A New Perspective on Gaussian Dynamic Term Structure Models

Abstract

In any canonical Gaussian dynamic term structure model (GDTSM), the conditional forecasts of the pricing factors are invariant to the imposition of no-arbitrage restrictions. This invariance is maintained even in the presence of a variety of restrictions on the factor structure of bond yields. To establish these results, we develop a novel canonical GDTSM in which the pricing factors are observable portfolios of yields. For our normalization, standard maximum likelihood algorithms converge to the global optimum almost instantaneously. We present empirical estimates and out-of-sample forecasts for several GDTSMs using data on U.S. Treasury bond yields. (JEL E43, G12, C13) Dynamic models of the term structure often posit a linear factor structure for a collection of yields, with these yields related to underlying factors P through a no-arbitrage relationship. Does the imposition of no-arbitrage in a Gaussian dynamic term structure model (GDTSM) improve the out-of-sample forecasts of yields relative to those from the unconstrained factor model, or sharpen model-implied estimates of expected excess returns? In practice, the answers to these questions are obscured by the imposition of over-identifying restrictions on the risk-neutral (Q) or historical (P) distributions of the risk factors, or on their market prices of risk, in addition to the cross-maturity restrictions implied by no-arbitrage. 1