Tempered Stable Ornstein-Uhlenbeck Processes: A Practical View

52 Pages Posted: 21 Jun 2013

Date Written: June 20, 2013

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

JEL Classification: C02, C46

Suggested Citation

Bianchi, Michele Leonardo and Rachev, Svetlozar and Fabozzi, Frank J., Tempered Stable Ornstein-Uhlenbeck Processes: A Practical View (June 20, 2013). Bank of Italy Temi di Discussione (Working Paper) No. 912, Available at SSRN: https://ssrn.com/abstract=2281903 or http://dx.doi.org/10.2139/ssrn.2281903

Michele Leonardo Bianchi (Contact Author)

Bank of Italy ( email )

Via Nazionale 91
00184 Rome, I - 00184
Italy

Svetlozar Rachev

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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