1 An introduction to derivatives 1
Definitions of various derivatives instruments 2
The modern history of financial derivates 6
The institutions and mechanisms of the futures markets 7
Variation margin 17
The mechanics of the options markets 18
Recent development in the derivatives markets 20
An intuitive introduciton to the uses of options,futures and swaps 21
Description of the remainder of this book 25
Summary 26
Questions 26
References 27
2 An introduction to quantitative techniques 29
Introduction 30
Some basic mathematics 30
The time value of money 34
The mathematics of asset yields 39
Frequency distributions of asset returns 48
Statistical analysis of the size and variability of asset retums 51
Probability distributions 57
Covariance,correlation and regression 69
An application of the mean,standard deviation and correlation coefficient 74
Questions 76
Summary 76
References and further reading 77
Appendix 2.1:The standardized normal distribution 78
Appendix 2.2:Percentage points of the t-distribution 79
3 The general principles of pricing forwards and futures contracts 81
Spot and forward contracts 82
Arbitrage and the pricing of financial instruments 82
Distinction between value and price 84
The pricing of forward and futures contracts on carryable financial assets 85
The pricing of forward and futures contracts on non-carryable financial assets 94
The differences between forward and futures prices 96
Summary 97
Questions 98
References 99
4 The general principles of valuing options 101
Introduction 102
Limits to an option s price 102
Intuitive explanation of factors influencing option values 103
Valuation of European options 106
Option price ssensitivities 118
Valuation of European put options 127
The effects of a breakdown in the assumptions 129
Questions 130
Summary 130
References and further reading 131
Appendix 4.1:The trinomial equivalent of the binomial option-pricing model 132
Appendix 4.2:Introduction to the stochastic calculus of the Black-Scholes model 134
5 Volatility 143
What is volatility? 144
Types of volatility 145
Esstimating volatility 146
The empirical characteristics of volatility 154
Forward volatilities 157
Empirical evidence of volatility forecasts 161
Summary 162
Questions 162
References and further reading 163
Appendix 5.1:Bisection 164
6 Option strategies 167
Introduction 167
Analysis of option strategies 169
Managing the long option position 178
Call option writing 180
Put option writing 187
Option strategies involving more than one option 189
Questions 199
Summary 199
Further reading 200
7 Equity options 201
Introduction 202
The application of equity option valuation models 203
The effect of dividend payments on option valuation 204
Valuation of American options 205
The binomial model applied to American options 209
Empirical tests of equity option-pricing models 213
Long-term equity warrants 218
Bonds with embedded equity options 220
Summary 222
References and further reading 223
Questions 223
8 Futures and options on equity indices 225
Introduction 226
The structure of equity indices 226
Futures on equity indices 228
Options on equity indices 235
Empirical analysis of index option-pricing models 247
Index futures and options in equity risk management 248
Applications of options on equity indices and on index futures 263
Summary 273
Questions 274
References 275
Appendix 8.1:Bivariate GARCH 276
Appendix 8.2:Proof of the derivation of the hedge ratio h 277
9 Currency forwards and futures 279
Introduction 280
The quotation of exchange rates 280
Foward exchange contracts and currency futures compared 282
The determination of forward exchange rates and currency futures prices 283
Managing currency risk with forwards or futures 290
Summary 298
Questions 298
References and further reading 299
10 Currency options 301
Introduction 302
Valuation of currency options 303
Validity of the models assumptions 311
Options on currency futures and forwards 314
Applications of currency options to currency risk management 318
Summary 323
Questions 323
References 324
11 Short-term interest rate futures 327
Introduction 327
The exchange-traded and the over-the-counter markets 328
Money market interest rate conventions 328
Futures and forwards on short-term interest rates 336
Applications of interest rate futures and FRAs 348
Summary 365
Questions 365
References and further reading 366
12 Bond futures 367
Types of bond futures and contract specifications 368
Special features of bond futures contracts 369
The pricing of bond futures contracts 372
Summary of bond futures pricing procedures 374
The concept of basis 378
Embedded options and the fair price of a future 383
Summary of factors affecting embedded options 387
Applications of bond futures to risk management 388
Summary 408
Questions 409
References and further reading 409
13 Options on debt instruments and interest rates 412
Introduction 412
Are interest rate options different to other options? 412
Applying Black-Scholes-type models to interest rate options 414
Applications of short-term interest rate options to risk management 420
Term structure models of option pricing 430
The nature of debt instruments with embedded options 446
Applying the Black-Derman-Toy model to bonds with embedded options 449
Summary 455
Questions 455
References and further reading 456
14 Swaps 459
Introduction 460
The reasons for the swap market s existence 460
The analysis of interest rate swaps 464
The analysis of currency swaps 466
The pricing and valuing of swaps 468
Calculating the price of an interest rate 472
Valuation of interest rate swaps 480
Non-generic interest rate swaps 483
Pricing and valuing of currency swaps 483
The risks associated with swaps 484
Applications of swaps to risk management 486
Asset swaps:synthetic instruments for asset management 488
Equity swaps 489
Commodity swaps 492
Options of swaps:swaptions 493
Applications of swaptions to risk management 496
Summary 498
Questions 499
Appendix 14.1:Deriving the swap zero coupon curve from the par swap yield curve 500
References and further reading 500
15 Exotic options 505
Introduction 506
Path dependence and independence 506
Correlation risk 506
Types of exotic options 507
Correlation risk 533
Questions 536
References and further reading 537
Appendix 15.1:Monte Carlo simulation 537
A general introduction to the theory of risk 543
16 Managing risk in derivatives portfolios 543
Data for measuring risk 548
Managing risks applicable to all derivatives portfolios 550
Managing exposure to default risk 551
Mitigating exposure to default risk 553
Managing exposure to interest rate risk 557
Managing interest rate risk 568
Hedging options portfolios 575
Critical analysis and internal control of model application 580
Value-at-risk models 583
Questions 589
References 590
Index 591