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Inference With Non-Gaussian Ornstein-Uhlenbeck Processes for Stochastic Volatility

Author

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  • James E. Griffin

    (University of Kent at Canterbury)

  • Mark F.J. Steel

    (University of Kent at Canterbury)

Abstract

Continuous-time stochastic volatility models are becoming a more and more popular way to describe moderate and high-frequency financial data. Recently, Barndorff-Nielsen and Shephard (2001a) proposed a class of models where the volatility behaves according to an Ornstein-Uhlenbeck process, driven by a positive Levy process without Gaussian component. They also consider superpositions of such processes and we extend that to the inclusion of an uncorrelated component. Our aim is to design and implement practically relevant inference methods for such models, within the Bayesian paradigm. The algorithm is based on Markov chain Monte Carlo methods and we use a series representation of Levy processes. Inference for such models is complicated by the fact that parameter changes will often induce a change of dimension in the representation of the process and the associated problem of overconditioning. We avoid this problem by dependent thinning methods. An application to stock price data shows the models perform very well, even in the face of data with rapid changes, especially if a superposition of processes is used. After introducing some extra flexibility, the model can even be used to describe spot interest rate data with considerable success.

Suggested Citation

  • James E. Griffin & Mark F.J. Steel, 2002. "Inference With Non-Gaussian Ornstein-Uhlenbeck Processes for Stochastic Volatility," Econometrics 0201002, University Library of Munich, Germany, revised 04 Apr 2003.
  • Handle: RePEc:wpa:wuwpem:0201002
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    1. Shibin Zhang & Xinsheng Zhang, 2008. "Exact Simulation of IG-OU Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 337-355, September.
    2. 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.
    3. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    4. Brix, Anne Floor & Lunde, Asger & Wei, Wei, 2018. "A generalized Schwartz model for energy spot prices — Estimation using a particle MCMC method," Energy Economics, Elsevier, vol. 72(C), pages 560-582.
    5. Asger Lunde & Anne Floor Brix & Wei Wei, 2015. "A Generalized Schwartz Model for Energy Spot Prices - Estimation using a Particle MCMC Method," CREATES Research Papers 2015-46, Department of Economics and Business Economics, Aarhus University.
    6. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    7. Griffin, J.E. & Steel, M.F.J., 2010. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2594-2608, November.
    8. 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.
    9. Kevin W. Lu, 2022. "Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 365-396, July.
    10. Todorov, Viktor, 2011. "Econometric analysis of jump-driven stochastic volatility models," Journal of Econometrics, Elsevier, vol. 160(1), pages 12-21, January.
    11. N. Chopin & P. E. Jacob & O. Papaspiliopoulos, 2013. "SMC-super-2: an efficient algorithm for sequential analysis of state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 397-426, June.
    12. Roberto León-González, 2019. "Efficient Bayesian inference in generalized inverse gamma processes for stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 899-920, September.
    13. Almut E. D. Veraart, 2008. "Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances," CREATES Research Papers 2008-57, Department of Economics and Business Economics, Aarhus University.
    14. 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.
    15. Friedrich Hubalek & Petra Posedel, 2011. "Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 11(6), pages 917-932.
    16. Gonzalez, Jhonny & Moriarty, John & Palczewski, Jan, 2017. "Bayesian calibration and number of jump components in electricity spot price models," Energy Economics, Elsevier, vol. 65(C), pages 375-388.
    17. 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.
    18. Friedrich Hubalek & Petra Posedel, 2008. "Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models," Papers 0807.3479, arXiv.org.
    19. Anzarut, Michelle & Mena, Ramsés H., 2019. "A Harris process to model stochastic volatility," Econometrics and Statistics, Elsevier, vol. 10(C), pages 151-169.
    20. 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).
    21. Sylvia Frühwirth-Schnatter & Leopold Sögner, 2009. "Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma law," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 159-179, March.
    22. 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.
    23. S. C. Kou & X. Sunney Xie & Jun S. Liu, 2005. "Bayesian analysis of single‐molecule experimental data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 469-506, June.

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    Keywords

    Bayesian methods; Deposit spot rate; Levy process; Markov chain Monte Carlo; Stock price;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G0 - Financial Economics - - General

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