An Elementary Introduction to Mathematical Finance

This unique book on the basics of option pricing is mathematically accurate and yet accessible to readers with limited mathematical training. It will appeal to professional traders as well as undergraduates studying the basics of finance. The author assumes no prior knowledge of probability, and offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this second edition are: a new chapter on optimization methods in finance; a new section on Value at Risk and Conditional Value at Risk; a new and simplified derivation of the Black-Scholes equation, together with derivations of the partial derivatives of the Black-Scholes option cost function and of the computational Black-Scholes formula; three different models of European call options with dividends; a new, easily implemented method for estimating the volatility parameter.

• Author is a big-name textbook writer who is known for presenting advanced concepts simply and well

• A new chapter on optimization methods in finance, a new section on Value at Risk and Conditional Value at Risk

• Many new examples and exercises

Contents

1. Probability; 2. Normal random variables; 3. Geometric Brownian motion; 4. Interest rates and present value analysis; 5. Pricing contracts via Arbitrage; 6. The Arbitrage Theorem; 7. The Black-Scholes formula; 8. Valuing by expected utility; 9. Exotic options; 10. Beyond geometric Brownian motion models; 11. Autoregressive models and mean reversion; 12. Optimization methods in finance.

Reviews

Reviews of the first edition: ‘… an excellent introduction to the subject … the book is ideally suited for self-study and provides a very accessible entry point to this fascinating field.’ P. P. Boyle, ISI Short Book Reviews

‘… provides an excellent introduction to the mathematics of finance … very useful as a text for an introductory course’. Julian O’Shea, Zentralblatt MATH

‘… this excellent text achieves its aim to provide a highly accessible and at the same time accurate presentation of the subject. I would recommend it for libraries to purchase.’ Georgi Boshnakov, The Statistician

‘… provides an accessible and relatively deep insight into basic and advanced topics of mathematical finance … The lucid style of the exposition will be appreciated by readers interested in the topic, and by researchers, students and practitioners.’ European Maths Society Journal

'The book is organized in a very natural way … the book gives a good survey of the various tasks and problems of financial mathematics. the main principles underlying the subject (e.g. arbitrage, present value, expected utility, risk-neutral pricing) are explained in a very clear fashion and are separated from the complex mathematics that usually accompanies them in more advanced texts on finance. The friendly and enthusiastic writing style, the numerous exercises, and the simple derivations of many deep results also play their part in making the book an ideal basis for an introductory lecture series in financial mathematics. It can definitely be recommended to professionals or undergraduates as good reading for a fist contact to the topic.' Journal of the American Statistical Association

Hardback ISBN-10: 0521814294 ISBN-13: 9780521814294) Published January 2003 270 pages 236 x 157 mm £28.00