Information loss in volatility measurement with flat price trading
Information loss in volatility measurement with flat price trading
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 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 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-Nielsen and Shephard (J Royal Stat Soc Ser B (Stat Methodol) 64:253–280, 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 (J Financ Econom 16:526–569, 2018) and Mykland and Zhang (Ann Stat 34:1931–1963, 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.
Bernoulli process, Brownian semimartingale, Calvo pricing, Flat trading, Microstructure noise, Quarticity function, Realized volatility, Stopping times
2957-2999
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Yu, Jun
b0708df0-aac1-4595-b2fd-4c5c1aa38160
June 2023
Phillips, Peter Charles Bonest
f67573a4-fc30-484c-ad74-4bbc797d7243
Yu, Jun
b0708df0-aac1-4595-b2fd-4c5c1aa38160
Phillips, Peter Charles Bonest and Yu, Jun
(2023)
Information loss in volatility measurement with flat price trading.
Empirical Economics, 64 (6), .
(doi:10.1007/s00181-022-02353-y).
Abstract
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 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 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-Nielsen and Shephard (J Royal Stat Soc Ser B (Stat Methodol) 64:253–280, 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 (J Financ Econom 16:526–569, 2018) and Mykland and Zhang (Ann Stat 34:1931–1963, 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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Accepted/In Press date: 16 December 2022
e-pub ahead of print date: 11 January 2023
Published date: June 2023
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An early version of this paper was circulated as a working paper (Phillips and Yu ) but never published. This version brings the paper up to date and adds further analysis, simulations and discussion. Thanks go to the Editor and two referees for their comments and suggestions on the paper and to Neil Shephard, Jean Jacod and Sungbae An for helpful comments on aspects of the research. Phillips acknowledges support from a Lee Kong Chian Fellowship at SMU, the Kelly Fund at the University of Auckland, and the NSF under Grant No. SES 18-50860. Yu acknowledges that this research/project is supported by the Ministry of Education, Singapore, under its Academic Research Fund (AcRF) Tier 2 (Award Number MOE-T2EP402A20-0002). He also acknowledges the financial support from the Lee Foundation.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Keywords:
Bernoulli process, Brownian semimartingale, Calvo pricing, Flat trading, Microstructure noise, Quarticity function, Realized volatility, Stopping times
Identifiers
Local EPrints ID: 473661
URI: http://eprints.soton.ac.uk/id/eprint/473661
ISSN: 0377-7332
PURE UUID: 062230ba-5330-4c11-bdd8-7316356f3a7a
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Date deposited: 27 Jan 2023 17:33
Last modified: 17 Mar 2024 07:37
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Jun Yu
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