Static and Dynamic Nested Sampling for Yield Curve Model Selection

In the previous chapter, we introduced a Bayesian framework for calibrating the Nelson and SiegelNelson, Charles R.Siegel, Andrew F. model of the term structure of interest rates using Markov Chain Monte Carlo (MCMC) methods. In this chapter, we extend this Bayesian framework by now considering model selection using the Bayesian evidence metric. We utilize the static and dynamic nested sampling algorithms to compute the Bayesian evidence metric on training data and use this evidence to select the appropriate model for the yield curve. The population of models we compare are different variations or subsets of the Nelson and SiegelNelson, Charles R.Siegel, Andrew F. model. We also introduce the automatic relevance determinationAutomatic relevance determination Nelson and SiegelNelson, Charles R.Siegel, Andrew F. (ARD-NS) model, which we train using the No-U-Turn Sampler MCMC technique. This ARD-NS model allows one to automatically rank the short-term, medium-term, and long-term factor loading to determine which one is driving the yield curve at that particular moment in a probabilistically robust manner. We analyze simulated yield curve data and a time series of US corporate bond yield curves. Our analysis shows that the evidence framework is robust in detecting the model generating the underlying yield curve data, and results from the ARD-NS model show that the yield curve dynamics are mostly driven by the medium-term (i.e., curvature) factor loading for the period under consideration. This framework can easily be extended to cover a broader class of term structure models.