Nonparametric Option Pricing with Generalized Entropic Estimators

Abstract

We propose a family of nonparametric estimators for an option price that require only the use of underlying return data, but can also easily incorporate information from observed option prices. Each estimator comes from a risk-neutral measure minimizing generalized entropy according to a different Cressie-Read discrepancy. We apply our method to price S&P 500 options and the cross-section of individual equity options, using distinct amounts of option data in the estimation. Estimators incorporating mild nonlinearities produce optimal pricing accuracy within the Cressie-Read family and outperform several benchmarks such as the Black-Scholes and different GARCH option pricing models. Overall, we provide a powerful option pricing technique suitable for scenarios of limited option data availability.

Keywords: Risk-Neutral Measure, Option Pricing, Risk Premium, Nonparametric Estimation, Stochastic Volatility, Jumps, Cressie-Read Discrepancies

JEL Classification: C1, C5, C6, G1