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Information Loss in Volatility Measurement with Flat Price Trading

  • Peter C.B. Phillips
  • Jun Yu

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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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 321307000000000805.

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Date of creation: 26 Jan 2007
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Handle: RePEc:cla:levrem:321307000000000805
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  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Jin Wu, 2005. "A Framework for Exploring the Macroeconomic Determinants of Systematic Risk," American Economic Review, American Economic Association, vol. 95(2), pages 398-404, May.
  2. Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 2006-W03, University of Oxford, Department of Economics.
  3. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(04), pages 677-719, August.
  4. 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.
  5. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
  6. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
  7. 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.
  8. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  9. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
  10. 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.
  11. repec:dgr:uvatin:20010077 is not listed on IDEAS
  12. 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.
  13. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  14. Neil Shephard & Ole E. Barndorff-Nielsen, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," Economics Series Working Papers 240, University of Oxford, Department of Economics.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
  21. 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.
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