Out-of-Sample Performance of Spot Interest Rate Models

Most of the existing large empirical literature on interest rate modeling focus on the in-sample performance of different models, in spite of the fact that the evolution of interest rates in the future not in the past is most relevant in many financial applications, such as pricing, hedging and risk management. In this paper, we provide probably the first comprehensive empirical study (to our knowledge) of the out-of-sample performance of a wide range of popular models in forecasting the conditional probability density of future interest rates. Density forecasting is important for at least two reasons. First, 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. Second, the conditional density, which completely characterizes the full dynamics of an interest rate model, is an essential input to many important financial applications, such as evaluating the Value at Risk and pricing fixed income derivatives. Using a rigorous econometric procedure developed in Hong (2000) for density forecast evaluation , we examine the out-of-sample performance of various single-factor diffusion models, GARCH models, regime-switching models and jump-diffusions models. We examine the contributions of each model in capturing the three important features of interest rate data: mean-reversion, conditional heteroskedasticity, and excess kurtosis or heavy-tailed distribution. In particular, we focus on the relative importance of linear versus nonlinear drift specifications in modeling conditional mean, level versus GARCH effects in modeling conditional variance, and regime-switching versus jump-diffusion models in capturing the tail distribution of interest rate data. Consistent with the findings of in-sample analysis, we find that for out-of-sample density forecasts, it is important to model the above three important features. Contrary to in-sample findings, we find that models that perform well in out-of-sample forecasts are the ones that have simpler specifications for all the above important features for interest rates. Out results point out the potential risk of over-parameterization in the existing interest rate models and show that simplicity is indeed a virtue in out-of-sample applications.