Pure Jump Modelling of Price Processes

Abstract

There has been growing evidence from financial markets that the price processes exhibit jumps in addition to diffusions. Number of models have been suggested to incorporate this fact. One possible approach is to neglect the diffusion part completely and study only pure jump process which may possibly exhibit infinite activity. More recent popular models include CGMY model (Variance Gamma being a special case), or General Hyperbolic Model. In this talk, I will explain these models and show the consequences for pricing financial instruments. In particular, option prices (European, American or Asian) satisfy integro-differential equations.