This book is a comprehensive and readable description of the applications of mathematics to option pricing. It covers the subject from basic modelling to sophisticated analytical and numerical treatments of the most up-to-date derivative products.
Special features of the book include:
- The financial foundations of option pricing models. Clear descriptions of their mathematical formulation
- The basic mathematical tools necessary for analysis of the Black-Scholes equation
- European American exercise features in the unifying framework of complementary problems and variational inequalities
- Detailed models and analysis of exotic and path-dependent options, including compound options, Asians, lookbacks and barriers
- Models for transaction costs
- Interest rate derivative products: bonds, bond options, convertible bonds, swaps, caps and floors
- First exit times and moving averages
- Practical treatment of accurate numerical methods for option pricing models
1. An Introduction to Options and Markets
2. The Random Nature of the Stock Market
3. Basic Option Theory
4. Partial Differential Equations
5. Explicit Solutions of the Diffusion Equation in Fixed Domains
6. American Options as Free Boundary Problems
7. American Options as Variational Inequalities
8. Dividends and Time-dependent Parameters
9. Exotic Options
10. Barrier Options
11. Asian Options
12. Lookback Options
13. Options with Transaction Costs
14. Interest Rate Derivative Products
15. Convertible Bonds
16. Numerical Methods
17. Finite-difference Approximations
18. The Explicit Finite-difference Method
19. Implicit Finite-difference Methods
20. Methods for Free Boundary Problems
21. Methods for American Options
22. Methods for Exotic Options
Appendix a. The Probability Density Function
Appendix b. First Exit Times
Appendix c. Lattice Methods
Appendix d. Finite-element Methods
Appendix e. Summary of Differential Equations
Appendix f. Bibliography
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