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In this paper, the relevance of the Feller conditions in discrete timemacro-finance term structure models is investigated. The Feller conditions areusually imposed on a continuous time multivariate square root process to ensurethat the roots have nonnegative arguments. For a discrete time approximatemodel, the Feller conditions do not give this guarantee. Moreover, in amacro-finance context the restrictions imposed might be economicallyunappealing. At the same time, it has also been observed that even without theFeller conditions imposed, for a practically relevant term structure model,negative arguments rarely occur. Using models estimated on German data, wecompare the yields implied by (approximate) analytic exponentially affineexpressions to those obtained through Monte Carlo simulations of very highnumbers of sample paths. It turns out that the differences are rarelystatistically significant, whether the Feller conditions are imposed or not.Moreover, economically the differences are negligible, as they are always belowone basis point.

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