Tools for Computational Finance Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years spurred by the enormous economical success of financial derivatives a need for sophisticated computational technology has developed. For ex­ ample to price an American put quantitative analysts have asked for the numerical solution of a free boundary partial differential equation. Fast and accurate numerical algorithms have become essential tools to price financial derivatives and to manage portfolio risks. The required methods aggregate to the new field of Computational Finance. This discipline still has an aura of mysteriousness; the first specialists were sometimes called rocket scientists. So far the emerging field of computational finance has hardly been discussed in the mathematical finance literature. This book attempts to fill the gap. Basic principles of computational finance 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 Differential Equations for Options Part IV (Appendices A1 ... A7): Further Requisits and Additional Material. 1 Modeling Tools for Financial Options 2 Generating Random Numbers with Specified Distributions 3 Numerical Integration of Stochastic Differential Equations 4 Finite Differences and Standard Options 5 Finite Element Methods 6 Pricing of Exotic Options Appendices Al Financial Derivatives A2 Essentials of Stochastics A3 The Black Scholes Equation A4 Numerical Methods A6 Function Spaces A7 Complementary Formula References.