ESTIMATING THE SKEWNESS IN DISCRETELY OBSERVED LÉVY PROCESSES
针对Lévy过程模型中的偏度参数θ，在离散采样下构建有效估计量，并证明局部渐近正态性，适用于金融数据建模。
We consider models for financial data by Lévy processes, including hyperbolic, normal inverse Gaussian, and Carr, Geman, Madan, and Yor (CGMY) processes. They are given by their Lévy triplet (μ(θ),σ2,eθxg(x)ν(dx)), where μ denotes the drift, σ2 the diffusion, and eθxg(x)ν(dx) the Lévy 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. Rüschendorf for his steady encouragement, the referees for helpful comments, and the German National Scholarship Foundation for financial support.