The parable of the bookmaker 1
Chapter 1 Introduction 3
1.1 Expectation pricing 4
1.2 Arbitrage pricing 7
1.3 Expectation vs arbitrage 9
Chapter 2 Discrete processes 10
2.1 The binomial branch model 10
2.2 The binomial tree model 17
2.3 Binomial representation theorem 28
2.4 Overture to continuous models 41
Chapter 3 Continuous processes 44
3.1 Continuous processes 45
3.2 Stochastic calculus 51
3.3 It？ calculus 57
3.4 Change ofmeasure-the C-M-G theorem 63
3.5 Martingale representation theorem 76
3.6 Construction strategies 80
3.7 Black-Scholes model 83
3.8 Black-Scholes in action 92
Chapter 4 Pricing market securities 99
4.1 Foreign exchange 99
4.2 Equities and dividends 106
4.3 Bonds 112
4.4 Market price of risk 116
4.5 Quantos 122
Chapter 5 Interest rates 128
5.1 The interest rate market 129
5.2 A simple model 135
5.3 Single-factor HJM 142
5.4 Short-rate models 149
5.5 Multi-factor HJM 158
5.6 Interest rate products 163
5.7 Multi-factor models 172
Chapter 6 Bigger models 178
6.1 General stock model 178
6.2 Log-normal models 181
6.3 Multiple stock models 183
6.4 Numeraires 189
6.5 Foreign currency interest-rate models 193
6.6 Arbitrage-free complete models 196
Appendices A1 Further reading 201
A2 Notation 205
A3 Answers to exercises 209
A4 Glossary of technical terms 216
Index 228