Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds

The Journal of the American Statistical Association, 2011

33 Pages Posted: 12 Dec 2009 Last revised: 29 Mar 2011

Alejandro Cruz-Marcelo

Capital One Auto Finance

Katherine Ensor

Rice University - George R. Brown School of Engineering

Gary R. Rosner

University of Texas at Houston - M.D. Anderson Cancer Center

Date Written: December 9, 2009

Abstract

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.

Keywords: Credit spread; Dirichlet process mixture; Hierarchical model; Nonparametric Bayes; Treasury bond; Yield curve.

JEL Classification: E43, C11

Suggested Citation

Cruz-Marcelo, Alejandro and Ensor, Katherine and Rosner, Gary R., Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds (December 9, 2009). The Journal of the American Statistical Association, 2011. Available at SSRN: https://ssrn.com/abstract=1521323

Alejandro Cruz-Marcelo (Contact Author)

Capital One Auto Finance ( email )

7933 Preston Road
Plano, TX 75093
United States

Katherine Ensor

Rice University - George R. Brown School of Engineering ( email )

United States

Gary R. Rosner

University of Texas at Houston - M.D. Anderson Cancer Center ( email )

1515 Holocombe Blvd
Houston, TX 77030
United States

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