Tempered stable Ornstein-Uhlenbeck processes: a practical view

Michele Leonardo Bianchi (), Svetlozar T. Rachev () and Frank Fabozzi ()
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Michele Leonardo Bianchi: Bank of Italy
Svetlozar T. Rachev: Stony Brook University

No 912, Temi di discussione (Economic working papers) from Bank of Italy, Economic Research and International Relations Area

Abstract: We study the one-dimensional Ornstein-Uhlenbeck (OU) processes with marginal law given by the tempered stable and tempered infinitely divisible distributions proposed by Rosinski (2007) and Bianchi et al. (2010b), respectively. In general, the use of non-Gaussian OU processes is impeded by difficulty in calibration and simulation. Accordingly, we investigate the law of transition between consecutive observations of OU processes and - with a view to practical applications - evaluate the characteristic function of integrated tempered OU processes in three cases: classical tempered stable, variance gamma, and rapidly decreasing tempered stable. Then we analyze how one can draw a random sample from this class of processes using both the classical inverse transform algorithm and an acceptance-rejection method based on the simulation of a stable random sample. Finally, with a maximum likelihood estimation method based on the fast Fourier transform, we assess the performance of the simulation algorithm empirically.

Keywords: Ornstein-Uhlenbeck processes; tempered stable distributions; tempered infinitely divisible distributions; integrated processes; acceptance-rejection sampling; maximum likelihood estimation. (search for similar items in EconPapers)
JEL-codes: C02 C46 (search for similar items in EconPapers)
Date: 2013-06
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:bdi:wptemi:td_912_13

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