The Concepts and Practice of Mathematical Finance

by Mark S. Joshi

• ISBN13: 9780521823555
• ISBN10: 0521823552
• Format: Hardcover
• Copyright: 2004-01-26
• Publisher: Cambridge University Press

Summary

For those starting out as practitioners of mathematical finance, this is an ideal introduction. It provides the reader with a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black-Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Uniquely, the book includes extensive discussion of the ideas behind the models, and is even-handed in examining various approaches to the subject. Thus each pricing problem is solved using several methods. Worked examples and exercises, with answers, are provided in plenty, and computer projects are given for many problems. The author brings to this book a blend of practical experience and rigorous mathematical background, and supplies here the working knowledge needed to become a good quantitative analyst.

Table of Contents

Preface

1. Risk

2. Pricing methodologies and arbitrage

3. Trees and option pricing

4. Practicalities

5. The Ito calculus

6. Risk neutrality and martingale measures

7. The practical pricing of a European option

8. Continuous barrier options

9. Multi-look exotic options

10. Static replication

11. Multiple sources of risk

12. Options with early exercise features

13. Interest rate derivatives

14. The pricing of exotic interest rate derivatives

15. Incomplete markets and jump-diffusion processes

16. Stochastic volatility

17. Variance gamma models

18. Smile dynamics and the pricing of exotic options

Appendix A. Financial and mathematical jargon

Appendix B. Computer projects

Appendix C. Elements of probability theory

Appendix D. Hints and answers to questions

Bibliography

Index.