Probability weighting functions implied in options prices

The empirical pricing kernels estimated from index options are non-monotone (Rosenberg and Engle, 2002 and Bakshi et al., 2010) and the corresponding risk-aversion functions can be negative (Aït-Sahalia and Lo, 2000 and Jackwerth, 2000). We show theoretically that these and several other properties of empirical pricing kernels are consistent with rank-dependent utility model with probability weighting function, which overweights tail events. We also estimate the pricing kernels nonparametrically from the Standard & Poor's 500 index options and construct empirical probability weighting functions. The estimated probability weights typically have the inverse-S shape, which overweights tail events and is widely supported by the experimental decision theory.