Advanced Search
MyIDEAS: Login to save this paper or follow this series

A Fractionally Integrated Wishart Stochastic Volatility Model

Contents:

Author Info

  • Manabu Asai

    (Faculty of Economics Soka University, Japan and Wharton School University of Pennsylvania)

  • Michael McAleer

    (Econometric Institute Erasmus School of Economics Erasmus University Rotterdam and Tinbergen Institute, The Netherlands and Institute of Economic Research Kyoto University, Japan and Department of Quantitative Economics Complutense University of Madrid, Spain)

Abstract

There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. We conduct a two-step procedure, namely estimating the parameter of fractional integration via log-periodgram regression in the rst step, and estimating the remaining parameters via the generalized method of moments in the second step. Monte Carlo results for the procedure shows reasonable performances in nite samples. The empirical results for the bivariate data of the S&P 500 and FTSE 100 indexes show that the data favor the new FIWSV processes rather than one-factor and two-factor models of Wishart autoregressive processes for the covariance structure.

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.kier.kyoto-u.ac.jp/DP/DP848.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 848.

as in new window
Length: 29pages
Date of creation: Feb 2013
Date of revision:
Handle: RePEc:kyo:wpaper:848

Contact details of provider:
Postal: Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501
Phone: +81-75-753-7102
Fax: +81-75-753-7193
Email:
Web page: http://www.kier.kyoto-u.ac.jp/eng/index.html
More information through EDIRC

Related research

Keywords: Di usion process; Multivariate stochastic volatility; Long memory; Fractional Brownian motion; Generalized Method of Moments.;

Other versions of this item:

Find related papers by JEL classification:

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. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo.
  2. Massimiliano Caporin & Michael McAleer, 2010. "Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models," Working Papers in Economics 10/06, University of Canterbury, Department of Economics and Finance.
  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  4. Eugenie Hol & Siem Jan Koopman & Borus Jungbacker, 2004. "Forecasting daily variability of the S\&P 100 stock index using historical, realised and implied volatility measurements," Computing in Economics and Finance 2004 342, Society for Computational Economics.
  5. Manabu Asai & Michael McAleer, 2013. "Leverage and Feedback Effects on Multifactor Wishart Stochastic Volatility for Option Pricing," Tinbergen Institute Discussion Papers 13-003/III, Tinbergen Institute.
  6. Tim Bollerslev & Natalia Sizova & George Tauchen, 2009. "Volatility in Equilibrium: Asymmetries and Dynamic Dependencies," Working Papers 10-73, Duke University, Department of Economics.
  7. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
  8. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2011. "Asymmetry and Long Memory in Volatility Modelling," Documentos de Trabajo del ICAE 2011-29, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  9. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics.
  11. Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers 96.406, Toulouse - GREMAQ.
  12. Tim Bollerslev & Hao Zhou, 2001. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Finance and Economics Discussion Series 2001-49, Board of Governors of the Federal Reserve System (U.S.).
  13. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
  14. Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
  15. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
  16. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  17. C. Gourieroux, 2006. "Continuous Time Wishart Process for Stochastic Risk," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 177-217.
  18. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  19. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  20. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
  21. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
  22. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
  23. Gourieroux, Christian & Sufana, Razvan, 2010. "Derivative Pricing With Wishart Multivariate Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 438-451.
Full references (including those not matched with items on IDEAS)

Citations

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:kyo:wpaper:848. 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: (Ryo Okui).

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.