Abstract
We consider models for financial data by Levy processes, including hyperbolic, normal inverse Gaussian, and Carr, Geman, Madan, and Yor (CGMY) processes. They are given by their Levy triplet (μ(θ),σ2,eθxg(x)ν(dx)), where μ denotes the drift, σ2 the diffusion, and eθxg(x)ν(dx) the Levy measure, and the unknown parameter θ models the skewness of the process. We provide local asymptotic normality results and construct efficient estimators for the skewness parameter θ taking into account different discrete sampling schemes.I thank Prof. Dr. L. Ruschendorf for his steady encouragement, the referees for helpful comments, and the German National Scholarship Foundation for financial support.
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