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Information Loss in Volatility Measurement with Flat Price Trading

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  • Peter C.B.Phillips

    (Yale University, University of Auckland,University of York & Singapore Management University)

  • Jun Yu

    (Sim Kee Boon Institute for Financial Economics, Singapore Management University)

Abstract

A model of financial asset price determination is proposed that incorporates flat trading features into an e¡é cient price process. The model involves the superposition of a Brownian semimartin- gale process for the efficient price and a Bernoulli process that determines the extent of flat price trading. The approach is related to sticky price modeling and the Calvo pricing mecha- nism in macroeconomic dynamics. A limit theory for the conventional realized volatility (RV) measure of integrated volatility is developed. The results show that RV is still consistent but has an inflated asymptotic variance that depends on the probability of flat trading. Estimated quarticity is similarly affected, so that both the feasible central limit theorem and the infer- ential framework suggested in Barndorff-Nielson and Shephard (2002) remain valid under flat price trading even though there is information loss due to flat trading e¡èects. The results are related to work by Jacod (1993) and Mykland and Zhang (2006) on realized volatility measures with random and intermittent sampling, and to ACD models for irregularly spaced transac- tions data. Extensions are given to include models with microstructure noise. Some simulation results are reported. Empirical evaluations with tick-by-tick data indicate that the effect of flat trading on the limit theory under microstructure noise is likely to be minor in most cases, thereby affirming the relevance of existing approaches.

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File URL: http://www.smu.edu.sg/institutes/skbife/downloads/CoFiE/Working%20Papers/Information%20Loss%20in%20Volatility%20Measurement%20with%20Flat%20Price%20Trading.pdf
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Bibliographic Info

Paper provided by Sim Kee Boon Institute for Financial Economics in its series Working Papers with number CoFie-01-2008.

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Length: 45 Pages
Date of creation: May 2008
Date of revision:
Publication status: Published in SMU-SKBI CoFie Working Paper
Handle: RePEc:skb:wpaper:cofie-01-2008

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Keywords: Bernoulli process; Brownian semimartingale; Calvo pricing; Flat trading; Microstruc- ture noise; Quarticity function; Realized volatility; Stopping times.;

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References

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  1. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
  2. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Wu, Jin, 2005. "A framework for exploring the macroeconomic determinants of systematic risk," CFS Working Paper Series 2005/04, Center for Financial Studies (CFS).
  3. Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Series Working Papers 2005-FE-09, University of Oxford, Department of Economics.
  4. 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.
  5. 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.
  6. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
  7. Mankiw, N. Gregory & Reis, Ricardo, 2002. "Sticky Information Versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve," Scholarly Articles 3415324, Harvard University Department of Economics.
  8. 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.
  9. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
  10. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.
  11. 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.
  12. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
  13. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
  14. 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.
  15. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  16. 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.
  17. H. Peter Boswijk, 2001. "Testing for a Unit Root with Near-Integrated Volatility," Tinbergen Institute Discussion Papers 01-077/4, Tinbergen Institute.
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  19. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
  20. Corradi, Valentina, 2000. "Reconsidering the continuous time limit of the GARCH(1, 1) process," Journal of Econometrics, Elsevier, vol. 96(1), pages 145-153, May.
  21. 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.
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Citations

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Cited by:
  1. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2009. "Jump-Robust Volatility Estimation using Nearest Neighbor Truncation," NBER Working Papers 15533, National Bureau of Economic Research, Inc.
  2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Economics Papers 2008-W10, Economics Group, Nuffield College, University of Oxford.
  3. Liu, Cheng & Tang, Cheng Yong, 2014. "A quasi-maximum likelihood approach for integrated covariance matrix estimation with high frequency data," Journal of Econometrics, Elsevier, vol. 180(2), pages 217-232.
  4. Shirley J. Huang & Jun Yu, . "Bayesian Analysis of Structural Credit Risk Models with Microstructure Noises," Working Papers CoFie-07-2008, Sim Kee Boon Institute for Financial Economics.

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