Semiparametric Estimation of Probability Weighting Functions Implicit in Option Prices

This paper develops a semiparametric estimation method that jointly identifies the probability weighting and utility functions implicit in option prices. Our econometric method avoids direct specification of the objective conditional return distributions, which are instead obtained by transforming the options’ implied risk-neutral distributions according to the posited rank-dependent utility model. We nonparametrically estimate the probability weighting function using the kernel density of suitable utility-adjusted probability integral transforms. The parameters of the utility function are estimated by maximizing the resulting profile likelihood. We establish the asymptotic properties of our estimation procedure, and demonstrate its good finite sample performance in Monte Carlo simulations. Empirical results based on S&P 500 index option prices and returns over the period 1996–2023 reveal the relevance of probability weighting, in particular at the monthly horizon where the weighting function is inverse-S shaped, which is robust to various specifications of the utility function.