MEASURES OF DEPENDENCE FOR ORNSTEIN-UHLENBECK PROCESSES WETH 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 a-stable behavior. However, for the a-stable models the correlation is not defined, therefore in order to compare the structure of dependence for Ornstein-Uhlenbeck process with tempered stable and a-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 a-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.