Article2008

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

30 citations0/0 files storedJournal of Applied Probability

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

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.

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References

2003Limit Theorems for Stochastic Processes 1998Robustness of the Black and Scholes Formula 2003What Type of Process Underlies Options? A Simple Robust Test 2004Computing the implied volatility in stochastic volatility models 2002Asymptotics and calibration of local volatility models 1978Sur l'int�grabilit� uniforme des martingales exponentielles 1999A market model for stochastic implied volatility 2006Approximation and Calibration of Short-Term Implied Volatilities Under Jump-Diffusion Stochastic Volatility

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