Fitting the Smile Revisited: A Least Squares Kernel Estimator for the Implied Volatility Surface

Matthias Fengler and Qihua Wang

No 2003,25, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: Nonparametric methods for estimating the implied volatility surface or the implied volatility smile are very popular, since they do not impose a specific functional form on the estimate. Traditionally, these methods are two-step estimators. The first step requires to extract implied volatility data from observed option prices, in the second step the actual fitting algorithm is applied. These two-step estimators may be seriously biased when option prices are observed with measurement errors. Moreover, after the nonlinear transformation of the option prices the error distribution will be complicated and less tractable. In this study, we propose a one-step estimator for the implied volatility surface based on a least squares kernel smoother of the Black-Scholes formula. Consistency and the asymptotic distribution of the estimate are provided. We demonstrate the estimator using German DAX index option data to recover the smile and the implied volatility surface.

Keywords: implied volatility surface; smile; Black-Scholes formula; least squares kernel smoothing (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (5)

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