Empirical Likelihood Methods Based on Characteristic Functions With Applications to Lévy Processes

Levy processes have been receiving increasing attention in financial modeling. One distinctive feature of such models is that their characteristic functions are readily available. Inference based on characteristic functions is very useful for studying Levy processes. By incorporating the recent advances in nonparametric approaches, empirical likelihood methods based on characteristic functions are developed in this paper for parameter estimation, testing a particular parametric class including the presence of a jump component in the Levy process and testing for symmetry of a distribution. Simulation and case studies confirm the effectiveness of the proposed method.