Computable error estimates of a finite difference scheme for option pricing in exponential Lévy models

Handle URI:
http://hdl.handle.net/10754/566088
Title:
Computable error estimates of a finite difference scheme for option pricing in exponential Lévy models
Authors:
Kiessling, Jonas; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
Option prices in exponential Lévy models solve certain partial integro-differential equations. This work focuses on developing novel, computable error approximations for a finite difference scheme that is suitable for solving such PIDEs. The scheme was introduced in (Cont and Voltchkova, SIAM J. Numer. Anal. 43(4):1596-1626, 2005). The main results of this work are new estimates of the dominating error terms, namely the time and space discretisation errors. In addition, the leading order terms of the error estimates are determined in a form that is more amenable to computations. The payoff is only assumed to satisfy an exponential growth condition, it is not assumed to be Lipschitz continuous as in previous works. If the underlying Lévy process has infinite jump activity, then the jumps smaller than some (Formula presented.) are approximated by diffusion. The resulting diffusion approximation error is also estimated, with leading order term in computable form, as well as the dependence of the time and space discretisation errors on this approximation. Consequently, it is possible to determine how to jointly choose the space and time grid sizes and the cut off parameter (Formula presented.). © 2014 Springer Science+Business Media Dordrecht.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Nature
Journal:
BIT Numerical Mathematics
Issue Date:
6-May-2014
DOI:
10.1007/s10543-014-0490-4
Type:
Article
ISSN:
00063835
Sponsors:
The authors would like to recognize the support of the PECOS center at ICES, University of Texas at Austin (Project Number 024550, Center for Predictive Computational Science). Support from the VR project "Effektiva numeriska metoder for stokastiska differentialekvationer med tillampningar" and King Abdullah University of Science and Technology (KAUST) is also acknowledged. The research has also been supported by the Swedish Foundation for Strategic Research (SSF) via the Center for Industrial and Applied Mathematics (CIAM) at KTH. The second author is a member of the KAUST SRI center for Uncertainty Quantification.
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKiessling, Jonasen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2015-08-12T09:27:47Zen
dc.date.available2015-08-12T09:27:47Zen
dc.date.issued2014-05-06en
dc.identifier.issn00063835en
dc.identifier.doi10.1007/s10543-014-0490-4en
dc.identifier.urihttp://hdl.handle.net/10754/566088en
dc.description.abstractOption prices in exponential Lévy models solve certain partial integro-differential equations. This work focuses on developing novel, computable error approximations for a finite difference scheme that is suitable for solving such PIDEs. The scheme was introduced in (Cont and Voltchkova, SIAM J. Numer. Anal. 43(4):1596-1626, 2005). The main results of this work are new estimates of the dominating error terms, namely the time and space discretisation errors. In addition, the leading order terms of the error estimates are determined in a form that is more amenable to computations. The payoff is only assumed to satisfy an exponential growth condition, it is not assumed to be Lipschitz continuous as in previous works. If the underlying Lévy process has infinite jump activity, then the jumps smaller than some (Formula presented.) are approximated by diffusion. The resulting diffusion approximation error is also estimated, with leading order term in computable form, as well as the dependence of the time and space discretisation errors on this approximation. Consequently, it is possible to determine how to jointly choose the space and time grid sizes and the cut off parameter (Formula presented.). © 2014 Springer Science+Business Media Dordrecht.en
dc.description.sponsorshipThe authors would like to recognize the support of the PECOS center at ICES, University of Texas at Austin (Project Number 024550, Center for Predictive Computational Science). Support from the VR project "Effektiva numeriska metoder for stokastiska differentialekvationer med tillampningar" and King Abdullah University of Science and Technology (KAUST) is also acknowledged. The research has also been supported by the Swedish Foundation for Strategic Research (SSF) via the Center for Industrial and Applied Mathematics (CIAM) at KTH. The second author is a member of the KAUST SRI center for Uncertainty Quantification.en
dc.publisherSpringer Natureen
dc.subjectA posteriori error estimatesen
dc.subjectDiffusion approximationen
dc.subjectError expansionen
dc.subjectFinite difference methoden
dc.subjectInfinite activityen
dc.subjectJump-diffusion modelsen
dc.subjectLévy processen
dc.subjectOption pricingen
dc.subjectParabolic integro-differential equationen
dc.subjectWeak approximationen
dc.titleComputable error estimates of a finite difference scheme for option pricing in exponential Lévy modelsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalBIT Numerical Mathematicsen
dc.contributor.institution106 Blandford Street, London, W1U 8AG, United Kingdomen
kaust.authorTempone, Raulen
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