The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models

This paper analyzes the role of jumps in continuous-time short rate models. I first develop a test to detect jump-induced misspecification and, using Treasury bill rates, find evidence for the presence of jumps. Second, I specify and estimate a nonparamet-ric jump-diffusion model. Results indicate that jumps play an important statistical role. Estimates of jump times and sizes indicate that unexpected news about the macroeconomy generates the jumps. Finally, I investigate the pricing implications of jumps. Jumps generally have a minor impact on yields, but they are important for pricing interest rate options. THERE IS STRONG ANECDOTAL EVIDENCE that jumps play an important role in de-termining the dynamics of interest rate movements, although most models are based on diffusions and explicitly rule out their possibility. For example, Figure 1 displays the daily changes in the 3-month Treasury bill (T-bill) rate from 1991 to 1993, a period during which the short rate fell from 7 to just more than 3 percent; of note are the relatively infrequent but large spikes, interpreted here as “jumps.” Given the magnitude of the jumps, the obvious question is: what generated these movements? It turns out that each of the large movements in Figure 1 coincided with the arrival to the Treasury market of significant information regarding the current or future state of the economy. This observation also holds over other time periods during which news about the macroeconomy generated the largest movements in yields.1 Thus, at least anecdotally, jumps appear to be an important conduit through which macroeconomic information enters the term structure