Computational Methods for Quantitative Finance : Finite Element Methods for Derivative Pricing Many mathematical assumptions on which classical derivative pricing methods are based have come under scrutiny in recent years. The present volume offers an introduction to deterministic algorithms for the fast and accurate pricing of derivative contracts in modern finance. This unified non Monte Carlo computational pricing methodology is capable of handling rather general classes of stochastic market models with jumps including in particular all currently used Lévy and stochastic volatility models. It allows us e.g. to quantify model risk in computed prices on plain vanilla as well as on various types of exotic contracts. The algorithms are developed in classical Black Scholes markets and then extended to market models based on multiscale stochastic volatility to Lévy additive and certain classes of Feller processes. The volume is intended for graduate students and researchers as well as for practitioners in the fields of quantitative finance and applied and computational mathematics with a solid background in mathematics statistics or economics. 1.Introduction Part I.Basic techniques and models: 2.Notions of mathematical finance 3.Elements of numerical methods for PDEs 4.Finite element methods for parabolic problems 5.European options in BS markets 6.American options 7.Exotic options 8.Interest rate models 9.Multi asset options 10.Stochastic volatility models . 11.Lévy models 12.Sensitivities and Greeks Part II.Advanced techniques and models: 13.Wavelet methods 14.Multidimensional diffusion models 15.Multidimensional Lévy models 16.Stochastic volatility models with jumps 17.Multidimensional Feller processes Apendices: A.Elliptic variational inequalities B.Parabolic variational inequalities References. Index.