Out-of-Sample Performance of Spot Interest Rate Models

The current large empirical literature on interest rate modeling typically focuses on the in-sample performance and ignores the out-of-sample performance of existing models. We fill the gap in this literature by providing probably the first comprehensive empirical study (to our knowledge) of the out-of-sample performance of a wide variety of popular interest rate models in forecasting the probability density of future interest rates. Out-of-sample density forecasts are important for at least two reasons: (i) out-of-sample analysis helps minimize the data snooping bias due to excessive searching for more complicated models using the same or similar data sets; (ii) the conditional probability density, which completely characterizes the dynamics of an interest rate model, is an essential input to many important financial applications such as pricing fixed-income securities and interest rate risk management. Using a rigorous econometric procedure developed in Hong (2000) for density forecast evaluation, we examine the out-of-sample performance of single-factor diffusion, GARCH, regime-switching and jump-diffusion models. Among other things we focus on the relative importance of (i) linear versus nonlinear drift specification in modeling conditional mean, (ii) level versus GARCH effect in modeling conditional variance, and (iii) regime-switching versus jumps in capturing the tail distribution of interest rate data. Consistent with the in-sample findings in the literature, we find that for out-of-sample density forecasts, it is important to model mean-reversion, conditional heteroskedasticity, and excess kurtosis or heavy-tails of interest rates. Contrary to the in-sample findings, we find that models that perform well in out-of-sample forecasts are those with simpler specifications for all the above three important features. Our results point out the potential risk of overparameterization in the existing interest rate models and show that simplicity is indeed a virtue in out-of-sample applications