An Introduction to Financial Option Valuation Mathematics, Stochastics and Computation

An Introduction to Financial Option Valuation Mathematics, Stochastics and Computation Book Description

This is a lively
textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black-Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.

Contents


1. Introduction

2. Option valuation preliminaries

3. Random variables

4. Computer simulation

5. Asset price movement

6. Asset price model: part I

7. Asset price model: part II

8. Black-Scholes PDE and formulas

9. More on hedging

10. The Greeks

11. More on the Black-Scholes formulas

12. Risk neutrality

13. Solving a nonlinear equation

14. Implied volatility

15. The Monte Carlo method

16. The binomial method

17. Cash-or-nothing options

18. American options

19. Exotic options

20. Historical volatility

21. Monte Carlo part II: variance reduction by antithetic variates

22. Monte Carlo part III: variance reduction by control variates

23. Finite difference methods

24. Finite difference methods for the Black-Scholes PDE.

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