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

TL;DR

This paper introduces a Bayesian Beta Markov Random Field model for calibrating implied risk neutral densities across different maturities and dates, capturing dependencies and enabling efficient information pooling.

Contribution

It proposes a novel Bayesian dynamic Beta Markov Random Field model for joint calibration of implied densities, improving flexibility and dependence modeling over previous methods.

Findings

Model captures time dependence within maturities.

Model accounts for cross-maturity dependencies.

Enhanced calibration accuracy demonstrated.

Abstract

We build on the work in Fackler and King 1990, 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 problem encompasses model flexibility, parameter parsimony and, more importantly, information pooling across densities.