Estimation and Calibration of Levy Models via Fourier Methods

In this chapter we discuss different aspects of statistical estimation for Levy-based processes based on low-frequency observations. In particular, we consider the estimation of the Levy triplet and the Blumenthal-Getoor index in Levy and time-changed Levy models. Moreover, a calibration problem in exponential Levy models based on option data is studied. The common feature of all these statistical problems is that they can be conveniently formulated in the Fourier domain. We introduce a general spectral estimation/calibration approach that can be applied to these and many other statistical problems related to Levy processes. On the theoretical side, we provide a comprehensive convergence analysis of the proposed algorithms and address each time the question of optimality.