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Jump-robust volatility estimation using nearest neighbor truncation

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  • Torben G. Andersen
  • Dobrislav Dobrev
  • Ernst Schaumburg

Abstract

We propose two new jump-robust estimators of integrated variance based on high-frequency return observations. These MinRV and MedRV estimators provide an attractive alternative to the prevailing bipower and multipower variation measures. Specifically, the MedRV estimator has better theoretical efficiency properties than the tripower variation measure and displays better finite-sample robustness to both jumps and the occurrence of “zero” returns in the sample. Unlike the bipower variation measure, the new estimators allow for the development of an asymptotic limit theory in the presence of jumps. Finally, they retain the local nature associated with the low-order multipower variation measures. This proves essential for alleviating finite sample biases arising from the pronounced intraday volatility pattern that afflicts alternative jump-robust estimators based on longer blocks of returns. An empirical investigation of the Dow Jones 30 stocks and an extensive simulation study corroborate the robustness and efficiency properties of the new estimators.

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Bibliographic Info

Paper provided by Federal Reserve Bank of New York in its series Staff Reports with number 465.

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Date of creation: 2010
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Handle: RePEc:fip:fednsr:465

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Keywords: Stocks - Rate of return ; Stock market ; Stock - Prices;

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  1. Ole E. Barndorff-Nielsen & Neil Shephard & Matthias Winkel, 2005. "Limit theorems for multipower variation in the presence of jumps," OFRC Working Papers Series 2005fe06, Oxford Financial Research Centre.
  2. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2011. "A Functional Filtering and Neighborhood Truncation Approach to Integrated Quarticity Estimation," CREATES Research Papers 2011-23, School of Economics and Management, University of Aarhus.
  3. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2009. "Duration-Based Volatility Estimation," Global COE Hi-Stat Discussion Paper Series gd08-034, Institute of Economic Research, Hitotsubashi University.
  4. Kim Christensen & Roel Oomen & Mark Podolskij, 2010. "Realised quantile-based estimation of the integrated variance," Post-Print peer-00732538, HAL.
  5. Peter C.B.Phillips & Jun Yu, 2008. "Information Loss in Volatility Measurement with Flat Price Trading," Working Papers CoFie-01-2008, Sim Kee Boon Institute for Financial 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. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
  8. Alain Chaboud & Benjamin Chiquoine & Erik Hjalmarsson & Mico Loretan, 2007. "Frequency of observation and the estimation of integrated volatility in deep and liquid financial markets," International Finance Discussion Papers 905, Board of Governors of the Federal Reserve System (U.S.).
  9. 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.
  10. Yacine Ait-Sahalia & Per A. Mykland & Lan Zhang, 2005. "Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise," NBER Working Papers 11380, National Bureau of Economic Research, Inc.
  11. Corsi, Fulvio & Pirino, Davide & Renò, Roberto, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Journal of Econometrics, Elsevier, vol. 159(2), pages 276-288, December.
  12. 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.
  13. Joel Hasbrouck, 1999. "The Dynamics of Discrete Bid and Ask Quotes," Journal of Finance, American Finance Association, vol. 54(6), pages 2109-2142, December.
  14. Mark Podolskij & Mathias Vetter, 2007. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," CREATES Research Papers 2007-27, School of Economics and Management, University of Aarhus.
  15. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C1-C32, November.
  16. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, 09.
  17. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
  18. Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," OFRC Working Papers Series 2005fe09, Oxford Financial Research Centre.
  19. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
  20. Almut Veraart, 2008. "Inference for the jump part of quadratic variation of Itô semimartingales," CREATES Research Papers 2008-17, School of Economics and Management, University of Aarhus.
  21. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," Center for Financial Institutions Working Papers 02-27, Wharton School Center for Financial Institutions, University of Pennsylvania.
  22. repec:oup:jfinec:v:9:y::i:4:p:657-684 is not listed on IDEAS
  23. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
  24. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
  25. Jim Griffin & Roel Oomen, 2008. "Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 230-253.
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