A New Perspective on Gaussian DTSMs

Abstract:     
This paper shows that, within any Gaussian dynamic term structure model (GDTSM), the historical distribution of the pricing factors P is invariant to the imposition of no-arbitrage restrictions, as well as to additional constraints that impinge only on the risk-neutral dynamics of P. It follows that, in these settings, GDTSM-implied forecasts of future values of P are identical to those from an unrestricted vector autoregressive model of P. 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 also extend our analysis to GDTSMs with reduced-rank risk premiums and to those with macroeconomic variables as pricing factors. Empirical estimates and out-of-sample forecasting results are presented for several GDTSMs using data on U.S. Treasury bond yields.

Keywords: Dynamic term structure model, gaussian, estimation

JEL Classifications: E43, G12, C13

Working Paper Series