A transform approach to compute prices and Greeks of barrier options driven by a class of Levy processes

Marc Jeannin and Martijn Pistorius

Quantitative Finance, 2010, vol. 10, issue 6, 629-644

Abstract: In this paper we propose a transform method to compute the prices and Greeks of barrier options driven by a class of Levy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Levy model with hyper-exponential jumps. Inversion of these single Laplace transforms yields rapid, accurate results. These results are employed to construct an approximation of the prices and sensitivities of barrier options in exponential generalized hyper-exponential Levy models. The latter class includes many of the Levy models employed in quantitative finance such as the variance gamma (VG), KoBoL, generalized hyperbolic, and the normal inverse Gaussian (NIG) models. Convergence of the approximating prices and sensitivities is proved. To provide a numerical illustration, this transform approach is compared with Monte Carlo simulation in cases where the driving process is a VG and a NIG Levy process. Parameters are calibrated to Stoxx50E call options.

Keywords: Levy process; American options; American style derivative securities; Barrier options; martingales (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (19)

Downloads: (external link)
http://www.tandfonline.com/doi/abs/10.1080/14697680902896057 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:10:y:2010:i:6:p:629-644

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RQUF20

DOI: 10.1080/14697680902896057

Access Statistics for this article

Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral

More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().