Volume 30 Number 1 June 2005

Bayesian Estimation of Short Rate Models

Philip Gray

Abstract

Estimating continuous-time short-rate models is challenging since the likelihood function for most popular models is unknown. While approximate likelihood functions are often used, this practice induces bias into the estimation process. This paper explores a Bayesian method of estimating short-rate models. While the approach also employs an approximate likelihood, data augmentation is utilised to mitigate discretisation bias. The results suggest that Bayesian estimates of posterior densities for model parameters closely resemble true posterior densities. While non-essential for point estimation, a small degree of data augmentation is useful in recovering accurate posterior densities and reducing the bias in estimates of bond price. These findings are encouraging for cases the many where exact likelihood-based estimation is impossible and approximations must be relied upon.