Improved Implementation of Local Volatility and Its Application to S&P 500 Index Options

Abstract

We examine the empirical performance of a spline-based, local volatility surface for the period 2000–2005. Our findings indicate that the proposed model outperforms the best-performing implied volatility–based model reported in the current literature for European-style S&P 500 Index options. These results are achieved by a thin-plate spline-based representation and an alternate knot-placement method that has not been explored in previous work. Also, besides the spline-based representation, we find that no additional regularization is required. Although the primary objective of our study is the improved pricing of European-style options, our results have implications for pricing exotic options that employ Dupire's equation.