This easy-to-read book offers a snapshot of computational issues arising in financial mathematics. The new third edition is thoroughly revised and significantly extended. The largest addition is a new section on analytic methods, focused mainly on interpolation approach and quadratic approximation. New sections and subsections are devoted to risk-neutrality, early-exercise curves, multidimensional Black-Scholes models, the integral representation of options and the derivation of the Black-Scholes equation. New figures, numerous exercises, and the addition of more background material make this guide a real must-to-have for everyone working in the world of financial engineering.

Zusammenfassung
Basic principles underlying the transactions of ?nancial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical ?nance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of ?nancial derivatives, a need for sophisticated computational technology has developed. For - ample, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial di?erential equation. Fast and accurate numerical algorithms have become essential tools to price ?nancial derivatives and to manage portfolio risks. The required methods aggregate to the new ?eld of Computational Finance. This discipline still has an aura of mysteriousness; the ?rst specialists were sometimes called rocket scientists. So far, the emerging ?eld of computational ?nance has hardly been discussed in the mathematical ?nance literature. This book attempts to ?ll the gap. Basic principles of computational ?nance are introduced in a monograph with textbook character. The book is divided into four parts, arranged in six chapters and seven appendices. The general organization is Part I (Chapter 1): Financial and Stochastic Background Part II (Chapters 2, 3): Tools for Simulation Part III (Chapters 4, 5, 6): Partial Di?erential Equations for Options PartIV(AppendicesA1...A7):FurtherRequisitsandAdditionalMaterial.

Inhalt

Modeling Toole for Financial Options.- Generating Random Numbers with Specified Distribution.- Monte Carlo Simulation with Stochastic Differential Equations.- Standard Methods for Standard Options.- Finite Element Methods.- Pricing of Exotic Options.