Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds
Capital One Auto Finance
Rice University - George R. Brown School of Engineering
Gary R. Rosner
University of Texas at Houston - M.D. Anderson Cancer Center
December 9, 2009
The Journal of the American Statistical Association, 2011
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 model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. 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. After describing the proposed model, 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 are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material.
Number of Pages in PDF File: 33
Keywords: Credit spread; Dirichlet process mixture; Hierarchical model; Nonparametric Bayes; Treasury bond; Yield curve.
JEL Classification: E43, C11
Date posted: December 12, 2009 ; Last revised: March 29, 2011