Closed Forms for European Options in a Local Volatility Model
32 Pages Posted: 1 Oct 2008
Date Written: September 30, 2008
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
JEL Classification: G13
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