A Threshold Stochastic Volatility Model with Realized Volatility
AbstractRapid development in the computer technology has made the financial transaction data visible at an ultimate limit level. The realized volatility, as a proxy for the "true" volatility, can be constructed using the high frequency data. This paper extends a threshold stochastic volatility specification proposed in So, Li and Lam (2002) by incorporating the high frequency volatility measures. Due to the availability of the volatility time series, the parameters estimation can be easily implemented via the standard maximum likelihood estimation (MLE) rather than using the simulated Bayesian methods. In the Monte Carlo section, several mis-specification and sensitivity experiments are conducted. The proposed methodology shows good performance according to the Monte Carlo results. In the empirical study, three stock indices are examined under the threshold stochastic volatility structure. Empirical results show that in different regimes, the returns and volatilities exhibit asymmetric behavior. In addition, this paper allows the threshold in the model to be flexible and uses a sequential optimization based on MLE to search for the "optimal" threshold value. We find that the model with a flexible threshold is always preferred to the model with a fixed threshold according to the log-likelihood measure. Interestingly, the "optimal" threshold is found to be stable across different sampling realized volatility measures.
Download InfoIf 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.
Bibliographic InfoPaper provided by University of Waterloo, Department of Economics in its series Working Papers with number 1003.
Length: 29 pages
Date of creation: May 2010
Date of revision: May 2010
Find related papers by JEL classification:
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-15 (All new papers)
- NEP-ECM-2010-05-15 (Econometrics)
- NEP-ETS-2010-05-15 (Econometric Time Series)
- NEP-MST-2010-05-15 (Market Microstructure)
- NEP-ORE-2010-05-15 (Operations Research)
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.:
- 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.
- Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
- MEDDAHI, Nour, 2001.
"A Theoretical Comparison Between Integrated and Realized Volatilies,"
Cahiers de recherche
2001-26, Universite de Montreal, Departement de sciences economiques.
- Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
- Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2000.
"Econometric analysis of realised volatility and its use in estimating stochastic volatility models,"
2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
- 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.
- Martens, Martin & van Dijk, Dick, 2007.
"Measuring volatility with the realized range,"
Journal of Econometrics,
Elsevier, vol. 138(1), pages 181-207, May.
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002.
"Modeling and Forecasting Realized Volatility,"
02-12, Duke University, Department of Economics.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
- 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.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007.
"Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility,"
The Review of Economics and Statistics,
MIT Press, vol. 89(4), pages 701-720, November.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2005. "Roughing it Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," NBER Working Papers 11775, National Bureau of Economic Research, Inc.
- 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.
- Jun Yu, 2004.
"On leverage in a stochastic volatility model,"
Econometric Society 2004 Far Eastern Meetings
497, Econometric Society.
- Michael McAleer & Marcelo Cunha Medeiros, 2006.
"Realized volatility: a review,"
Textos para discussÃ£o
531 Publication status: F, Department of Economics PUC-Rio (Brazil).
- Bollerslev, Tim & Zhou, Hao, 2006. "Volatility puzzles: a simple framework for gauging return-volatility regressions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 123-150.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- 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.
- Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 525-554.
- Carmen Broto & Esther Ruiz, 2002.
"Estimation Methods For Stochastic Volatility Models: A Survey,"
Statistics and Econometrics Working Papers
ws025414, Universidad Carlos III, Departamento de Estadística y Econometría.
- Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Pat Gruber).
If references are entirely missing, you can add them using this form.