Threshold Estimation for a Spectrally Negative Lévy Process

Abstract

Consider a spectrally negative Lévy process with unknown diffusion coefficient and Lévy 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 Lévy process. The asymptotic properties are given for the proposed estimator. Simulation studies are also given to show the finite sample performance of our estimator.

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“…Instead, we adapt the Fourier-Cosine series method to approximate them based on Formula (5). Throughout this section, we set K = 2 12 and a = 100 for the Fourier-Cosine method. Furthermore, those formulae can be approximated via FFT method by Formula (4.1) in [18] with parameters m = 50 and K = 2 13 .…”

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