A Bayesian Beta Markov Random Field calibration of the term structure of implied risk neutral densities

We build on Fackler and King (1990) and propose a 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. The model is a Bayesian dynamic beta Markov random field which allows for possible time dependence between densities with the same maturity and for dependence across maturities at the same point in time. The assumptions on the prior distribution allow us to compound the needs of model flexibility, parameter parsimony and information pooling across densities.