A Three-factor Econometric Model of the U.S. Term Structure"We estimate a three-factor model to fit both the time-series dynamics and cross-sectional shapes of the U.S. term structure. In the model, three unobserved factors drive a discrete-time stochastic discount process, with one factor reverting to a fixed mean and a second factor reverting to a third factor. To exploit the conditional density of yields, we estimate the model with a Kalman filter, a procedure that also allows us to use data for six maturities without making special assumptions about measurement errors. The estimated model reproduces the basic shapes of the average term structure, including the hump in the yield curve and the flat slope of the volatility curve. A likelihood ratio test favors the model over a nested two-factor model. Another likelihood ratio test, however, rejects the no-arbitrage restrictions the model imposes on the estimates. An analysis of the measurement errors suggests that the three factors still fail to capture enough of the comovement and persistence of yields"--Abstract. |
Common terms and phrases
120 Maturity Actual and Implied affine yields arbitrage conditions arbitrage restrictions autocorrelations Backus and Zin bond prices bond returns bond yields capture Chen and Scott coefficients conditional density conditional expectation conditional moments correlation derive the factors discrete-time estimate the model Federal Reserve Bank fixed mean full-sample estimates Gong and Remolona hump Implied Volatility Interest Rates Kalman filter likelihood function likelihood ratio test linear long end Longstaff Maturity in months maximum likelihood procedure McCulloch and Kwon mean reversion rate measurement equations measurement errors one-factor model parameter estimates parameters reported percent a month price of risk pricing kernel rates of mean reported in Table sample period Schwartz second factor reverts shocks short end short rate six maturities slow mean reversion stochastic discount factor stochastic processes term premia third factor Three-Factor Econometric Model three-factor model time-series transition equations two-factor model U.S. term structure variance volatility curve Φι