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

Matthias Fengler & Qihua Wang

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abstract Nonparametric methods for estimating the implied volatility surface 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, then the actual fitting algorithm is applied. These two-step estimators may be seriously biased when option prices are observed with measurement errors. Moreover, the nonlinear transformation of the option prices will make the error distribution less tractable. In this study, we propose a new one-step estimator for the implied volatility surface based on a least squares kernel smoother of the Black-Scholes formula. We demonstrate the estimator using German DAX index option data to recover the implied volatility surface.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=433200
   
type working paper (English)
   
keywords implied volatility surface, smile, Black-Scholes formula, least squares kernel smoothing
   
date of appearance 2003
series title Discussion Paper
publisher SEPS, University of St. Gallen, Switzerland (St. Gallen)
review not reviewed
   
citation Fengler, M., & Wang, Q. (2003). Fitting the Smile Revisited: A Least Squares Kernel Estimator for the Implied Volatility Surface. Discussion Paper: SEPS, University of St. Gallen, Switzerland (St. Gallen).