SOME PRICING TOOLS FOR THE VARIANCE GAMMA MODEL

Jean-Philippe Aguilar ()
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Jean-Philippe Aguilar: Modeling Department, BRED Banque Populaire, 18 quai de la Râpée, Paris 75012, France

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 04, 1-35

Abstract: We establish several closed pricing formulas for various path-independent payoffs, under an exponential Lévy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools from Mellin transform theory as well as from multidimensional complex analysis. Particular focus is made on the symmetric process, but extension to the asymmetric process is also provided. Speed of convergence and comparison with numerical methods (Fourier transform, quadrature approximations, Monte Carlo simulations) are also discussed; notable feature is the accelerated convergence of the series for short-term options, which constitutes an interesting improvement of numerical Fourier inversion techniques.

Keywords: Lévy process; variance gamma process; stochastic volatility; option pricing (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219024920500259

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