IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Realized stochastic volatility with leverage and long memory

  • Shinichiro Shirota

    (Graduate School of Economics, University of Tokyo)

  • Takayuki Hizu

    (Mitsubishi UFJ Trust and Banking)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

The daily return and the realized volatility are simultaneously modeled in the stochastic volatility model with leverage and long memory. The dependent variable in the stochastic volatility model is the logarithm of the squared return, and its error distribution is approximated by a mixture of normals. In addition, we incorporate the logarithm of the realized volatility into the measurement equation, assuming that the latent log volatility follows an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process to describe its long memory property. Using a state space representation, we propose an ecient Bayesian estimation method implemented using Markov chain Monte Carlo method (MCMC). Model comparisons are performed based on the marginal likelihood, and the volatility forecasting performances are investigated using S&P500 stock index returns.

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.cirje.e.u-tokyo.ac.jp/research/dp/2012/2012cf869.pdf
Download Restriction: no

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-869.

as
in new window

Length: 35 pages
Date of creation: Nov 2012
Date of revision:
Handle: RePEc:tky:fseres:2012cf869
Contact details of provider: Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033
Phone: +81-3-5841-5644
Fax: +81-3-5841-8294
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
Email:


More information through EDIRC

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. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  2. Ghysels, Eric & Sinko, Arthur, 2011. "Volatility forecasting and microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 257-271, January.
  3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  4. 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.
  5. Dobrislav P. Dobrev & Pawel J. Szerszen, 2010. "The information content of high-frequency data for estimating equity return models and forecasting risk," Finance and Economics Discussion Series 2010-45, Board of Governors of the Federal Reserve System (U.S.).
  6. John M. Maheu & Thomas H. McCurdy, 2007. "Components of Market Risk and Return," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(4), pages 560-590, Fall.
  7. Makoto Takahashi & Yasuhiro Omori & Toshiaki Watanabe, 2007. "Estimating Stochastic Volatility Models Using Daily Returns and Realized Volatility Simultaneously," CIRJE F-Series CIRJE-F-515, CIRJE, Faculty of Economics, University of Tokyo.
  8. Jun Yu, 2004. "On leverage in a stochastic volatility model," Econometric Society 2004 Far Eastern Meetings 497, Econometric Society.
  9. Asai, Manabu & McAleer, Michael & Medeiros, Marcelo C., 2012. "Modelling and forecasting noisy realized volatility," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 217-230, January.
  10. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, March.
  11. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  12. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
  13. Nakajima, Jouchi & Omori, Yasuhiro, 2009. "Leverage, heavy-tails and correlated jumps in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2335-2353, April.
  14. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  15. John M. Maheu & Thomas H. McCurdy, 2009. "Do High-Frequency Measures of Volatility Improve Forecasts of Return Distributions?," Working Paper Series 19_09, The Rimini Centre for Economic Analysis, revised Jan 2009.
  16. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
  17. Hasbrouck, Joel, 2007. "Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading," OUP Catalogue, Oxford University Press, number 9780195301649, March.
  18. Yacine Ait-Sahalia & Per A. Mykland, 2003. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," NBER Working Papers 9611, National Bureau of Economic Research, Inc.
  19. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
  20. Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
  21. Omori, Yasuhiro & Watanabe, Toshiaki, 2008. "Block sampler and posterior mode estimation for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2892-2910, February.
  22. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
  23. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
  24. 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.
  25. Pierre Giot & Sébastien Laurent, 2002. "Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models," Computing in Economics and Finance 2002 52, Society for Computational Economics.
  26. Pérez, Ana & Ruiz, Esther & Veiga, Helena, 2009. "A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3593-3600, August.
  27. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
  28. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
  29. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," CREATES Research Papers 2007-18, School of Economics and Management, University of Aarhus.
  30. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Papers 2006-W03, Economics Group, Nuffield College, University of Oxford.
  31. 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.
  32. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, Elsevier.
  33. Esther Ruiz & Helena Veiga, 2006. "Modelling Long-Memory Volatilities With Leverage Effect: Almsv Versus Fiegarch," Statistics and Econometrics Working Papers ws066016, Universidad Carlos III, Departamento de Estadística y Econometría.
  34. 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.
  35. Andersen, Torben G. & Bollerslev, Tim & Meddahi, Nour, 2011. "Realized volatility forecasting and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 220-234, January.
  36. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  37. Dobrislav Dobrev & Pawel Szerszen, 2010. "The information content of high-frequency data for estimating equity return models and forecasting risk," International Finance Discussion Papers 1005, Board of Governors of the Federal Reserve System (U.S.).
  38. Andrew Patton, 2006. "Volatility Forecast Comparison using Imperfect Volatility Proxies," Research Paper Series 175, Quantitative Finance Research Centre, University of Technology, Sydney.
  39. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
  40. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
  41. Peter Reinhard Hansen & Zhuo Huang & Howard Howan Shek, 2012. "Realized GARCH: a joint model for returns and realized measures of volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 877-906, 09.
  42. Wang, Joanna J.J. & Chan, Jennifer S.K. & Choy, S.T. Boris, 2011. "Stochastic volatility models with leverage and heavy-tailed distributions: A Bayesian approach using scale mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 852-862, January.
  43. repec:dgr:uvatin:20110132 is not listed on IDEAS
  44. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
  45. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2012cf869. 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: (CIRJE administrative office)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.