Testing Alternative Measure Changes in Nonparametric Pricing and Hedging of European Options

Haley and Walker [Haley, M.R., & Walker, T. (2010). Journal of Futures Markets, 30, 983-1006] present the Euclidean and Empirical Likelihood nonparametric option pricing models as alternative tilts to Stutzer's [Stutzer, M. (1996). Journal of Finance, 51, 1633-1652] Canonical pricing method. We empirically test the comparative strengths of each of these methods using a large sample of traded options on the S&P100 Index. Furthermore, we explore an additional tilt based on Pearson's chi-square, and derive and empirically test nonparametric delta hedges for each of these approaches. Differences in the pricing performance of the various tilts are a function of differences between the sample distribution and the real distribution of the underlying. When the sample distribution displays fatter (thinner) tails and/or higher (lower) volatility than the true distribution, the Euclidean (Pearson's chi-square) model outperforms. Significantly, when these nonparametric methods utilize information contained in a small number of observed option prices they often outperform the implied volatility Black and Scholes [Black, F., & Scholes, M. (1973). Journal of Political Economy, 81, 637-654] model. These pricing performance differences do not translate into static and dynamic hedging performance differences. However, each of the nonparametric models induce an implied volatility smile and term structure that generally agree in form with the smile and term structure embedded in market prices.