Financial Calculus : An Introduction to Derivative Pricing

✍ Scribed by Martin Baxter, Andrew Rennie

• Publisher: Cambridge University Press
• Year: 1996
• Tongue: English
• Leaves: 241
• Category: Library

✦ Synopsis

Here is the first rigorous and accessible account of the mathematics behind the pricing, construction, and hedging of derivative securities. With mathematical precision and in a style tailored for market practioners, the authors describe key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model. Starting from discrete-time hedging on binary trees, the authors develop continuous-time stock models (including the Black-Scholes method). They stress practicalities including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. The authors provide a full glossary of probabilistic and financial terms.

✦ Table of Contents

Title
......Page 1
Copyright
......Page 2
Contents
......Page 3
Preface
......Page 5
The parable of the bookmaker
......Page 9
1 Introduction
......Page 11
1.1 Expectation pricing......Page 12
1.2 Arbitrage pricing......Page 15
1.3 Expectation vs arbitrage
......Page 17
2.1 The binomial branch model
......Page 18
2.2 The binomial tree model
......Page 25
2.3 Binomial representation theorem
......Page 36
2.4 Overture to continuous models
......Page 49
3 Continuous processes
......Page 52
3.1 Continuous processes
......Page 53
3.2 Stochastic calculus
......Page 59
3.3 Ito calculus
......Page 65
3.4 Change of measure - the C-M-G theorem
......Page 71
3.5 Martingale representation theorem
......Page 84
3.6 Construction strategies
......Page 88
3.7 Black-Scholes model
......Page 91
3.8 Black-Scholes in action
......Page 100
4.1 Foreign exchange
......Page 107
4.2 Equities and dividends
......Page 114
4.3 Bonds
......Page 120
4.4 Market price of risk
......Page 124
4.5 Quantos
......Page 130
5 Interest rates
......Page 136
5.1 The interest rate market
......Page 137
5.2 A simple model
......Page 143
5.3 Single-factor HJM
......Page 150
5.4 Short-rate models
......Page 157
5.5 Multi-factor HJM
......Page 166
5.6 Interest rate products
......Page 171
5.7 Multi-factor models
......Page 180
6.1 General stock model
......Page 186
6.2 Log-normal models
......Page 189
6.3 Multiple stock models
......Page 191
6.4 Numeraires
......Page 197
6.5 Foreign currency interest rate models
......Page 201
6.6 Arbitrage-free complete models
......Page 204
A1 Further reading
......Page 209
A2 Notation
......Page 213
A3 Answers to exercises
......Page 217
A4 Glossary of technical terms
......Page 224
Index
......Page 236