Empirical performance of a spline-based implied volatility surface

Abstract

Since the crash of 1987, it has been observed by option market participants that implied volatilities for out-of-the-money options are higher than predicted by the constant volatility Black-Scholes (1973) model. Option prices also exhibit dependence on time to expiry. The collection of these implied volatilities across strike and maturity is known as the implied volatility surface (IVS). We propose a nonparametric spline-based representation of the IVS and evaluate its empirical performance. Our findings indicate that the proposed model significantly outperforms the best performing implied volatility model reported in the current literature for the purpose of pricing European-style S&P500 index options. We further contribute to the empirical finance literature by choosing a proper model evaluation criterion. By measuring the leave-one-out cross-validation model pricing error of the thin-plate spline-based model, we demonstrate that this superior performance is not the result of overfitting. Although we have previously shown that spline-based models have superior empirical performance, the models considered in this study have advantages over the previously considered models.