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

A Reduced Form Framework for Modeling Volatility of Speculative Prices based on Realized Variation Measures

Contents:

Author Info

  • Torben G. Andersen
  • Tim Bollerslev
  • Xin Huang

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

Building on realized variance and bi-power variation measures constructed from high-frequency financial prices, we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility. We decompose the total daily return variability into the continuous sample path variance, the variation arising from discontinuous jumps that occur during the trading day, as well as the overnight return variance. Our empirical results, based on long samples of high-frequency equity and bond futures returns, suggest that the dynamic dependencies in the daily continuous sample path variability is well described by an approximate long-memory HAR-GARCH model, while the overnight returns may be modelled by an augmented GARCH type structure. The dynamic dependencies in the non-parametrically identified significant jumps appear to be well described by the combination of an ACH model for the time-varying jump intensities coupled with a relatively simple log-linear structure for the jump sizes. Lastly, we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out-of-sample forecasts for the total return volatility.

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: ftp://ftp.econ.au.dk/creates/rp/07/rp07_14.pdf
Download Restriction: no

Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-14.

as in new window
Length: 31
Date of creation: 16 Aug 2007
Date of revision:
Handle: RePEc:aah:create:2007-14

Contact details of provider:
Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Stochastic Volatility; Realized Variation; Bipower Variation; Jumps; Hazard Rates; Overnight Volatility;

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. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
  2. 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.
  3. James D. Hamilton & Oscar Jorda, . "A model for the federal funds rate target," Department of Economics 99-07, California Davis - Department of Economics.
  4. repec:att:wimass:9710 is not listed on IDEAS
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2006. "Real-time price discovery in global stock, bond and foreign exchange markets," International Finance Discussion Papers 871, Board of Governors of the Federal Reserve System (U.S.).
  6. 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.
  7. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2001. "An Empirical Investigation of Continuous-Time Equity Return Models," NBER Working Papers 8510, National Bureau of Economic Research, Inc.
  8. Torben G. Andersen & Tim Bollerslev & Per Frederiksen & Morten �rregaard Nielsen, 2010. "Continuous-time models, realized volatilities, and testable distributional implications for daily stock returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 233-261.
  9. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  10. Barndorff-Nielsen, Ole E. & Shephard, Neil & Winkel, Matthias, 2006. "Limit theorems for multipower variation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 796-806, May.
  11. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
  12. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, Elsevier.
  13. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  14. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
  15. Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December.
  16. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
  17. Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Series Working Papers 2005-FE-09, University of Oxford, Department of Economics.
  18. Rohit Deo & Clifford Hurvich & Yi Lu, 2005. "Forecasting Realized Volatility Using a Long Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment," Econometrics 0501002, EconWPA.
  19. Chan, Wing H & Maheu, John M, 2002. "Conditional Jump Dynamics in Stock Market Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 377-89, July.
  20. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford.
  21. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
  22. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
  23. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
  24. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
  25. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Vega, Clara, 2004. "Real-time price discovery in stock, bond and foreign exchange markets," CFS Working Paper Series 2004/19, Center for Financial Studies (CFS).
  26. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Papers 2003-W21, Economics Group, Nuffield College, University of Oxford.
  27. Martin Martens & Dick van Dijk & Michiel de Pooter, 2004. "Modeling and Forecasting S&P 500 Volatility: Long Memory, Structural Breaks and Nonlinearity," Tinbergen Institute Discussion Papers 04-067/4, Tinbergen Institute.
  28. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  29. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  30. Thomakos, Dimitrios D. & Wang, Tao, 2003. "Realized volatility in the futures markets," Journal of Empirical Finance, Elsevier, vol. 10(3), pages 321-353, May.
  31. Chan, Kalok & Chan, K C & Karolyi, G Andrew, 1991. "Intraday Volatility in the Stock Index and Stock Index Futures Markets," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 657-84.
  32. Neely, Christopher J., 1999. "Target zones and conditional volatility: The role of realignments," Journal of Empirical Finance, Elsevier, vol. 6(2), pages 177-192, April.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. Markku Lanne, 2006. "Forecasting Realized Volatility by Decomposition," Economics Working Papers ECO2006/20, European University Institute.
  38. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  39. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, vol. 73(1), pages 279-296, 01.
  40. Anderson, Heather M. & Vahid, Farshid, 2007. "Forecasting the Volatility of Australian Stock Returns: Do Common Factors Help?," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 76-90, January.
  41. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
  42. 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.
  43. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
  44. Tina Hviid Rydberg & Neil Shephard, 2002. "Dynamics of trade-by-trade price movements: decomposition and models," Economics Papers 2002-W1, Economics Group, Nuffield College, University of Oxford.
  45. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  46. 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.
  47. Kenneth D. West & Michael W. McCracken, 1998. "Regression-Based Tests of Predictive Ability," NBER Technical Working Papers 0226, National Bureau of Economic Research, Inc.
  48. Siem Jan Koopman & Borus Jungbacker & Eugenie Hol, 2004. "Forecasting Daily Variability of the S&P 100 Stock Index using Historical, Realised and Implied Volatility Measurements," Tinbergen Institute Discussion Papers 04-016/4, Tinbergen Institute.
  49. 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.
  50. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
  51. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, vol. 59(2), pages 755-793, 04.
  52. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  53. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
  54. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, 06.
  55. Fleming, Jeff & Kirby, Chris & Ostdiek, Barbara, 2003. "The economic value of volatility timing using "realized" volatility," Journal of Financial Economics, Elsevier, vol. 67(3), pages 473-509, March.
  56. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
  57. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
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. Stefano Grassi & Paolo Santucci de Magistris, 2013. "It's all about volatility of volatility: evidence from a two-factor stochastic volatility model," Studies in Economics 1404, Department of Economics, University of Kent.
  2. Julien Chevallier & Benoît Sévi, 2011. "On the volatility-volume relationship in energy futures markets using intraday data," EconomiX Working Papers 2011-16, University of Paris West - Nanterre la Défense, EconomiX.
  3. Mihaela Craioveanu & Eric Hillebrand, 2012. "Why It Is Ok To Use The Har-Rv(1,5,21) Model," Working Papers 1201, University of Central Missouri, Department of Economics & Finance, revised Aug 2012.
  4. Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(3), pages 326-360, Summer.
  5. Fuertes, Ana-Maria & Olmo, Jose, 2013. "Optimally harnessing inter-day and intra-day information for daily value-at-risk prediction," International Journal of Forecasting, Elsevier, vol. 29(1), pages 28-42.
  6. Stefano Grassi & Paolo Santucci de Magistris, 2013. "It’s all about volatility (of volatility): evidence from a two-factor stochastic volatility model," CREATES Research Papers 2013-03, School of Economics and Management, University of Aarhus.
  7. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.
  8. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 284-304.
  9. Stefano Grassi & Nima Nonejad & Paolo Santucci de Magistris, 2014. "Forecasting with the Standardized Self-Perturbed Kalman Filter," CREATES Research Papers 2014-12, School of Economics and Management, University of Aarhus.
  10. Golosnoy, Vasyl & Hamid, Alain & Okhrin, Yarema, 2014. "The empirical similarity approach for volatility prediction," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 321-329.
  11. Liao, Yin, 2013. "The benefit of modeling jumps in realized volatility for risk prediction: Evidence from Chinese mainland stocks," Pacific-Basin Finance Journal, Elsevier, vol. 23(C), pages 25-48.
  12. Fulvio Corsi & Francesco Audrino, 2008. "Modeling Tick-by-Tick Realized Correlations," University of St. Gallen Department of Economics working paper series 2008 2008-05, Department of Economics, University of St. Gallen.
  13. Jozef Barunik & Lukas Vacha, 2012. "Realized wavelet-based estimation of integrated variance and jumps in the presence of noise," Papers 1202.1854, arXiv.org, revised Feb 2013.
  14. Jozef Barunik & Lukas Vacha, 2012. "Modeling and forecasting exchange rate volatility in time-frequency domain," Papers 1204.1452, arXiv.org, revised Aug 2013.
  15. Hua, Jian & Manzan, Sebastiano, 2013. "Forecasting the return distribution using high-frequency volatility measures," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4381-4403.
  16. Stefano Grassi & Nima Nonejad & Paolo Santucci de Magistris, 2014. "Forecasting with the Standardized Self-Perturbed Kalman Filter," Studies in Economics 1405, Department of Economics, University of Kent.

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:aah:create:2007-14. 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: ().

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.