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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 efficient price process. The model involves the superposition of a Brownian semimartingale process for the effcient price and a Bernoulli process that determines the extent of price trading. The approach is related to sticky price modeling and the Calvo pricing mechanism 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 inferential framework suggested in Barndorff-Nielson and Shephard (2002) remain valid under flat price trading even though there is information loss due to flat trading effects. 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 transactions 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://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd08-039.pdf
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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd08-039.

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Date of creation: Mar 2009
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Handle: RePEc:hst:ghsdps:gd08-039
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  1. 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.
  2. 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.
  3. N. Gregory Mankiw & Ricardo Reis, 2001. "Sticky information versus sticky prices: a proposal to replace the New-Keynesian Phillips curve," Proceedings, Federal Reserve Bank of San Francisco, issue Jun.
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