Calibration of pure jump levy process - pricing of options of using CGMY model using particle filter

Abstract

The goal of the paper is to show that some types of Lévy processes such as the CGMY model are particularly suitable for option pricing. We wish to review some fundamental mathematic properties of Lévy distributions, such as the one of infinite divisibility, and how they translate observed features of asset price returns. We explain how these processes are related to Brownian motion, the central process in finance, through stochastic time changes which can in turn be interpreted as a measure of the economic activity. Lastly, we focus on a particular class of pure jump Lévy processes, the CGMY models, and report on the goodness of fit through holding out of data obtained on the option prices.