Volatility-dependent probability weighting and the dynamics of the pricing kernel puzzle

Abstract

In order to estimate volatility-dependent probability weighting functions, we obtain risk neutral and physical densities from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) stochastic volatility and jumps model. Across volatility levels, we find pronounced inverse S-shapes, i.e. small probabilities are overweighted, and probability weighting almost monotonically increases in volatility, indicating higher skewness preferences and crash aversion in volatile market environments. Moreover, by estimating probabilistic risk attitudes, equivalent to the share of risk aversion related to probability weighting, we shed further light on the pricing kernel puzzle. While pricing kernels estimated from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) model display the typical U-shape as documented in the literature, pricing kernels—net of probability weighting—are strictly monotonically decreasing and thus in line with economic theory. Equivalently, we find risk aversion to be positive across wealth levels. Our results are robust to alternative maturities, wealth percentiles, alternative functional forms, a nonparametric empirical setting and variations of the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) coefficient estimates.