An Empirical Assessment of Spot Rate Model Stability

The purpose of this paper is to add to the empirical evidence on the efficacy of alternative simulation models of the short term interest rate. This is done by constructing consistent specification tests that allow us to carry out a “horse-race” comparing various one, two, and three factor models (possibly with jumps), across multiple historical sample periods. We begin by outlining a three factor version of the simulation based specification test of Bhardwaj, Corradi and Swanson (BCS: 2008), which is based on a comparison of simulated and true conditional distributions and confidence intervals. Our evaluation involves comparing six affine models of the short rate during four historical periods, referred to as: “Post Bretton-Woods”; “Pre-1990s”; “The Stable 1990s”; and “Post 1990s”. Based on the examination of Eurodollar rate data, we find that the CIR model, which is often rejected in the literature, performs best among the candidate models in “The Stable 1990s”, while there is little to choose between one and two factor models when considering the “Post 1990s” period. Examination of “Pre 1990s” data, on the other hand, suggests there is little to choose between 2 and 3 factor models, and the one factor CIR model performs poorly. Moreover, under the “Post Bretton-Woods” period, the “best” performer is the three factor CHEN (1996) model examined by Andersen, Benzoni and Lund (2004). We conclude that the choice of model for simulating the future distribution of short rates is highly sample dependent.