Unconstrained fitting of implied volatility surfaces using a mixture of normals

Riccardo Rebonato and Maria Teresa Cardoso

Journal of Risk

Abstract: ABSTRACT The paper presents a method of estimating a smooth volatility surface from the market prices of plain-vanilla options. Obtaining reliable surfaces is important for risk management purposes and for calibrating models. The method we suggest uses a mixture of (log)normals that are combined in an unconstrained fashion to produce risk-neutral densities that display both kurtosis and skew. The method is shown to provide excellent fits to a variety of model or market volatility surfaces.

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