Empirical likelihood estimation of levy processes

Abstract

Over the last couple of decades, there has been an increased interest in constructing financial models based on Levy processes. This was mainly due to the new wave of awareness of the jumps present in price processes. In addition to this, Levy processes have desirable mathematical features. We study two kinds of models belonging to this class, namely the Merton Jump-Diffusion and the Variance Gamma process. An estimation technique, known as the Empirical Likelihood Estimation method, is described for estimating the parameters of the processes. The technique is built on empirical likelihood methods based on characteristic functions. Under certain conditions the maximum empirical likelihood estimator gives consistency, asymptotic normality and asymptotic efficiency. The trajectories of the processes are simulated and test procedures for parameter estimation are carried out. An empirical investigation is made on the Malta Stock Exchange Index prices