Discrete Time Affine Term Structure Models With Squared Gaussian Shocks (DTATSM-SGS)

Abstract

The tractability of discrete time affine term structure models (DTATSM) is fully preserved when adding squared Gaussian shocks (SGS) to factor processes. SGS guarantee non-negative factors under parameter restrictions that do not affect market prices of risk. DTATSM-SGS mirror continuous time affine models, but need no Feller conditions. New affine specifications become admissible. Changes of measure can alter not only the conditional mean, but also the conditional covariance of factors and yields through the second-order Esscher transform. This enables DTATSM-SGS to better match US Treasury yields volatility, while the conditional moments of factors and yields are still in closed form. The empirical comparison of DTATSM-SGS and similar models based on autoregressive Gamma processes reveals no clear winner in fitting US Treasury yields.