Stochastic Volatility, Mean Drift, and Jumps in the Short Rate Diffusion: Sources of Steepness, Level and Curvature

We introduce continuous-time models that capture the salient features of the short-term interest rate and remain tractable for asset pricing applications. We extend classical specifications within and outside of the affine class to multi-factor settings with latent variables that are readily interpreted as the conditional mean and volatility of the interest rate, and further enrich the specifications by incorporating a jump component. We conduct inference through EMM using U.S. 3-month T-Bill rates. The EMM diagnostics are used to obtain satisfactory specifications and to identify features of the interest rate dynamics that explain the inadequate performance of nested models. Finally, we explore the bond pricing implications and perform illustrative calibrations for the yield curve. We select a three-factor specification featuring stochastic volatility and mean drift as well as jumps. The final model provides an excellent fit to all the structural characteristics of the U.S. short rate dynamics. The inclusion of the stochastic volatility factor is critical, whereas the stochastic mean offers a relatively minor, but still significant, improvement to the model. The mean drift indicates evolving inflationary expectations or time-variation in the real interest rate, or both. Further, jumps are critical to the quality of the fit and help relieve the stochastic volatility factor from accommodating outlier behavior. Our three-factor jump-diffusion models pass the strenuous EMM diagnostics with the affine specification producing a superior in-sample fit. This provides support for jump-diffusion models of the form suggested by Duffie, Pan, and Singleton (2000). Finally, the evidence from the term structure is supportive of the inclusion of stochastic volatility and mean drift factors. Specifically, our factors may readily be identified with forces inducing steepness, level and curvature shifts in the yield curve.