Fall Seminar Series - September 30, 2004
University of Minnesota
School of Statistics
College of Liberal Arts

Semiparametric Estimation for the Interest Rate Term Structure

Yan Yu
Department of Quantitative Analysis and Operations Management
University of Cincinnati

Thursday, September 30, 2004
Note time chang: 3:30 PM, 115 Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall

Abstract

We provide a new methodology for estimating the term structure of corporate debt using a semiparametric penalized spline model. The method is applied to a case study of AT &T bonds. Typically, very few data are available on individual corporate bond prices, too little to find a nonparametric estimate of term structure from these bonds alone. This problem is solved by ``borrowing strength'' from Treasury bond data. More specifically, we combine a nonparametric model for the term structure of Treasury bonds with a parametric component for the credit spread. Our methodology generalizes the work of Fisher, Nychka, and Zervos (1995) in several ways. First, their model was developed for Treasury bonds only and cannot be applied directly to corporate bonds. Second, we more fully investigate the problem of choosing the smoothing parameter, a problem that is complicated because the forward rate is the derivative -log{D(t)}, where the discount function D is the function fit to the data. In our case study, estimation of the derivative requires substantially more smoothing than selected by generalized cross-validation (GCV). Another problem for smoothing parameter selection is possible correlation of the errors. We compare three methods of choosing the penalty parameter: generalized cross validation (GCV), the residual spatial autocorrelation (RSA) method of Ellner and Seifu (2002), and an extension of Ruppert's (1997) EBBS to splines. Third, we provide approximate sampling distributions based on asymptotics for the Treasury forward rate and the bootstrap for corporate bonds. Confidence bands and tests of interesting hypotheses, e.g., about the functional form of the credit spreads, are also discussed.

This talk is based on a recent paper that appeared in JASA, April 2004.

This is a joint work with Prof. Robert Jarrow and Prof. David Ruppert at Cornell University.