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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.

Dynamic term structure model, gaussian, estimation

Abstract:
A bond or swap that is sold before it matures has an uncertain return. There is strong empirical evidence that long-term interest rates contain a time-varying risk premium. Interest rate options may contain information about this risk premium because their prices are sensitive to the volatility and market prices of the risk factors that drive interest rates. We ask whether risk premiums estimated using interest rate option prices are better able to predict changes in long-term interest rates. More specifically, we estimate 3-factor affine term structure models using the joint time series of interest rate cap prices and swap rates with different maturities. Our main finding is that the risk premiums estimated using interest rate option prices are better able to predict excess returns, both in- and out-of-sample. In contrast to previous literature, the arbitrage-free models with the most predictive power contain a stochastic volatility component.