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.