McKean’s Method 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 Society for Computational Economics in its series Computing in Economics and Finance 2003 with number 39.
Date of creation: 01 Aug 2003
Date of revision:
Jump-diffusion model; American option; Free boundary problem;
Other versions of this item:
- Carl Chiarella & Andrew Ziogas, 2004. "McKean's Methods Applied to American Call Options on Jump-Diffusion Processes," Research Paper Series 117, Quantitative Finance Research Centre, University of Technology, Sydney.
- 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
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