Identification of the local speed function in a Levy model for option pricing

Details

Ressource 1Download: BIB_D05494090793.P001.pdf (552.38 [Ko])
State: Public
Version: author
Serval ID
serval:BIB_D05494090793
Type
Article: article from journal or magazin.
Collection
Publications
Title
Identification of the local speed function in a Levy model for option pricing
Journal
Journal of Integral Equations and Applications
Author(s)
Kindermann S., Mayer P., Albrecher H., Engl H.
ISSN
0897-3962
Publication state
Published
Issued date
2008
Peer-reviewed
Oui
Volume
20
Number
2
Pages
161-200
Language
english
Abstract
We propose a non-parametric stable calibration method based on Tikhonov regularization for the local speed function in a local L´evy model. The jump term in this model introduces an integral operator into the classic BlackScholes partial differential equation such that the associated model calibration to observed option prices can be treated as a parameter identification problem for a partial integrodifferential equation. This problem is shown to be ill-posed and thus requires regularization. It is proven that nonlinear Tikhonov regularization is a stable and convergent method for this problem. Furthermore, convergence rate results are established under an abstract source condition. Finally the theoretical results are underpinned by numerical illustrations including a real-world example.
Open Access
Yes
Create date
09/02/2009 19:57
Last modification date
20/08/2019 16:50
Usage data