Abstracts

In this paper, we develop Markov Chain Monte Carlo (MCMC) algorithms to conduct a Bayesian inference analysis for multi-factor affine term structure models (ATSM).
We propose efficient sampling algorithms for the posterior distribution of parameters and latent states via the MCMC methods. The MCMC algorithms allow us to remove the stringent assumption imposed to break the stochastic singularity, and help us to decompose the high-dimensional inference problem into iterations of univariate sampling problems. With this sampling scheme, we conduct a full-fledged Bayesian analysis on two market data sets covering different economic regimes. The Bayesian inference delivers promising results in in-sample fitting, out-of-sample forecasting and model comparison.
First, we show the strength of the MCMC methods in reconstructing yield observations under the no arbitrage condition. The fitting errors are smaller than those obtained by the inversion-MLE method and the model-free method. We are also able to reconstruct the short rates, which is documented as a challenging task. The inferred short rates from the MCMC algorithm closely resemble the one month yield data.
Second, with the MCMC sampling method, we forecast future yield levels with satisfactory precision. We are able to forecast the twelve weeks ahead yield levels with out-of-sample errors within a couple of basis points. We run a horse-race among several conventional prediction methods. The Bayesian forecast performance of the three-factor model with one restricted variable dominates the ordinary least square prediction and frequentist-type prediction for all maturities. It also dominates the random walk prediction for all maturities greater or equal to one year.
At last, with the MCMC method, we conduct a Bayesian model comparison for different ATSMs. We find that the ranking of the models by the Bayesian model selection criteria is consistent with both in-sample fitting and out-of-sample forecast performances. We apply the model comparison analysis on the two data sets. The first data has the feature of non-normality and a humped shape of the volatility curve. It supports the three-factor model with one restricted state variable. The second data has the feature of non-normality, but has downward shape of volatility curve. It supports the three-factor model with Gaussian dynamics.