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. Indeed, the area is an expanding source for novel and relevant "real-world" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation. The authors present a unified approach to modeling derivative products as partial differential equations, using numerical solutions where appropriate. The authors assume some mathematical background, but provide clear explanations for material beyond elementary calculus, probability, and algebra. This volume will become the standard introduction for advanced undergraduate students to this exciting new field.

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-choles 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.

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