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Tools for Computational Finance

Rüdiger Seydel

Springer Finance

This book elaborates on computational issues arising in many problems of mathematical finance. R. Seydel manages to give a rigorous and all-inclusive overview of various numerical tools and methods suitable for pricing financial derivatives and managing portfolio risks.

The book could be naturally divided in four parts. The first part, coinciding with chapter 1, offers a ‘smooth’ introduction to fundamental concepts of financial options, mathematical finance and stochastic calculus (terms and functioning of options, Brownian motion, stochastic differential equations, Black-Scholes model, risk neutral valuation, etc.). This provides the essential theoretical background on the material following in the book. Part II, which includes chapters 2 & 3, deals with the simulation of financial instruments. Various issues are discussed here, among which are the generation of random numbers with specified distribution and the numerical integration of stochastic differential equations. The third and largest part of the book (ch. 4, 5 & 6) presents a variety of numerical methods for solving partial differential equations that arise in the pricing of financial derivatives. The techniques of finite differences and finite elements are presented in detail and, in addition, various tools and ideas are given for dealing with numerical instabilities or spurious solutions occurring in the pricing of ‘exotic’ products.

In my opinion, this book is mainly tailored to financial researchers and practitioners with an applied mathematics or engineering background. Various methods are introduced from a ‘problem-solving’ point of view, been eventually formulated and summarised as algorithms which are offered for straightforward implementation in computer programmes. This expository style, which is similar to Kloeden’s and Platen’s “Numerical Solutions of SDEs through computer experiments”, makes the book unique among others and will definitely attract a broad range of readers coming from the financial academia or practice.

Reviewed by Nikos Thomaidis, PhD Student, University of Aegean, Chios Island, Greece. Click here to buy this book at Amazon.co.uk.

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