McKean's Methods Applied to American Call Options on Jump-Diffusion Processes
AbstractIn 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.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 117.
Date of creation: 01 Feb 2004
Date of revision:
american options; jump-diffusion; volterra integral equation; free-boundary problem;
Other versions of this item:
- Andrew Ziogas & Carl Chiarella, 2003. "McKean’s Method applied to American Call Options on Jump-Diffusion Processes," Computing in Economics and Finance 2003 39, Society for Computational Economics.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-06-02 (All new papers)
- NEP-CMP-2004-06-02 (Computational Economics)
- NEP-FIN-2004-06-02 (Finance)
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Research Paper Series
83, Quantitative Finance Research Centre, University of Technology, Sydney.
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