On American Options Under the Variance Gamma Process
AbstractAmerican 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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Bibliographic InfoArticle provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 14 (2007)
Issue (Month): 2 ()
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Web page: http://taylorandfrancis.metapress.com/link.asp?target=journal&id=100141
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- 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.
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