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- Product code: 3729
- ISBN: 0521552893,
ISBN13: 9780521552899,
243 pages, hardback
Published by Cambridge University Press on 1996
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Description of Financial Calculus |
The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided.
This unique, modern and up-to-date book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders, whether existing or trainees, in investment banks in the major financial centres throughout the world.
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Reviews"This witty, elegant, compact book breaks fresh ground. I think it represents the first of what may come to be a new generation of industry-oriented introductory books on derivative pricing theory, based on the use of modern probabilistic methods."
- Risk Magazine
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Contents of Financial Calculus |
Preface
The Parable of the Bookmaker
1. Introduction
2. Discrete Processes
The binomial branch model
The binomial tree model
Binomial representation theorem
Overture to continuous models
3. Continuous Processes
Continuous processes
Stochastic calculus
Ito calculus
Change of measure - the C-M-G theorem
Martingale representation theorem
Construction strategies
Black-Scholes model
Black-Scholes in action
4. Pricing Market Securities
Foreign exchange
Equities and dividends
Bonds
Market price of risk
Quantos
5. Interest Rates
The interest rate market
A simple model
Single-factor HJM
Short-rate models
Multi-factor HJM
Interest rate products
Multi-factor models
6. Bigger Models
General stock model
Log-normal models
Multiple stock models
Numeraires
Foreign currency interest-rate models
Arbitrage-free complete models
Appendices
Further reading
Notation
Answers to exercises
Glossary of technical terms
Index
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