Tools for Computational Finance

North American Actuarial Journal, Jul 2004 by Shiu, Elias S W

Seydel, Rüdiger, 2003, Tools for Computational Finance, 2nd edition, Springer, Berlin, xvi + 240 pages, $44.95 ISBN 3-540-40604-2

The author of this textbook is Chair Professor of Applied Mathematics (Computer Science) at the Institute of Mathematics, University of Köln, Germany. It is based on courses on computational finance that the author has given since 1997. Its goal is to provide useful numerical tools and algorithms for pricing financial options and other derivative securities.

In general, there are two methods to price a derivative security. The first method is to calculate the expectation of the discounted payoffs, with the expectation being taken with respect to a risk-neutral probability measure (an equivalent martingale measure). This is a consequence of the so-called fundamental theorem of asset pricing. The second method is to find a (partial) differential equation satisfied by the price function of the derivative security; then solve the differential equation subject to the appropriate boundary condition(s). For the first method, this book has a large section on Monte Carlo simulation. For the second method, there are three chapters on numerical solutions of partial differential equations.

The book is written for an audience without sophisticated mathematical training. It has six chapters and an appendix, which provides additional material on finance, probability theory, and computational methods. There are exercises at the end of each chapter. The author maintains a website which contains hints for the exercises, colored graphs and photographs.

Elias S. W. Shiu, A.SA, Ph.D.

Principal Financial Group Foundation Professor

Department of Statistics and Actuarial Science

The University of Iowa

Iowa City, Iowa 52242-1409

and

Visiting Chair Professor of Actuarial and Investment Science

Department of Applied Mathematics

The Hong Kong Polytechnic University

Hung Hom, Hong Kong

e-mail: eshiu@stat.uiowa.edu