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Estimating Quadratic Variation When Quoted Prices Change by a Constant Increment

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Author Info
Jeremy Large

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Abstract

For financial assets whose best quotes almost always change by jumping by the market`s price tick size (one cent, five cents, etc.), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It measures the prevalence of alternations, where quotes jump back to their just-previous price. It defines a simple property called "uncorrelated alternation", which under conditions implies that the estimator is consistent in an asymptotic limit theory, where jumps become very frequent and small. Feasible limit theory is developed, and in simulations works well.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 340.

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Date of creation: 2007
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Handle: RePEc:oxf:wpaper:340

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Keywords: Realized Volatility Realized Variance Quadratic Variation Market Microstructure High-Frequency Data Prue Jump Process

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Find related papers by JEL classification:
C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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  1. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March. [Downloadable!] (restricted)
  2. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  3. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
  4. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 18(2), pages 351-416. [Downloadable!] (restricted)
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  5. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30. [Downloadable!] (restricted)
    Other versions:
  6. 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. [Downloadable!] (restricted)
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  7. Yong Zeng, 2003. "A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering," Mathematical Finance, Blackwell Publishing, vol. 13(3), pages 411-444. [Downloadable!] (restricted)
  8. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society. [Downloadable!]
  9. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  10. Hans Degryse & Frank Jong & Maarten Ravenswaaij & Gunther Wuyts, 2005. "Aggressive Orders and the Resiliency of a Limit Order Market," Review of Finance, Springer, vol. 9(2), pages 201-242, 06. [Downloadable!] (restricted)
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  11. Ball, Clifford A, 1988. " Estimation Bias Induced by Discrete Security Prices," Journal of Finance, American Finance Association, vol. 43(4), pages 841-65, September. [Downloadable!] (restricted)
  12. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February. [Downloadable!] (restricted)
  13. Neil Shephard & Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 264, University of Oxford, Department of Economics. [Downloadable!]
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  14. 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. [Downloadable!] (restricted)
  15. Gottlieb, Gary & Kalay, Avner, 1985. " Implications of the Discreteness of Observed Stock Prices," Journal of Finance, American Finance Association, vol. 40(1), pages 135-53, March. [Downloadable!] (restricted)
  16. Roel C. A. Oomen, 2005. "Properties of Bias-Corrected Realized Variance Under Alternative Sampling Schemes," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 555-577. [Downloadable!] (restricted)
  17. Peter Hansen & Jeremy Large & Asger Lunde, 2008. "Moving Average-Based Estimators of Integrated Variance," Econometric Reviews, Taylor and Francis Journals, vol. 27(1-3), pages 79-111. [Downloadable!] (restricted)
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