A Bayesian Beta Markov Random Field Calibration of the Term Structure of Implied Risk Neutral Densities

Abstract

We build on the derivative pricing calibration literature, and propose a more general calibration model for implied risk neutral densities. Our model allows for the joint calibration of a set of densities at different maturities and dates through a Bayesian dynamic Beta Markov Random Field. Our approach allows for possible time dependence between densities with the same maturity, and for dependence across maturities at the same point in time. This approach to the risk neutral density calibration problem encompasses model flexibility, parameter parsimony, and, more importantly, information pooling across densities. This proposed methodology can be naturally extended to other areas where multidimensional calibration is needed.