Multivariate Feller conditions in term structure models: Why do(n't) we care?

TL;DR

This paper examines the importance of Feller conditions in discrete macro-finance term structure models, finding that their practical impact on yields is minimal whether imposed or not.

Contribution

It demonstrates that Feller conditions are largely unnecessary in discrete models, as they rarely affect yield calculations significantly.

Findings

Differences in yields are statistically insignificant.

Negative arguments rarely occur without Feller conditions.

Economic impact of Feller conditions is negligible.

Abstract

In this paper, the relevance of the Feller conditions in discrete time macro-finance term structure models is investigated. The Feller conditions are usually imposed on a continuous time multivariate square root process to ensure that the roots have nonnegative 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. At the same time, 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.