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 book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders.

Review: '... a very readable and useful introduction to the pricing of derivatives ... A recommendable book.' Wil Schilders, ITW Nieuws

'... the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities.' L'Enseignement Mathematique

"...a rigorous and accessible account of the probabilistic structure behind the pricing, construction, and hedging of derivative securities....Real examples from stock, currency, and interest rate markets are used. The text also gives a clear view and introduction to modern mathematical finance for probabilists and statisticians." The Journal of the American Statistical Association

"This is an excellent book for anyone who want an intuitive understanding of the use of stochastic calculus in financial engineering." riskbook.com 

The parable of the bookmaker; 1. Introduction; 2. Discrete processes; 3. Continuous processes; 4. Pricing market securities; 5. Interest rates; 6. Bigger models; Appendix 1. Further reading; Appendix 2. Notation; Appendix 3. Answers to exercises; Appendix 4. Glossary of technical terms; Index.