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.

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.