Microstructure noise, realized volatility, and optimal sampling
Recorded prices are known to diverge from their "efficient" values due to the presence of market microstructure contaminations. The microstructure noise creates a dichotomy in the model-free estimation of integrated volatility. While it is theoretically necessary to sum squared returns that are computed over very small intervals to better identify the underlying quadratic variation over a period, the summing of numerous contaminated return data entails substantial accumulation of noise. Using asymptotic arguments as in the extant theoretical literature on the subject, we argue that the realized volatility estimator diverges to infinity almost surely when noise plays a role. While realized volatility cannot be a consistent estimate of the quadratic variation of the log price process, we show that a standardized version of the realized volatility estimator can be employed to uncover the second moment of the (unobserved) noise process. More generally, we show that straightforward sample moments of the noisy return data provide consistent estimates of the moments of the noise process. Finally, we quantify the finite sample bias/variance trade-off that is induced by the accumulation of noisy observations and provide clear and easily implementable directions for optimally sampling contaminated high frequency return data for the purpose of volatility estimation
|Date of creation:||11 Aug 2004|
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- Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, 05.
- Federico M. Bandi & Benoit Perron, 2006.
"Long Memory and the Relation Between Implied and Realized Volatility,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 4(4), pages 636-670.
- Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics 0305004, EconWPA.
- 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.
- 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.
- 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.
- 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.
- 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.
- Roel C.A. Oomen, 2004. "Statistical Models for High Frequency Security Prices," Econometric Society 2004 North American Winter Meetings 77, Econometric Society.
- 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.
- 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.
- Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
- S. Baranzoni & P. Bianchi & L. Lambertini, 2000. "Multiproduct Firms, Product Differentiation, and Market Structure," Working Papers 368, Dipartimento Scienze Economiche, Universita' di Bologna.
- Madhavan, Ananth, 2000. "Market microstructure: A survey," Journal of Financial Markets, Elsevier, vol. 3(3), pages 205-258, August.
- 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.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford.
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