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American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach

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Author Info

  • Carl Chiarella
  • Andrew Ziogas

Abstract

We consider the American option pricing problem in the case where the underlying asset follows a jump-diffusion process. We apply the method of Jamshidian to transform the problem of solving a homogeneous integro-partial differential equation (IPDE) on a region restricted by the early exercise (free) boundary to that of solving an inhomogeneous IPDE on an unrestricted region. We apply the Fourier transform technique to this inhomogeneous IPDE in the case of a call option on a dividend paying underlying to obtain the solution in the form of a pair of linked integral equations for the free boundary and the option price. We also derive new results concerning the limit for the free boundary at expiry. Finally, we present a numerical algorithm for the solution of the linked integral equation system for the American call price, its delta and the early exercise boundary. We use the numerical results to quantify the impact of jumps on American call prices and the early exercise boundary.

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File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802221672
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 16 (2009)
Issue (Month): 1 ()
Pages: 37-79

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Handle: RePEc:taf:apmtfi:v:16:y:2009:i:1:p:37-79

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Web page: http://www.tandfonline.com/RAMF20

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Related research

Keywords: American options; jump-diffusion; Volterra integral equation; free boundary problem; Fourier transform;

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Cited by:
  1. Mahayni, Antje & Schoenmakers, John G.M., 2011. "Minimum return guarantees with fund switching rights—An optimal stopping problem," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1880-1897.

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