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Duration-Based Volatility Estimation

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Author Info
Torben G. Andersen
Dobrislav Dobrev
Ernst Schaumburg

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Abstract

We develop a novel approach to estimating the integrated variance of a general jump-diffusion with stochastic volatility. Our approach exploits the relationship between the speed (distance traveled per fixed time unit) and passage time (time taken to travel a fixed distance) of the Brownian motion. The new class of duration-based IV estimators derived in this paper is shown to be robust to both jumps and market microstructure noise. Moreover, their asymptotic and finite sample properties compare favorably to those of commonly used robust IV estimators.

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File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd08-034.pdf
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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd08-034.

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Date of creation: Mar 2009
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Handle: RePEc:hst:ghsdps:gd08-034

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  1. 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. [Downloadable!] (restricted)
  2. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January. [Downloadable!] (restricted)
  3. Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Papers 2005-W06, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  4. 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. [Downloadable!]
  5. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, 06. [Downloadable!] (restricted)
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  6. Lunde A. & Timmermann A., 2004. "Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 253-273, July. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
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  8. 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.
  9. Ole E. Barndorff-Nielsen & Neil Shephard & Matthias Winkel, 2005. "Limit theorems for multipower variation in the presence of jumps," Economics Papers 2005-W07, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  10. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37. [Downloadable!] (restricted)
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  11. Park, Hun Y, 1993. "Trading Mechanisms and Price Volatility: Spot versus Futures," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 175-79, February. [Downloadable!] (restricted)
  12. 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. [Downloadable!]
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  13. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395. [Downloadable!] (restricted)
  14. 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.
  15. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-74, January. [Downloadable!] (restricted)
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  16. Joel Hasbrouck, 1999. "The Dynamics of Discrete Bid and Ask Quotes," Journal of Finance, American Finance Association, vol. 54(6), pages 2109-2142, December. [Downloadable!] (restricted)
  17. Cho, David Chinhyung & Frees, Edward W, 1988. " Estimating the Volatility of Discrete Stock Prices," Journal of Finance, American Finance Association, vol. 43(2), pages 451-66, June. [Downloadable!] (restricted)
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