Threshold Estimation for a Spectrally Negative Levy Process

摘要

Consider a spectrally negative Levy process with unknown diffusion coefficient and Levy measure and suppose that the high frequency trading data is given. We use the techniques of threshold estimation and regularized Laplace inversion to obtain the estimator of survival probability for a spectrally negative Levy process. The asymptotic properties are given for the proposed estimator. Simulation studies are also given to show the finite sample performance of our estimator.