Measures of dependence for Ornstein–Uhlenbeck processes with tempered stable distribution
In this paper we investigate the dependence structure for Ornstein–Uhlenbeck process with tempered stable distribution that is natural extension of the classical Ornstein–Uhlenbeck process with Gaussian and alpha-stable behavior. However, for the alpha-stable models the correlation is not defined, therefore in order to compare the structure of dependence for Ornstein–Uhlenbeck process with tempered stable and alpha-stable distribution, we need another measures of dependence defined for infinitely divisible processes such as Levy correlation cascade or codifference. We show that for analyzed tempered stable process the rate of decay of the Levy correlation cascade is different than in the stable case, while the codifference of the alpha-stable Ornstein–Uhlenbeck process has the same asymptotic behavior as in tempered stable case. As motivation of our study we calibrate the Ornstein–Uhlenbeck process with tempered stable distribution to real financial data.
|Date of creation:||2011|
|Date of revision:|
|Publication status:||Published in Acta Phys. Polon. B 42(10), 2049-2062 (2011).|
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- Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
- Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
- Young Kim & Svetlozar Rachev & Michele Bianchi & Frank Fabozzi, 2009. "Computing VAR and AVaR in Infinitely Divisible Distributions," Yale School of Management Working Papers amz2569, Yale School of Management.
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