IDEAS home Printed from https://ideas.repec.org/p/bdi/wptemi/td_912_13.html
   My bibliography  Save this paper

Tempered stable Ornstein-Uhlenbeck processes: a practical view

Author

Listed:
  • Michele Leonardo Bianchi

    (Bank of Italy)

  • Svetlozar T. Rachev

    (Stony Brook University)

  • Frank J. Fabozzi

    (EDHEC Business School)

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.

Suggested Citation

  • Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2013. "Tempered stable Ornstein-Uhlenbeck processes: a practical view," Temi di discussione (Economic working papers) 912, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_912_13
    as

    Download full text from publisher

    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2013/2013-0912/en_tema_912.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    2. Piotr Jelonek, 2012. "Generating Tempered Stable Random Variates from Mixture Representation," Discussion Papers in Economics 12/14, Division of Economics, School of Business, University of Leicester.
    3. Marco Corazza & Florence Legros & Cira Perna & Marilena Sibillo, 2017. "Mathematical and Statistical Methods for Actuarial Sciences and Finance," Post-Print hal-01776135, HAL.
    4. Wylomanska-, Agnieszka, 2010. "Measures of dependence for Ornstein-Uhlenbeck processes with tempered stable distribution," MPRA Paper 28535, University Library of Munich, Germany, revised 2010.
    5. 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.
    6. 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.
    7. Thomas Kokholm & Elisa Nicolato, 2010. "Sato Processes in Default Modelling," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 377-397.
    8. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michele Bianchi & Frank Fabozzi, 2014. "Discussion of ‘on simulation and properties of the stable law’ by Devroye and James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 353-357, August.
    2. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hasan Fallahgoul & Gregoire Loeper, 2021. "Modelling tail risk with tempered stable distributions: an overview," Annals of Operations Research, Springer, vol. 299(1), pages 1253-1280, April.
    2. Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2018. "Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 339-378, March.
    3. Michele Bianchi & Frank Fabozzi, 2014. "Discussion of ‘on simulation and properties of the stable law’ by Devroye and James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 353-357, August.
    4. Ole E. Barndorff-Nielsen & Neil Shephard, 2012. "Basics of Levy processes," Economics Papers 2012-W06, Economics Group, Nuffield College, University of Oxford.
    5. Borak, Szymon & Misiorek, Adam & Weron, Rafał, 2010. "Models for heavy-tailed asset returns," SFB 649 Discussion Papers 2010-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.
    7. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    8. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    9. Michele Leonardo Bianchi, 2014. "Are the log-returns of Italian open-end mutual funds normally distributed? A risk assessment perspective," Temi di discussione (Economic working papers) 957, Bank of Italy, Economic Research and International Relations Area.
    10. Gong, Xiaoli & Zhuang, Xintian, 2017. "Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 148-159.
    11. Lorenzo Mercuri & Edit Rroji, 2018. "Risk parity for Mixed Tempered Stable distributed sources of risk," Annals of Operations Research, Springer, vol. 260(1), pages 375-393, January.
    12. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    13. Catalina Bolance & Montserrat Guillen & David Pitt, 2014. "Non-parametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers 2014-01, Universitat de Barcelona, UB Riskcenter.
    14. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    15. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    16. Ting‐Pin Wu & Son‐Nan Chen, 2008. "Valuation of floating range notes in a LIBOR market model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(7), pages 697-710, July.
    17. Ernst Eberlein & Nataliya Koval, 2006. "A cross-currency Levy market model," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 465-480.
    18. Fred Espen Benth & Martin Groth & Rodwell Kufakunesu, 2007. "Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 347-363.
    19. Catania, Leopoldo & Grassi, Stefano & Ravazzolo, Francesco, 2019. "Forecasting cryptocurrencies under model and parameter instability," International Journal of Forecasting, Elsevier, vol. 35(2), pages 485-501.
    20. Devolder, Pierre & Melis, Roberta, 2015. "Optimal Mix Between Pay As You Go And Funding For Pension Liabilities In A Stochastic Framework," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 551-575, September.

    More about this item

    Keywords

    Ornstein-Uhlenbeck processes; tempered stable distributions; tempered infinitely divisible distributions; integrated processes; acceptance-rejection sampling; maximum likelihood estimation.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bdi:wptemi:td_912_13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bdigvit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.