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Measures of dependence for Ornstein–Uhlenbeck processes with tempered stable distribution


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  • Agnieszka Wylomanska


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.

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Bibliographic Info

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/11/04.

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Length: 16 pages
Date of creation: 2011
Date of revision:
Publication status: Published in Acta Phys. Polon. B 42(10), 2049-2062 (2011).
Handle: RePEc:wuu:wpaper:hsc1104

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Keywords: Ornstein-Uhlenbeck process; alpha-stable distribution; subdiffusion; Measure of dependence; Levy correlation cascade; codifference; interest rates;

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  1. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
  2. 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.
  3. 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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Cited by:
  1. Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2013. "Tempered stable Ornstein-Uhlenbeck processes: a practical view," Temi di discussione (Economic working papers) 912, Bank of Italy, Economic Research and International Relations Area.


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