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Threshold Estimation of Jump-Diffusion Models and Interest Rate Modeling

2008; RELX Group (Netherlands); Linguagem: Inglês

10.2139/ssrn.1158439

1556-5068

Cecilia Mancini, Roberto Renò,

Financial Risk and Volatility Modeling

We reconstruct the level-dependent diffusion coefficient of a univariate semimartingale with jumps which is observed discretely. The consistency and asymptotic normality of our estimator are provided in presence of both finite and infinite activity (finite variation) jumps. Our results rely on kernel estimation, using the properties of the local time of the data generating process and 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 function. We also reconstruct the drift and the jump intensity coefficients when they are level-dependent and jumps have finite activity, through consistent and asymptotically normal estimators. Simulated experiments show that the newly proposed estimators are better performing in finite samples than alternative estimators, and this allows us to reexamine the estimation of a univariate model for the short term interest rate, for which we find less jumps and more variance due to the diffusion part than previous studies.