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ESTIMATING THE SKEWNESS IN DISCRETELY OBSERVED LÉVY PROCESSES

Published online by Cambridge University Press:  01 October 2004

Jeannette H.C. Woerner
Jeannette H.C. Woerner
Affiliation:
University of Göttingen
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Abstract

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.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 5 , October 2004 , pp. 927 - 942
Copyright
© 2004 Cambridge University Press

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