Estimating the term structure with a semi-parametric Bayesian population model: An application to corporate bonds

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a new framework for estimating the term structure of interest rates for corporate bonds. The proposed model jointly estimates term structures by means of a Bayesian hierarchical model with a non-parametric prior probability model based on Dirichlet process mixtures. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. The modeling methodology borrows strength across similar term structures for purposes of estimation. After describing the new approach, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests indicate superior performance of our method as compared with the popular approach of grouping the corporate bonds by credit rating.We also discuss the relative performance of different modeling strategies that introduce dependence on covariates into Bayesian nonparametric models. We show that 1) nonparametric models using different strategies for modeling covariates can show noteworthy differences when they are being used for prediction, even though they produce otherwise similar posterior inference results, and 2) when the predictive density is a mixture, it is convenient to make the weights depend on the covariates in order to produce better estimators. Such claims are supported by comparing the Linear DDP (an extension of the Sethuraman representation) and the Conditional DP (which augments the nonparametric distribution to include the covariates); we apply those methods to a simulated data set and to data from a pharmacokinetic meta-analysis.