The Mathematics of Financial Derivatives A Student Introduction [Paperback]

The authors describe the modelling of financial derivative products from an applied mathematician's viewpoint.The rapidly growing area of finance is an expanding source for the development of novel and relevant real-world mathematics. This text describes the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation.The rapidly growing area of finance is an expanding source for the development of novel and relevant real-world mathematics. This text describes the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation.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 BlackScholes 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. FulS'