The use of Bayes factors to compare interest rate term structure models

Abstract

Studies of the term structure of interest rates try to explain the relationship between the yield to maturity on zero-coupon bonds and their time to maturity. Over the years, many theoretical models have been developed to explain the stylized facts of U.S. Treasury yields; however, model comparison, parameter estimation and hypothesis testing remain thorny issues. The purpose of this paper is to show that Bayesian methods and Markov Chain Monte Carlo (MCMC) methods, in particular, may help resolve a number of these problems, especially those related to model comparison. We use MCMC to compare the seminal models of Vasicek and Cox, Ingersoll and Ross (CIR). The most surprising result of our analysis is that one of these two models is almost 50 000 times more likely than the other. In contrast, results in the previous literature have been much more ambiguous because they are based on a variety of goodness-of-fit measures. A Monte Carlo study shows that these results are not spurious: the MCMC method is able to select the correct data generation model, whereas goodness-of-fit measures are virtually indistinguishable regardless of whether the data were generated from Vasicek or CIR.