Computable error estimates of a finite difference scheme for option pricing in exponential Lévy models
Type
ArticleAuthors
Kiessling, JonasTempone, Raul

KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2014-05-06Online Publication Date
2014-05-06Print Publication Date
2014-12Permanent link to this record
http://hdl.handle.net/10754/566088
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Show full item recordAbstract
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.Citation
Kiessling, J., & Tempone, R. (2014). Computable error estimates of a finite difference scheme for option pricing in exponential Lévy models. BIT Numerical Mathematics, 54(4), 1023–1065. doi:10.1007/s10543-014-0490-4Sponsors
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.Publisher
Springer NatureJournal
BIT Numerical Mathematicsae974a485f413a2113503eed53cd6c53
10.1007/s10543-014-0490-4