Articlegreen2010

EXPANSION FORMULAS FOR EUROPEAN OPTIONS IN A LOCAL VOLATILITY MODEL

Eric Benhamou · Emmanuel Gobet A · Mohammed Miri

49 citations0/0 files storedInternational Journal of Theoretical and Applied Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

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.

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References

2006The Malliavin Calculus and Related Topics 1994Implied Binomial Trees 2000Derivatives in Financial Markets with Stochastic Volatility 1989Computing the Constant Elasticity of Variance Option Pricing Formula 1999Equivalent Black volatilities 2005A General Asymptotic Implied Volatility for Stochastic Volatility Models 2005Stochastic Volatility Model with Time‐dependent Skew 2009Smart expansion and fast calibration for jump diffusions

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2013Closed-Form Expansion, Conditional Expectation, and Option Valuation 2013Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models 2013Adjoint Expansions in Local Lévy Models 2014On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model 2013Weak approximation of averaged diffusion processes

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