A practical guide to pricing and hedging with Levy processes

Abstract

This dissertation provides an accessible framework for simulating, pricing and hedging options contracts, using L evy processes that offers several insights and advantages when compared to conventional techniques (particularly when short dated options or options near maturity are considered). A minimal review of L evy processes is provided for those unacquainted with the subject, presenting fundamental theorems central to the subsequent analysis. A flexible subclass (the Variance Gamma `family') is then selected and studied, characterizing relevant properties, with which simulation algorithms are then developed. The significance of risk neutral prices in such a market made incomplete by jumps is described and an efficient method for calculating such prices is given. In the final sections, several avenues for mitigating risk by hedging in the underlying asset are explored and a numerical `hedging race' is conducted and analyzed to compare the performance of several techniques on realistic data.