A Note on Monte Carlo Greeks for Jump Diffusion and Other Levy Processes

Abstract

In this paper we present a method to derive generic Monte Carlo estimators for the Greeks for jump diffusion and other Levy processes. For instance we consider models of Merton type and Levy processes obtained by subordinating a Brownian Motion. We use proxy schemes introduced by Fries and Kampen (2005), Fries (2007) or Fries and Joshi (2006). The main idea is to use an integration by parts argument and apply it to the density.

For illustration we consider Digital, Lookback and Knock-Out options in a Merton Jump Diffusion model as well as in a Variance Gamma model.

Keywords: Monte-Carlo Sensitivities, Likelihood Ratio, Importance Sampling, Greeks, Proxy Simulation, Levy Process, Jump Diffusion, Merton Model, Variance Gamma, Digital Option, Lookback Option, Knock-Out Option

JEL Classification: C15, G13