating a Mortgage Pool's Cash Flow
With Prepayment 66322.3 Mortgage-Backed Securities 665
CONTENTS xxv
22.3.1 Features of Mortgage-Backed Securities 66822.3.1.1 Cash Flows 66822.3.1.2 Price Quotes 66822.3.1.3 Extension Risk and Average Life 670
22.4 MBS Derivatives 67122.4.1 Collateralized Mortgage Obligations 671
22.4.1.1 Sequential-Pay Tranches 67122.4.1.2 Other Sequential-Pay-Structured CMOs 67222A.I3 Planned Amortization Class 67222.4.1.4 Other PAC-Structured CMOs 675
22.4.2 Stripped Mortgage-Backed Securities 67522.5 Evaluating Mortgage-Backed Securities 678
22.5.1 Yield Analysis 67822.5.2 Monte Carlo Simulation 680
22.6 Other Asset-Back Securities 68122.6.1 Automobile Loan-Backed Securities 68122.6.2 Credit-Card Receivable-Backed Securities 68122.6.3 Home Equity Loan-Backed Securities 681
22.7 Conclusion 681Key Terms 682Selected References 682Problems and Questions 683Web Exercises 687
Appendix 22A Valuing a MBS With a Binomial Interest Rate: ExampleUsing A 2-Period Case 687
A Exponents and Logarithms 691A.I Exponential Functions 691A.2 Logarithms 693A. 3 Rules of Logarithms 693A.4 Uses of Logarithm 693
A.4.1 Solving for R 694A.4.2 Logarithmic Return 694A.4.3 Time 694
Selected Reference 695
B Statistical Concepts 696
C Bond Fundamentals 703C.I Introduction 703C.2 Bond Valuation 703
C.2.1 Pricing Bonds 703C.2.2 Bond Price Relations 704C.2.3 Pricing Bonds With Different Cash Flows and
Compounding Frequencies 706C.2.4 Semiannual Coupon Payments 706C.2.5 Compounding Frequency 707C.2.6 Valuing Bonds With Maturities Less than 1 Year 708C.2.7 Valuing Bonds at Non-Coupon Dates 709C.2.8 Price Quotes, Fractions, and Basis Points 710
xxvi EXHIBITS, FIGURES, AND TABLES
C.3 The Yield to Maturity and Other Rates of Return Measures 710C.3.1 Yield to Maturity 710
C.3.1.1 Rates on Zero-Coupon Bonds: Spot Rates 711C.3.1.2 Rate on Pure Discount Bond With Continuous
Compounding 711C.3.1.3 Spot Rates and Equilibrium Prices 712
C.3.2 Annual Realized Return 713C.3.3 Geometric Mean 714
C.3.3.1 Implied Forward Rate 715C.4 Term Structure of Interest Rates 717
C.4.1 Market Segmentation Theory 717C.4.2 Preferred Habitat Theory 718C.4.3 Pure Expectations Theory 718C.4.4 Liquidity Premium Theory 720
C.5 Bond Risk 720C.5.1 Default Risk 720C.5.2 Call Risk 721C.5.3 Market Risk 721C.5.4 Duration 722
Selected References 722
Guide To Derivative Excel Programs 723D.I Spreadsheet Programs 723
D.I.I Option Strategies 723Binomial Option Pricing Model 724Known Dividend-Payment Binomial Model 725Black-Scholes Option Pricing Model 726Implied Volatility 727D.I.5.1 Algorthim 727Binomial Interest Rate Folder 728Mortgage-Backed Securities Folder 728Bond Programs 729
753
Glossary
Glossary <
D.ID.I
.2
.3D.I.4D.I
D.ID.ID.I
730
.5
.6
.7
.8
af SymbolsIndex 758