Bayesian versus Maximum Likelihood Estimation of Term Structure Models Driven by Latent Diffusions

Abstract

This paper provides an econometric analysis of parameter estimation for continuous-time affine term structure models that are driven by latent diffusions. Simulating an affine two factor short rate model where one process is Gaussian and the other factor is square root we perform a comparison between Markov Chain Monte Carlo (MCMC) and maximum likelihood (ML) estimation. To cope with the discrepancy between a continuous-time formulation and data only available in discrete time, we use closed-form expansions of the transition densities. In order to find reasonable starting values for both MCMC and ML estimation we employ genetic algorithms with penalty functions for the parameter restrictions. For ML estimation we employ both simplex and gradient based solvers. We find that with only a few exceptions the MCMC estimates reveal the true parameters and are in general more consistent within different estimation procedures than maximum likelihood estimation. For both estimation methodologies we observe negative correlation between the estimates of the factor loadings and the estimates of the unconditional mean of the square root process. Finally we find that both methodologies identify time series of latent state variables that are more likely than the data generating process itself.