# Diffusion approximation of Lévy processes with a view towards finance

- Handle URI:
- http://hdl.handle.net/10754/561696
- Title:
- Diffusion approximation of Lévy processes with a view towards finance
- Authors:
- 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.
- KAUST Department:
- Publisher:
- Journal:
- Issue Date:
- Jan-2011
- DOI:
- 10.1515/MCMA.2011.003
- Type:
- Article
- ISSN:
- 09299629

- Appears in Collections:
- Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

# Full metadata record

DC Field | Value | Language |
---|---|---|

dc.contributor.author | Kiessling, Jonas | en |

dc.contributor.author | Tempone, Raul | en |

dc.date.accessioned | 2015-08-03T09:02:30Z | en |

dc.date.available | 2015-08-03T09:02:30Z | en |

dc.date.issued | 2011-01 | en |

dc.identifier.issn | 09299629 | en |

dc.identifier.doi | 10.1515/MCMA.2011.003 | en |

dc.identifier.uri | http://hdl.handle.net/10754/561696 | en |

dc.description.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. | en |

dc.publisher | De Gruyter | en |

dc.subject | A posteriori error estimates | en |

dc.subject | Adaptivity | en |

dc.subject | Diffusion approximation | en |

dc.subject | Error control | en |

dc.subject | Error expansion | en |

dc.subject | Infinite activity | en |

dc.subject | Lévy process | en |

dc.subject | Mathematical finance | en |

dc.subject | Monte carlo | en |

dc.subject | Weak approximation | en |

dc.title | Diffusion approximation of Lévy processes with a view towards finance | en |

dc.type | Article | en |

dc.contributor.department | Applied Mathematics and Computational Science Program | en |

dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | en |

dc.contributor.department | Stochastic Numerics Research Group | en |

dc.identifier.journal | Monte Carlo Methods and Applications | en |

dc.contributor.institution | Institute for Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden | en |

kaust.author | Tempone, Raul | en |

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