Threshold estimation of jump-diffusion models and interest rate modeling∗

We introduce nonparametric estimators of the coefficients of a univariate jump-diffusion process when observations are recorded discretely. We allow the drift, diffusion and intensity function to be level dependent. We also show that the estimator of the diffusion coefficient is consistent even if the jump process has infinite activity. Our results rely on the fact that it is possible to disentangle the discontinuous part of the state variable through those squared increments between observations exceeding a suitable threshold. We use our estimators to reexamine the estimation of models for the short interest rate. With respect to alternative estimates, the proposed threshold estimators provide very different results from those in the literature. Wewish to acknowlegeMichael Johannes andAngeloMelino for useful comments, as well as partecipants at the CIREQ conference on realized volatility, held in Montreal in April, 2006. All errors and omissions are our own. Dipartimento di Matematica per le Decisioni, via C. Lombroso 6/17, Università di Firenze, email: [email protected] Dipartimento di Economia Politica, Piazza S. Francesco 7, Università di Siena, email: [email protected] C. Mancini and R. Renò 1