An affine two-factor heteroskedastic macro-finance term structure model

We propose an affine macro-finance term structure model for interest rates that allows for both constant volatilities (homoskedastic model) and state-dependent volatilities (heteroskedastic model). In a homoskedastic model, interest rates are symmetric, which means that either very low interest rates are predicted too often or very high interest rates not often enough. This undesirable symmetry for constant volatility models motivates the use of heteroskedastic models where the volatility depends on the driving factors.

For a truly heteroskedastic model in continuous time, which involves a multivariate square root process, the so-called Feller conditions are usually imposed to ensure that the roots have non-negative arguments. For a discrete time approximate model, the Feller conditions do not give this guarantee. Moreover, in a macro-finance context, the restrictions imposed might be economically unappealing. It has also been observed that even without the Feller conditions imposed, for a practically relevant term structure model, negative arguments rarely occur.

Using models estimated on German data, we compare the yields implied by (approximate) analytic exponentially affine expressions to those obtained through Monte Carlo simulations of very high numbers of sample paths. It turns out that the differences are rarely statistically significant, whether the Feller conditions are imposed or not. Moreover, economically, the differences are negligible, as they are always below one basis point.
Keywords: Macro-finance models; affine term structure model; expected inflation; ex ante real short rate; Monte Carlo simulations