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

10 Pages Posted: 7 Aug 2007 Last revised: 18 Sep 2012

See all articles by Valdo Durrleman

Valdo Durrleman

Ecole Polytechnique - Centre de Mathematiques Appliquees - CNRS

Date Written: August 7, 2007

Abstract

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 volatility, spot volatility, robustness formula, martingale central limit theorem

JEL Classification: G13

Suggested Citation

Durrleman, Valdo, Convergence of At-The-Money Implied Volatilities to the Spot Volatility (August 7, 2007). Available at SSRN: https://ssrn.com/abstract=1005314 or http://dx.doi.org/10.2139/ssrn.1005314

Valdo Durrleman (Contact Author)

Ecole Polytechnique - Centre de Mathematiques Appliquees - CNRS ( email )

Palaiseau, 91128
France

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