Advanced Search
MyIDEAS: Login

Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models

Contents:

Author Info

  • Emanuele Taufer

    ()
    (DISA, Faculty of Economics, Trento University)

  • Nikolai Leonenko
  • Marco Bee

Abstract

Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression. In this paper we propose a characteristic function-based estimation method for non-Gaussian Ornstein-Uhlenbeck-based stochastic volatility models. After deriving explicit expressions of the characteristic functions for various cases of interest we analyze the asymptotic properties of the estimators and evaluate their performance by means of a simulation experiment. Finally, a real-data application shows that the superposition of two Ornstein-Uhlenbeck processes gives a good approximation to the dependence structure of the process.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.unitn.it/files/download/10530/07.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Department of Computer and Management Sciences, University of Trento, Italy in its series DISA Working Papers with number 0907.

as in new window
Length: 30 pages
Date of creation: Oct 2009
Date of revision: 02 Dec 2009
Handle: RePEc:trt:disawp:0907

Contact details of provider:
Postal: via Inama, 5 -- I-38100 Trento TN
Phone: +39-0461-882126
Fax: +39-0461-882124
Email:
Web page: http://www.unitn.it/disa
More information through EDIRC

Order Information:
Postal: DISA Università degli Studi di Trento via Inama, 5 I-38122 Trento TN Italy
Email:
Web: http://www.unitn.it/disa

Related research

Keywords: ornstein-uhlenbeck process; lévy process; stochastic volatility; characteristic function estimation;

Other versions of this item:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Emanuele Taufer & Nikolai Leonenko, 2007. "Simulation of Lévy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Quaderni DISA 123, Department of Computer and Management Sciences, University of Trento, Italy, revised 23 May 2007.
  2. John L. Knight & Stephen E. Satchell & Jun Yu, 2002. "Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(3), pages 319-335, 09.
  3. Michael Sørensen, 2000. "Prediction-based estimating functions," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 123-147.
  4. Jiang, George J & Knight, John L, 2002. "Estimation of Continuous-Time Processes via the Empirical Characteristic Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 198-212, April.
  5. 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.
  6. 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.
  7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  8. Gareth O. Roberts & Omiros Papaspiliopoulos & Petros Dellaportas, 2004. "Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 369-393.
  9. Knight, John L. & Yu, Jun, 2002. "Empirical Characteristic Function In Time Series Estimation," Econometric Theory, Cambridge University Press, vol. 18(03), pages 691-721, June.
  10. Geurt Jongbloed & Frank H. Van Der Meulen, 2006. "Parametric Estimation for Subordinators and Induced OU Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(4), pages 825-847.
  11. Ole E. Barndorff-Nielsen, 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.
  12. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
  13. Jun Yu, 2004. "Empirical Characteristic Function Estimation and Its Applications," Econometric Reviews, Taylor & Francis Journals, vol. 23(2), pages 93-123.
  14. Matthew P. S. Gander & David A. Stephens, 2007. "Simulation and inference for stochastic volatility models driven by Lévy processes," Biometrika, Biometrika Trust, vol. 94(3), pages 627-646.
  15. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  16. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
  17. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
  18. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
  19. T.W. Epps, 2005. "Tests for location-scale families based on the empirical characteristic function," Metrika, Springer, vol. 62(1), pages 99-114, 09.
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 in new window

Cited by:
  1. Nikolai Leonenko & EStuart Petherick & Emanuele Taufer, 2012. "Multifractal Scaling for Risky Asset Modelling," DISA Working Papers 2012/07, Department of Computer and Management Sciences, University of Trento, Italy, revised Jul 2012.
  2. Kotchoni, Rachidi, 2014. "The indirect continuous-GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 464-488.
  3. Leonenko, Nikolai & Petherick, Stuart & Taufer, Emanuele, 2013. "Multifractal models via products of geometric OU-processes: Review and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 7-16.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:trt:disawp:0907. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Roberto Gabriele).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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