Finite Element Based Monte Carlo Simulation of Option Prices on Lévy Driven Assets

Abstract

This paper extends the simulation algorithm by Andreasen & Huge (2011) to the simulation of option prices and deltas on Lévy driven assets. The simulation is performed relying on the inverse transition matrix of the discretized PDE. Each row describes the evolution of option prices and can thus be seen as the underlying’s transition probability distribution. We demonstrate how one can get accurate prices and deltas of European options on VG and CGMY via Monte Carlo simulations.

Keywords: Computational Finance; Derivative Pricing; Finite Element Method; Monte Carlo Simulation, Lévy Processes