Jose Figueroa-Lopez (UCSB, PSTAT).

Stock prices driven by Levy processes or other related jump processes have received a great deal of attention in recent years. The scope of these models goes from simple exponential Levy models to stochastic differential equation with Poisson jumps both on the volatility and on the returns. Several calibration methods have been proposed in the literature to deal with these models. In this talk we will review some classical methods, such as approximated maximum likelihood using FFT, and some recent methods using asymptotic limits of ``power'' variations. In particular, I will discuss in some detail nonparametric procedures.