An Empirical Comparison of Continuous Time Models of the Short Term Interest Rate

This paper compares the empirical performance of a wide variety of well-known diffusion models - with particular emphasis on the Black, Derman, and Toy (1990) term structure model - in capturing the dynamic behavior of interest rate volatility. Many popular models are nested within a more flexible time-varying BDT framework that allows us to determine the appropriate specification of the spot rate process. The empirical results for the one-month Treasury yields indicate that the equilibrium models that do not allow the drift and diffusion parameters to vary over time and parameterize the volatility only as a function of interest rate levels fail to model adequately the serial correlation in conditional variances. On the other hand, the serial-correlation-based arbitrage-free models with time-dependent parameters in the drift and diffusion functions may fail to capture adequately the relationship between interest rate levels and volatility. The results also suggest that time-varying volatilities within the BDT framework may lead to non-recombining binomial trees that increase the storage requirements and computational cost substantially in pricing interest rate contingent claims