Log In
Communities & Collections
All of KAUST
About
Home
Research
Articles
Diffusion approximation of Lévy processes with a view towards finance
Diffusion approximation of Lévy processes with a view towards finance
Type
Article
Authors
Kiessling, Jonas
Tempone, Raul
KAUST Department
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Stochastic Numerics Research Group
Date
2011-01
Abstract
Let the (log-)prices of a collection of securities be given by a d-dimensional Lévy process X t having infinite activity and a smooth density. The value of a European contract with payoff g(x) maturing at T is determined by E[g(X T)]. Let X̄ T be a finite activity approximation to X T, where diffusion is introduced to approximate jumps smaller than a given truncation level ∈ > 0. The main result of this work is a derivation of an error expansion for the resulting model error, E[g(X T) - g(X̄ T)], with computable leading order term. Our estimate depends both on the choice of truncation level ∈ and the contract payoff g, and it is valid even when g is not continuous. Numerical experiments confirm that the error estimate is indeed a good approximation of the model error. Using similar techniques we indicate how to construct an adaptive truncation type approximation. Numerical experiments indicate that a substantial amount of work is to be gained from such adaptive approximation. Finally, we extend the previous model error estimates to the case of Barrier options, which have a particular path dependent structure. © de Gruyter 2011.
Citation
Kiessling, J., & Tempone, R. (2011). Diffusion approximation of Lévy processes with a view towards finance. Monte Carlo Methods and Applications, 17(1). doi:10.1515/mcma.2011.003
Publisher
Walter de Gruyter GmbH
Journal
Monte Carlo Methods and Applications
DOI
10.1515/MCMA.2011.003
Permanent link to this record
http://hdl.handle.net/10754/561696
Collections
Articles
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Full item page