Essays on the Term Structure of Interest Rates

Abstract

In the first essay, a multiprocess mixture model (MM) is used to explain the time variation in the relationship between forward rates and future spot rates. I find considerable support for modeling the relationship between one-month spot rates and forward rates in a timevarying framework using data for the U.S. Treasury Bill market for the period 1959 to 1991. The posterior probabilities from the MM model confirm that the period between October 1979 to 1982 represents a change in policy regime for the U.S. Federal Reserve. More specifically, the probabilities show that a structural change took place in the slope of the relationship between spot and forward rates. This is in accord with the term premium becoming more variable with the level of interest rates. The term structure relationship is found to be stable in the period after 1982 when the Fed returned to partial interest rate targeting. Finally, I find that the predictive power of forward rates varies considerably over time and that this power decreases significantly in the periods identified with regime changes. In the second essay, I compare seven term structure estimation methods empirically in terms of zero and forward rate curves as well as price- and yield-prediction accuracy. A marked difference in the performance of the models between in- and out-of-sample predictions is documented. Particularly, models that generate relatively smooth yield and forward rate curves do not perform well in-sample but produce the best out-of-sample forecasts. The results support the conclusion from a previous study that modeling the forward rate function as a cubic spline with adaptive parameters produces the best overall results. The most interesting finding is that the Neslon-Siegel model estimated from Treasury Strips with only three parameters can price coupon bonds out-of-sample more accurately than more complicated estimation methods fitted to coupon bonds.