Testing Affine Yield Factor Models

This article empirically tests single and multifactor versions of the Vasicek (1977) and Cox, Ingersoll, and Ross (1985) term structure models. These models belong to the class of affine term structure models proposed by Duffie and Kan (1996), where the affine relationship is between the yield of the discount bond and the abstract state variable. The maximum likelihood estimation method we apply allows us to utilize the conditional density of the state variables of the aforementioned models. The advantage of the estimation method is that we can recover the unobservable state variables from the yields of the discount bonds. Our results show that the single-factor models are unable to fit both the short and long ends of the yield curve simultaneously. The two-factor models miss the curvature of the yield curve, even though they can fit the level and the slope of the yield curve. A three-factor model is needed if we also want to capture the curvature of the yield curve. Moreover, the three-factor Vasicek model outperforms the three-factor CIR model