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Convergence of At-The-Money Implied Volatilities to the Spot Volatility

Part of: Limit theorems Mathematical economics Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Valdo Durrleman
Valdo Durrleman*
Affiliation:
École Polytechnique
*
∗Postal address: Centre de Mathématiques Appliquées, École Polytechnique - CNRS, Route de Saclay, 91128 Palaiseau, France. Email address: [email protected]
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Abstract

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We study the convergence of at-the-money implied volatilities to the spot volatility in a general model with a Brownian component and a jump component of finite variation. This result is a consequence of the robustness of the Black-Scholes formula and of the central limit theorem for martingales.

Keywords

Implied volatilityspot volatilityrobustness formulamartingale central limit theorem

MSC classification

Secondary: 91B70: Stochastic models 60F05: Central limit and other weak theorems 60H05: Stochastic integrals
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 542 - 550
Copyright
Copyright © Applied Probability Trust 2008 

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