Another Look at Models of the Short-Term Interest Rate

The short-term rate of interest is fundamental to much of theoretical and empirical finance. Yet no consensus has emerged on the dynamics of its volatility. We show that models which parameterize volatility only as a function of interest rate levels tend to over-emphasize the sensitivity of volatility to levels and fail to model adequately the serial correlation in conditional variances. On the other hand, serial correlation-based models like GARCH models fail to capture adequately the relationship between interest rate levels and volatility. We introduce and test a new class of models for the dynamics of short- term interest rate volatility which allows volatility to depend on both interest rate levels and information shocks. Two important conclusions emerge. First, the sensitivity of interest rate volatility to interest rate levels has been overstated in the literature. While this relationship is important, adequately modeling volatility as a function of unexpected information shocks is also important. Second, we conclude that the volatility processes in many existing theoretical models of interest rates are misspecified, and suggest new paths toward improving the theory