| 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. |
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