The Mathematics of Financial Derivatives
A Student Introduction

The authors describe the modelling of financial derivative products from an applied mathematician's viewpoint.

Paul Wilmott (Author), Sam Howison (Author), Jeff Dewynne (Author)

9780521497893, Cambridge University Press

Paperback, published 29 September 1995

336 pages, 47 b/w illus. 143 music examples 143 exercises
22.9 x 15.2 x 1.8 cm, 0.45 kg

'The book is pleasantly readable and gives a good introduction.' C. Praagman, ITW Nieuws

Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods; the area is an expanding source for novel and relevant 'real-world' mathematics. In this book the authors describe the modelling of financial derivative products from an applied mathematician's viewpoint, from modelling through analysis to elementary computation. A unified approach to modelling derivative products as partial differential equations is presented, using numerical solutions where appropriate. Some mathematics is assumed, but clear explanations are provided for material beyond elementary calculus, probability, and algebra. Over 140 exercises are included. This volume will become the standard introduction to this exciting new field for advanced undergraduate students.

Part I. Basic Option Theory: 1. An introduction to options and markets
2. Asset price random walks
3. The Black-Scholes model
4. Partial differential equations
5. The Black–Scholes formulae
6. Variations on the Black-Scholes model
7. American options
Part II. Numerical Methods: 8. Finite-difference methods
9. Methods for American options
10. Binomial methods
Part III. Further Option Theory: 11. Exotic and path-dependent options
12. Barrier options
13. A unifying framework for path-dependent options
14. Asian options
15. Lookback options
16. Options with transaction costs
Part IV. Interest Rate Derivative Products: 17. Interest rate derivatives
18. Convertible bonds
Hints to selected exercises
Bibliography
Index.

Subject Areas: Mathematical modelling [PBWH], Finance [KFF]