McKean's Methods Applied to American Call Options on Jump-Diffusion Processes

Carl Chiarella and Andrew Ziogas

No 117, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In this paper we 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. We extend McKean's incomplete Fourier transform approach to solve the free boundary problem under Merton's framework, with the distribution for the jump size remaining unspecified. We show how our results are consistent with those of Gukhal (2001), who derived the same integral equation using the Geske-Johnson discretisation approach. The paper also derives some results concerning the limit for the free boundary at expiry, and presents an iterative numerical algorithm for solving the linked integral equation system for the American call's price 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: 81 pages
Date: 2004-02-01
New Economics Papers: this item is included in nep-cmp and nep-fin
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp117.pdf (application/pdf)

Related works:
Working Paper: McKean’s Method applied to American Call Options on Jump-Diffusion Processes (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:117

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