An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation / Edition 1

An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation / Edition 1

by Desmond Higham
     
 

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ISBN-10: 0521547571

ISBN-13: 9780521547574

Pub. Date: 03/31/2004

Publisher: Cambridge University Press

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,

Overview

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.

Product Details

ISBN-13:
9780521547574
Publisher:
Cambridge University Press
Publication date:
03/31/2004
Edition description:
New Edition
Pages:
296
Product dimensions:
6.85(w) x 9.72(h) x 0.71(d)

Table of 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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