EXPANSION FORMULAS FOR EUROPEAN OPTIONS IN A LOCAL VOLATILITY MODEL

Eric Benhamou (), E. Gobet () and M. Miri ()
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E. Gobet: Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, BP 53, 38041 Grenoble cedex 9, France
M. Miri: Pricing Partners, 204 rue de Crimée, 75019, Paris, France

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 04, 603-634

Abstract: Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms.

Keywords: Local volatility model; European options; asymptotic expansion; Malliavin calculus; small diffusion process; CEV model (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (19)

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Working Paper: Expansion formulas for European options in a local volatility model (2010)
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DOI: 10.1142/S0219024910005887

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