Estimating the term structure with a semiparametric bayesian hierarchical model: An application to corporate bonds

Alejandro Cruz-Marcelo, Katherine B. Ensor, Gary L. Rosner

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)387-395
Number of pages9
JournalJournal of the American Statistical Association
Issue number494
StatePublished - Jun 2011


  • Credit spread
  • Dirichlet process mixture
  • Hierarchical model
  • Nonparametric bayes
  • Treasury bond
  • Yield curve

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Estimating the term structure with a semiparametric bayesian hierarchical model: An application to corporate bonds'. Together they form a unique fingerprint.

Cite this