Expansion formulas for European options in a local volatility model

Eric Benhamou (1) , Emmanuel Gobet (2) , Mohammed Miri (1, 2)

1 Pricing Partners
2 MATHFI - Mathématiques financières

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.

Mots clés: Malliavin calculus; small diffusion process; CEV model; Local volatility model; European options; asymptotic expansion

Domaines: Probabilités [math.PR]; Economies et finances

Eric Benhamou, Emmanuel Gobet, Mohammed Miri. Expansion formulas for European options in a local volatility model. International Journal of Theoretical and Applied Finance, 2010, 13 (4), pp.603-634. ⟨10.1142/S0219024910005887⟩. ⟨hal-00325939⟩