Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes.

Abstract

Continuous non-Gaussian stationary processes of the OU-type are becoming increasingly popular given their flexibility in modelling stylized features of financial series such as asymmetry, heavy tails and jumps. The use of non-Gaussian marginal distributions makes likelihood analysis of these processes unfeasible for virtually all cases of interest. This paper exploits the self-decomposability of the marginal laws of OU processes to provide explicit expressions of the characteristic function which can be applied to several models as well as to develop e±cient estimation techniques based on the empirical characteristic function. Extensions to OU-based stochastic volatility models are provided.Ornstein-Uhlenbeck process; Lévy process; self-decomposable distribution; characteristic function; estimation