Title: A Bayesian estimate of the pricing kernel
Authors: Chiara Legnazzi - USI and Swiss Finance Institute, Lugano (Switzerland) [presenting]
Giovanni Barone-Adesi - University of Lugano (Switzerland)
Antonietta Mira - University of Lugano (Switzerland)
Abstract: The aim is to present a Bayesian nonparametric approach to model the Pricing Kernel, defined as the present value of the ratio between the risk neutral density, $q$, and the modified physical density, $p^*$. The risk neutral density is derived by fitting an asymmetric GARCH to the cross-section of the out-of-the-money call and put options written on the S\& P500 index. The modified physical density is defined as the sum with Poisson-Dirichlet weights of the risk neutral density rescaled for the equity premium and the traditional physical density, estimated through an asymmetric GARCH fitted on the S\& P500 log-returns. The nonparametric approach does not impose any a priori restriction on the shape of the Pricing Kernel and the Bayesian component allows to include into the physical density estimation some forward-looking information coming from the option market. As a result, the heterogeneity between the physical and the risk neutral measures, which is one of the main drivers of the pricing kernel puzzle, disappears and both densities are conditional on a comparable information set. The Pricing Kernel estimates gain accuracy in the tail estimation and display a monotonically decreasing shape across multiple time to maturities, consistently with the classical theory.