Estimation with applications of two-factor affine term structure models for Mexico, 1995-2004

This paper studies the term structure of interest rates for Mexico from 1995 to 2004, after the 1994 Tequila crisis. We estimate two-factor canonical, essentially, affine models, following Dai and Singleton (2000). We estimate the models by the Kalman filter, using the available 28, 91, 182, and 364 days-to-maturity zero-coupon bonds "Cetes." Let Y1 and Y2 be the two latent factors. We find that Y1 (Y2) is less (more) volatile, is slow (fast) mean-reverting, and its price of risk is close to zero (negative and decreasing in Y). Y1 (Y2) is like a curvature (steepness) factor, which explains long- (short-) term rates. Hence, the risk premium associated with holding long-term bonds is positive but small. These results are robust to the three two-factor affine models, and a level factor is not found. We prefer the two stochastic volatility models to the Gaussian model. Other applications are as follows: we compute the models when one factor is the short rate r (affine in Y1 and Y2), which reverts to a tendency m (affine in Y1) which is also part of the stochastic volatility. We price up to ten years-to-maturity coupon bonds out-of-sample, issued from 2000 on. The model reveals misspricing, which is consistent with bondholders overreaction. We estimate a two-factor model for the US treasury market as well, but a cointegration relationship between the two US and the two Mexico filtered state variables is not found. We conclude that the US yield curve is not a leading factor of Mexico short-rates.