Likelihood-based specification analysis of continuous-time models of the short-term interest rate

An extensive collection of continuous-time models of the short-term interest rate is evaluated over data sets that have appeared previously in the literature. The analysis, which uses the simulated maximum likelihood procedure proposed by Durham and Gallant (2002), provides new insights regarding several previously unresolved questions. For single factor models, I find that the volatility, not the drift, is the critical component in model specification. Allowing for additional flexibility beyond a constant term in the drift provides negligible benefit. While constant drift would appear to imply that the short rate is nonstationary, in fact, stationarity is volatility-induced. The simple constant elasticity of volatility model fits weekly observations of the three-month Treasury bill rate remarkably well but is easily rejected when compared with more flexible volatility specifications over daily data. The methodology of Durham and Gallant can also be used to estimate stochastic volatility models. While adding the latent volatility component provides a large improvement in the likelihood for the physical process, it does little to improve bond-pricing performance.