Asymptotic Normality of Bias Reduction Estimation for Jump Intensity Function in Financial Markets

Continuous-time diffusion models with jumps, especially the jump intensity coefficient, can depict the impact of sudden and large shocks to financial markets. It is possible to disentangle, from the discrete observations, the contributions given by the jumps and those by the diffusion part through threshold functions. Based on this threshold technique, we employ non-parametric local linear threshold estimator for the unknown jump intensity function of a semimartingale with jumps. The asymptotic normality of our estimator is provided in the presence of finite activity jumps under certain regular conditions. The finite-sample performance for the underlying estimator has been shown through a Monte Carlo experiment and an empirical analysis on high frequency returns of indexes in the USA and China.