Abstract
This paper estimates the interest rate term structures of Treasury and individual corporate bonds using a robust criterion. The Treasury term structure is estimated with Bayesian regression splines based on nonlinear least absolute deviation. The number and locations of the knots in the regression splines are adaptively chosen using the reversible jump Markov chain Monte Carlo method. Due to the small sample size, the individual corporate term structure is estimated by adding a positive parametric credit spread to the estimated Treasury term structure using a Bayesian approach. We present a case study of U.S. Treasury STRIPS (Separate Trading of Registered Interest and Principal of Securities) and AT&T bonds from April 1994 to December 1996. Compared with several existing term structure estimation approaches, the proposed method is robust to outliers in our case study.
Highlights
It is well known that least squares estimates can be sensitive to outliers
We extend the normal linear Bayesian regression splines model of Denison, Mallick, and Smith (1998) to the nonlinear term structure model based on the least absolute deviation criterion
This paper presents a robust approach to term structure estimation by adopting the nonlinear least absolute deviation criterion
Summary
It is well known that least squares estimates can be sensitive to outliers. bond prices often exhibit heavy tails with possible outliers (Schwartz 1998; Jarrow, Ruppert, and Yu 2004). Schwartz (1998) uses a robust measure and finds that almost 10% of the US Treasury securities in the Fixed Income database are outliers. This paper considers term structure estimation of Treasury and corporate bonds using a robust approach. Fisher, Nychka, and Zervos (1995), JRY (Jarrow, Ruppert, and Yu 2004) and Li and Yu (2005) present penalized (smoothing) splines approaches where the forward rate curve is smoothed with roughness penalty. In all these works, the least squares method is used and is not robust to outliers. Schwartz (1998) estimates the term structure by modeling the forward interest rate with a piecewise constant curve using fixed knots, minimizing the usual sum of squared residuals.
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