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Discrete space-simulation for Lévy processes

Johansson, Simon LU (2012) FMS820 20121
Mathematical Statistics
Abstract (Swedish)
In this thesis I will present a way of discretizing Lévy processes in
space instead of in time. The foundation is built on work done by
Adalbjörnsson,Quiroz and Wiktorsson, which shows how this is done for
Brownian motions with constant drift and volatility. I then start by
extending the method to multidimensional Brownian motions, which is then
extended to multidimensional SDE:s by using an Euler approximation. The
method is then extended to Jump-Diffusions. I
also present an approximation method for approximating Infinite activity
processes with Jump-Diffusions, and as result the simulation method is
extended to Infinite activity processes. Since the method bounds process
in space it’s natural to consider path-dependent... (More)
In this thesis I will present a way of discretizing Lévy processes in
space instead of in time. The foundation is built on work done by
Adalbjörnsson,Quiroz and Wiktorsson, which shows how this is done for
Brownian motions with constant drift and volatility. I then start by
extending the method to multidimensional Brownian motions, which is then
extended to multidimensional SDE:s by using an Euler approximation. The
method is then extended to Jump-Diffusions. I
also present an approximation method for approximating Infinite activity
processes with Jump-Diffusions, and as result the simulation method is
extended to Infinite activity processes. Since the method bounds process
in space it’s natural to consider path-dependent options. Case studies
on Barrier options are performed in order to show the convergence of the
algorithm. (Less)
Please use this url to cite or link to this publication:
author
Johansson, Simon LU
supervisor
organization
course
FMS820 20121
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
2701523
date added to LUP
2012-06-05 11:36:03
date last changed
2012-06-05 11:36:03
@misc{2701523,
  abstract     = {In this thesis I will present a way of discretizing Lévy processes in
space instead of in time. The foundation is built on work done by
Adalbjörnsson,Quiroz and Wiktorsson, which shows how this is done for
Brownian motions with constant drift and volatility. I then start by
extending the method to multidimensional Brownian motions, which is then
extended to multidimensional SDE:s by using an Euler approximation. The
method is then extended to Jump-Diffusions. I
also present an approximation method for approximating Infinite activity
processes with Jump-Diffusions, and as result the simulation method is
extended to Infinite activity processes. Since the method bounds process
in space it’s natural to consider path-dependent options. Case studies
on Barrier options are performed in order to show the convergence of the
algorithm.},
  author       = {Johansson, Simon},
  language     = {eng},
  note         = {Student Paper},
  title        = {Discrete space-simulation for Lévy processes},
  year         = {2012},
}