Stochastic Volatility , Mean Drift , and Jumps in the Short-Term Interest Rate

We find that an intuitively appealing and fairly manageable continuous-time model provides an excellent characterization of the U.S. short-term interest rate over the post Second World War period. Our three-factor jump-diffusion model consists of elements embodied in existing specifications, but our approach appears to be the first to successfully accommodate all such features jointly. Moreover, we conduct simultaneous and efficient inference regarding all model components which include a shock to the interest rate process itself, a time-varying mean reversion factor, a stochastic volatility factor and a jump process. Most intriguingly, we find that the restrictions implied by an affine representation of the jump-diffusion system are not rejected by the U.S. short rate data. This allows for a tractable setting for associated asset pricing applications. ∗Torben G. Andersen is at the Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, 847-467-1285, t-andersen@kellogg.northwestern.edu and the NBER. Luca Benzoni is at the Carlson School of Management, University of Minnesota, 321 19th Ave S, Minneapolis, MN 55455, 612-624-1075, lbenzoni@umn.edu. Jesper Lund is at Nykredit Bank, Quantitative Research, DK-1780 Copenhagen V, Denmark, 45-33421378, mail@jesperlund.com. We are grateful to Bjørn Eraker; Lorenzo Garlappi; Bob Goldstein; Lars Hansen; Bob Kimmel; Mike Johannes; Koji Kusuda; James MacKinnon; Nour Meddahi; Ken Singleton; Cristian Tiu; and seminar participants at the New York Federal Reserve; the University of Minnesota; the University of Rochester; the University of Texas at Austin; the University of Wisconsin at Madison; the Washington University in St. Louis; the CIRANOCIREQ-MITACS 2003 Financial Econometrics Conference; the 2004 Econometric Society Conference in San Diego for helpful comments and suggestions. We are indebted with Huyan Qiu, who provided outstanding research assistance. Of course, all errors remain our sole responsibility. The most recent version of the paper can be downloaded from http://www.umn.edu/∼lbenzoni