IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i6p2427-2437.html
   My bibliography  Save this article

Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution

Author

Listed:
  • Taufer, Emanuele
  • Leonenko, Nikolai

Abstract

A simulation procedure for obtaining discretely observed values of Ornstein-Uhlenbeck processes with given (self-decomposable) marginal distribution is provided. The method proposed, based on inversion of the characteristic function, completely circumvents the problems encountered when trying to reproduce small jumps of Lvy processes. Error bounds for the proposed procedure are provided and its performance is numerically assessed.

Suggested Citation

  • Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2427-2437
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00146-1
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wolfe, Stephen James, 1982. "On a continuous analogue of the stochastic difference equation Xn=[rho]Xn-1+Bn," Stochastic Processes and their Applications, Elsevier, vol. 12(3), pages 301-312, May.
    2. Rubenthaler, Sylvain, 2003. "Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 311-349, February.
    3. Todorov, Viktor & Tauchen, George, 2006. "Simulation Methods for Levy-Driven Continuous-Time Autoregressive Moving Average (CARMA) Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 455-469, October.
    4. Wiktorsson, Magnus, 2002. "Simulation of stochastic integrals with respect to Lévy processes of type G," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 113-125, September.
    5. Ole E. Barndorff‐Nielsen & Neil Shephard, 2003. "Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 277-295, June.
    6. Karlis, Dimitris, 2002. "An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 43-52, March.
    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    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. Taufer, Emanuele & Leonenko, Nikolai & Bee, Marco, 2011. "Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2525-2539, August.
    2. Imai Junichi, 2013. "Comparison of random number generators via Fourier transform," Monte Carlo Methods and Applications, De Gruyter, vol. 19(3), pages 237-259, October.
    3. Gong, Xiao-li & Zhuang, Xin-tian, 2016. "Option pricing and hedging for optimized Lévy driven stochastic volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 118-127.
    4. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes," Papers 2011.09147, arXiv.org.
    5. Leucht, Anne, 2012. "Characteristic function-based hypothesis tests under weak dependence," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 67-89.
    6. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2020. "A bivariate Normal Inverse Gaussian process with stochastic delay: efficient simulations and applications to energy markets," Papers 2011.04256, arXiv.org.
    7. Raknerud, Arvid & Skare, Øivind, 2012. "Indirect inference methods for stochastic volatility models based on non-Gaussian Ornstein–Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3260-3275.
    8. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    9. Shibin Zhang, 2011. "Transition Law-based Simulation of Generalized Inverse Gaussian Ornstein–Uhlenbeck Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 619-656, September.
    10. Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008.
    11. Piergiacomo Sabino, 2020. "Exact Simulation of Variance Gamma related OU processes: Application to the Pricing of Energy Derivatives," Papers 2004.06786, arXiv.org.

    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. Stefano Iacus & Lorenzo Mercuri, 2015. "Implementation of Lévy CARMA model in Yuima package," Computational Statistics, Springer, vol. 30(4), pages 1111-1141, December.
    2. Till Massing, 2018. "Simulation of Student–Lévy processes using series representations," Computational Statistics, Springer, vol. 33(4), pages 1649-1685, December.
    3. Dassios, Angelos & Qu, Yan & Zhao, Hongbiao, 2018. "Exact simulation for a class of tempered stable," LSE Research Online Documents on Economics 86981, London School of Economics and Political Science, LSE Library.
    4. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    5. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    6. Pham, Viet Son, 2020. "Lévy-driven causal CARMA random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7547-7574.
    7. Masuda, H. & Yoshida, N., 2005. "Asymptotic expansion for Barndorff-Nielsen and Shephard's stochastic volatility model," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1167-1186, July.
    8. S. Ghasemzadeh & M. Ganjali & T. Baghfalaki, 2022. "Quantile regression via the EM algorithm for joint modeling of mixed discrete and continuous data based on Gaussian copula," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1181-1202, December.
    9. Creal, Drew D., 2008. "Analysis of filtering and smoothing algorithms for Lévy-driven stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2863-2876, February.
    10. Anzarut, Michelle & Mena, Ramsés H., 2019. "A Harris process to model stochastic volatility," Econometrics and Statistics, Elsevier, vol. 10(C), pages 151-169.
    11. Piergiacomo Sabino & Nicola Cufaro Petroni, 2022. "Fast simulation of tempered stable Ornstein–Uhlenbeck processes," Computational Statistics, Springer, vol. 37(5), pages 2517-2551, November.
    12. Shaliastovich, Ivan & Tauchen, George, 2011. "Pricing of the time-change risks," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 843-858, June.
    13. Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008.
    14. Gennady Gorin & John J. Vastola & Meichen Fang & Lior Pachter, 2022. "Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    15. Behme, Anita & Chong, Carsten & Klüppelberg, Claudia, 2015. "Superposition of COGARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1426-1469.
    16. Semere Habtemicael & Musie Ghebremichael & Indranil SenGupta, 2019. "Volatility and Variance Swap Using Superposition of the Barndorff-Nielsen and Shephard type Lévy Processes," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 75-92, June.
    17. Aubain Hilaire Nzokem, 2023. "Pricing European Options under Stochastic Volatility Models: Case of Five-Parameter Variance-Gamma Process," JRFM, MDPI, vol. 16(1), pages 1-28, January.
    18. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    19. Stojanović, Vladica S. & Popović, Biljana Č. & Milovanović, Gradimir V., 2016. "The Split-SV model," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 560-581.
    20. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes," Papers 2011.09147, arXiv.org.

    More about this item

    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:eee:csdana:v:53:y:2009:i:6:p:2427-2437. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.