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Volatility Proxies for Discrete Time Models

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  • de Vilder, Robin G.
  • Visser, Marcel P.

Abstract

Discrete time volatility models typically employ a latent scale factor to represent volatility. High frequency data may be used to construct proxies for these scale factors. Examples are the intraday high-low range and the realized volatility. This paper develops a method for ranking and optimizing volatility proxies. It is possible to outperform the quadratic variation as a proxy for the discrete time scale factor. For the S&P 500 index data over the years 1988-2006 this is achieved by a proxy which puts, among other things, more weight on the highs than on the lows over intraday intervals.

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File URL: http://mpra.ub.uni-muenchen.de/11001/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 4917.

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Date of creation: 14 Sep 2007
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Handle: RePEc:pra:mprapa:4917

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Keywords: volatility proxy; realized volatility; quadratic variation; scale factor; arch/garch/stochastic volatility; intraday seasonality;

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References

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  1. Werker, B.J.M. & Drost, F.C., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-72561, Tilburg University.
  2. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 219-237, April.
  3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  4. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
  5. Neil Shephard & Ole E. Barndorff-Nielsen, 2004. "Multipower Variation and Stochastic Volatility," Economics Series Working Papers 2004-FE-22, University of Oxford, Department of Economics.
  6. 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.
  7. Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
  8. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  9. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Estimating quadratic variation using realized variance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 457-477.
  10. 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.
  11. Nour Meddahi & √Čric Renault, 2000. "Temporal Aggregation of Volatility Models," CIRANO Working Papers 2000s-22, CIRANO.
  12. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, 06.
  13. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  14. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
  15. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
  16. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
  17. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society.
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Cited by:
  1. Visser, Marcel P., 2008. "Garch Parameter Estimation Using High-Frequency Data," MPRA Paper 9076, University Library of Munich, Germany.
  2. Visser, Marcel P., 2008. "Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure," MPRA Paper 11100, University Library of Munich, Germany.

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