The Surprise Element: Jumps in Interest Rate Diffusions

That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of jump-di®usion models of the short rate to capture surprise e®ects, and show that these models o®er a good statistical distribution of short rate behavior, and are useful in understanding many empirical phenomena. Continuous-time and discrete-time estimators are used based on analytical derivations of the characteristic functions, moments and density functions of jump-di®usion stochastic processes for general jump distributions. Jump processes capture empirical features of the data which would not be captured by di®usion models, and there is strong evidence that existing di®usion models would be well-enhanced by jump and ARCH-type processes. The analytical and empirical methods in the paper support many applications, such as testing for Fed intervention e®ects, which are shown to be an important source of surprise jumps in interest rates. The jump model is shown to mitigate the non-linearity of interest rate drifts, so prevalent in pure-di®usion models. Day-of-week e®ects are modelled explicitly, and the jump model provides evidence of bond market overreaction, rejecting the martingale hypothesis for interest rates. Jump models mixed with Markov switching processes predicate that conditioning on regime is important in determining short rate behavior. Date: March 1999. I received useful comments from Yacine Ait-Sahalia, David Backus, David Bates, Rob Bliss, Bent Christensen, Greg Du®ee, Edwin Elton, Nick Firoozye, Martin Gruber, Steve Heston, Ravi Jagannathan, Apoorva Koticha, N.R. Prabhala, Ken Singleton, Rene Stulz, Marti Subrahmanyam, Rangarajan Sundaram, Walter Torous, Raman Uppal and Robert Whitelaw. Many thanks to Pierluigi Balduzzi, George Chacko and Silverio Foresi for their innumerable suggestions on this article. Stephen Lynagh provided capable research assistance. Any errors are mine. Please address all correspondence to Sanjiv Das at 361 Morgan Hall, Graduate School of Business Administration, Harvard University, Soldiers Field, Boston, MA 02163. Tel: 617-495-6080. Email: [email protected].