Alternative tilts for nonparametric option pricing

Abstract

This paper generalizes the nonparametric approach to option pricing of Stutzer (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie-Read family of divergence measures. While the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk-neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distribution of the underlying asset is estimated. In a simple Black-Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston (1993). Our extension of Stutzer's technique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed.

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

“…Examples include neural networks (Hutchinson, Lo, & Poggio, 1994), implied binomial latices (Rubinstein, 1994;Jackwerth & Rubinstein, 1996) and kernel density estimators (Aït-Sahalia & Lo, 1998;Broadie, Detemple, Ghysels, & Tórres, 2000a;Hamid & Habib, 2005;Birke & Pilz, 2009). That is, when the historical sample of index returns is lighter tailed than the real distribution of the underlying, the Pearson's chi-square based scheme outperforms the methods proposed by Stutzer (1996) and Haley and Walker (2010). This is consistent with the claims of Haley and Walker (2010) that the Euclidean-based scheme outperforms all other methods whenever the historical sample distribution is heavier tailed than real distribution of the underlying.…”

On the calibration of mortality forward curves

“…Results suggest that canonical valuation has merits in both applications. Further extensions of canonical valuation have been considered by Alcock and Carmichael (2008), Alcock and Auerswald (2010), Haley and Walker (2010), and Liu (2010).…”

“KLICing” there and back again: Portfolio selection using the empirical likelihood divergence and Hellinger distance

“…4 Other disparity choices have been successfully explored in similar applications. For example, Robertson et al (2005) explore forecasting using different disparity measures (among them EL); Haley and McGee (2006) demonstrate that portfolio selection based on the sum-of-squared deviations (Euclidean) distance is the disparity-based representation of SF and the SR; and Haley and Walker (2010), building on Stutzer (1996) and Gray and Newman (2005), explore the merits of alternative disparity measures in option pricing. Additionally, the econometrics literature on minimum-disparity estimation makes extensive use of the EL divergence and HE distance.…”