Introduction To Financial Option Valuation, An: Mathematics, St

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.

Review:
'... a well organized and well written text. The book 'does what it says on the cover', is written in plain English and I think is an excellent introductory text. It will be useful to students from a wide range of backgrounds and an essential complement to the standard undergraduate course which embeds mathematical finance into probability theory. Finally, with it being studded with references, it provides an easy entry into deeper material.' Chris Barnett, UK Nonlinear News ' ... this is a very accessible basic introduction to the subject and Des Higham's unique writing style with many quotes and side remarks makes the reading even more enjoyable.' L. Grune, Z. Angew. Math. Mech. 'A colleague and I use Desmond Higham's financial options book in our Computational Finance and Applied Optimal (stochastic) Control courses as a very good computational reference, but some of the motivations are very good too, such as call-put parity and the Black-Scholes derivation. Our students find it very helpful for its MATLAB code and we have cited it in a risk-neutral Monte-Carlo paper.' Floyd B. Hanson, University of Illinois at Chicago 'This book provides a clear introduction to elementary option pricing via Matlab. It is eminently suitable for advanced undergraduates and beginning graduates.' Dr Brad Baxter, Birkbeck College, University of London 'The material is presented in a ... vivid and pedagogical manner. ...It could equally well be ready by people with limited mathematical knowledge wanting to learn the basics of mathematical finance ...' Zentralblatt MATH

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.

Author Biography:
Des Higham is a Professor of Mathematics at the University of Strathclyde. He has written 2 previous books, MATLAB Guide 0898715164 and Learning LaTeX 08988715164.