On American Options Under the Variance Gamma Process

Ariel Almendral and Cornelis Oosterlee

Applied Mathematical Finance, 2007, vol. 14, issue 2, 131-152

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.

Keywords: Integro-differential equations; variance gamma; finite differences; FFT (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (19)

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DOI: 10.1080/13504860600724885

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