Applications of Fourier Transform to Smile Modeling : Theory and Implementation The sound modeling of the smile effect is an important issue in quantitative finance as for more than a decade the Fourier transform has established itself as the most efficient tool for deriving closed form option pricing formulas in various model classes. This book describes the applications of the Fourier transform to the modeling of volatility smile followed by a comprehensive treatment of option valuation in a unified framework covering stochastic volatilities and interest rates Poisson and Levy jumps including various asset classes such as equity FX and interest rates as well as various numberical examples and prototype programming codes. Readers will benefit from this book not only by gaining an overview of the advanced theory and the vast range of literature on these topics but also by receiving first hand feedback on the practical applications and implementations of the theory. The book is aimed at financial engineers risk managers graduate students and researchers. Option Valuation and the Volatility Smile Characteristic Functions in Option Pricing Stochastic Volatility Models Numerical Issues of Stochastic Volatility Models Simulating Stochastic Volatility Models Stochastic Interest Models Poisson Jumps Lévy Jumps Integrating Various Stochastic Factors Exotic Options with Stochastic Volatilities Libor Market Model with Stochastic Volatilities.