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

Agnieszka Wyłomańska

No HSC/11/04, HSC Research Reports from Hugo Steinhaus Center, Wroclaw University of Science and Technology

Abstract: 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.

Keywords: Ornstein-Uhlenbeck process; alpha-stable distribution; subdiffusion; Measure of dependence; Levy correlation cascade; codifference; interest rates (search for similar items in EconPapers)
JEL-codes: C46 C63 E47 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Acta Phys. Polon. B 42(10), 2049-2062 (2011).

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http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_11_04.pdf Original version, 2011 (application/pdf)

Related works:
Working Paper: Measures of dependence for Ornstein-Uhlenbeck processes with tempered stable distribution (2010)
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