Expansion formulas for European options in a local volatility model

Eric Benhamou (), Emmanuel Gobet () and Mohammed Miri ()
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Emmanuel Gobet: MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique
Mohammed Miri: Pricing Partners - Pricing Partners, MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique

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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: Malliavin calculus; small diffusion process; CEV model; Local volatility model; European options; asymptotic expansion (search for similar items in EconPapers)
Date: 2010-06
Note: View the original document on HAL open archive server: https://hal.science/hal-00325939v1
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Citations: View citations in EconPapers (15)

Published in International Journal of Theoretical and Applied Finance, 2010, 13 (4), pp.603-634. ⟨10.1142/S0219024910005887⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00325939

DOI: 10.1142/S0219024910005887

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