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Tempered stable Ornstein-Uhlenbeck processes: a practical view

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  • Michele Leonardo Bianchi

    ()
    (Bank of Italy)

  • Svetlozar T. Rachev

    ()
    (Stony Brook University)

  • Frank J. Fabozzi

    ()
    (EDHEC Business School)

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    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.

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    Bibliographic Info

    Paper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 912.

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    Date of creation: Jun 2013
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    Handle: RePEc:bdi:wptemi:td_912_13

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    Related research

    Keywords: Ornstein-Uhlenbeck processes; tempered stable distributions; tempered infinitely divisible distributions; integrated processes; acceptance-rejection sampling; maximum likelihood estimation.;

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    1. Agnieszka Wylomanska, 2011. "Measures of dependence for Ornstein–Uhlenbeck processes with tempered stable distribution," HSC Research Reports HSC/11/04, Hugo Steinhaus Center, Wroclaw University of Technology.
    2. Thomas Kokholm & Elisa Nicolato, 2010. "Sato Processes in Default Modelling," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 377-397.
    3. Massimo Libertucci & Francesco Piersante, 2012. "Start-up banks’ default and the role of capital," Temi di discussione (Economic working papers) 890, Bank of Italy, Economic Research and International Relations Area.
    4. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53.
    5. Matthias Scherer & Svetlozar T. Rachev & Young Shin Kim & Frank J. Fabozzi, 2012. "Approximation of skewed and leptokurtic return distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(16), pages 1305-1316, August.
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