A three-factor econometric model of the U.S. term structure

We estimate and test a model of the U.S. term structure that fits both the time series of interest rates and the cross-sectional shapes of the yield and volatility curves. In the model, three unobserved factors drive a stochastic discount process that prices assets so as to rule out arbitrage opportunities. The resulting bond yields are conveniently affine in the factors. We use monthly zero-coupon yield data from January 1986 to March 1996 and estimate the model by applying a Kalman filter that takes into account the model's no-arbitrage restrictions and using only three maturities at a time. The parameter estimates describe a first factor that reverts slowly to a fixed mean and a second factor that reverts relatively quickly to a time-varying mean serving as the third factor. The estimates are robust to the choice of maturities, suggesting that these factors give us an adequate model.