Mathematical Sciences

Lund University

Title Discrete space-simulation for Lévy processes
Authors Simon Johansson
Full-text Available as PDF
Year 2012
Document type StudentPublicationsH2
Language eng
Abstract Swedish In this thesis I will present a way of discretizing Lévy processes in<br> space instead of in time. The foundation is built on work done by<br> Adalbjörnsson,Quiroz and Wiktorsson, which shows how this is done for<br> Brownian motions with constant drift and volatility. I then start by<br> extending the method to multidimensional Brownian motions, which is then<br> extended to multidimensional SDE:s by using an Euler approximation. The<br> method is then extended to Jump-Diffusions. I<br> also present an approximation method for approximating Infinite activity<br> processes with Jump-Diffusions, and as result the simulation method is<br> extended to Infinite activity processes. Since the method bounds process<br> in space it’s natural to consider path-dependent options. Case studies<br> on Barrier options are performed in order to show the convergence of the<br> algorithm.