Empirical Performance of a Spline-Based Implied Volatility Surface

Abstract

We propose a nonparametric spline based representation of the implied volatility surface 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. 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.