Stochastic Calculus for Financial Modeling with Stochastic Volatility

I dedicate this work to my father that he rest in peace Mr. Amar Arbai. Index returns are subject of several sources of uncertainty. To better model market, searchers required a Levy process to master randomness. Through this book, we discuss some particular Levy process corresponding to different structure of financial series, to show whether the data are free or include diffusion component and whether the process contains finite or infinite variation. Then, we attempt to provide an alternative approach, Fourier transform, to pricing European option under SVJJ and CGMY models since their probability density functions are unknowns. For ending, we deal with necessary tools for understanding and implementing paths through Monte Carlo simulation and make use the efficient numerical pattern which serve to fulfill the closed-form analytical solution for European call option.