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 exยญ 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
CONTENT
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
