Computational and numerical methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to anyone working in computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the book goes on to detail computational methods using both stochastic and deterministic approaches.
1 Modeling Tools for Financial Options.- 2 Generating Random Numbers with Specified Distributions.- 3 Monte Carlo Simulation with Stochastic Differential Equations.- 4 Standard Methods for Standard Options.- 5 Finite-Element Methods.- 6 Pricing of Exotic Options.- 7 Beyond Black and Scholes.- A Financial Derivatives.- B Stochastic Tools.- C Numerical Methods.- D Extended Tree Methods.- E Complementary Material.- References.- Index.