American Call Options on Jump-Diffusion Processes: A Fourier Transform Approach

Carl Chiarella and Andrew Ziogas
Additional contact information
Andrew Ziogas: Integral Energy, Australia

No 174, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper considers the Fourier transform approach to derive the implicit integral equation for the price of an American call option in the case where the underlying asset follows a jump-diffusion process. Using the method of Jamshidian (1992), we demonstrate that the call option price is given by the solution to an inhomogeneous integro-partial differential equation in an unbounded domain, and subsequently derive the solution using Fourier transforms. We also extend McKean’s incomplete Fourier transform approach to solve the free boundary problem under Merton’s framework, for a general jump size distribution. We show how the two methods are related to each other, and also to the Geske-Johnson compound option approach used by Gukhal (2001). The paper also derives results concerning the limit for the free boundary at expiry, and presents a numerical algorithm for solving the linked integral equation system for the American call price, delta and early exercise boundary. This scheme is applied to Merton’s jump-diffusion model, where the jumps are log-normally distributed.

Keywords: American options; jump-diffusion; Volterra integral equation; free boundary problem (search for similar items in EconPapers)
JEL-codes: C61 D11 (search for similar items in EconPapers)
Pages: 89 pages
Date: 2006-05-01
New Economics Papers: this item is included in nep-cfn
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp174.pdf (application/pdf)

Related works:
Journal Article: American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach (2009)
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:uts:rpaper:174

Access Statistics for this paper

More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford ().