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On American Options Under the Variance Gamma Process

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Author Info

  • Ariel Almendral
  • Cornelis W. Oosterlee

Abstract

American options are considered in a market where the underlying asset follows a Variance Gamma process. A sufficient condition is given for the failure of the smooth fit principle for finite horizon call options. A second-order accurate finite-difference method is proposed to find the American option price and the exercise boundary. The problem is formulated as a Linear Complementarity Problem and solved numerically by a convenient splitting. Computations have been accelerated with the help of the Fast Fourier Transform. A stability analysis shows that the scheme is conditionally stable, with a mild stability condition of the form k�=�O(&7Clog(h)&7C-1). The theoretical results are verified numerically throughout a series of numerical experiments.

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File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600724885
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Bibliographic Info

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

Volume (Year): 14 (2007)
Issue (Month): 2 ()
Pages: 131-152

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Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:131-152

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

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Related research

Keywords: Integro-differential equations; variance gamma; finite differences; FFT;

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Cited by:
  1. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
  2. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
  3. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
  4. Fang, Fang & Oosterlee, Kees, 2008. "Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions," MPRA Paper 9248, University Library of Munich, Germany.
  5. Erhan Bayraktar & Hao Xing, 2009. "Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions," Computational Statistics, Springer, vol. 70(3), pages 505-525, December.

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