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Continuous time analysis of fleeting discrete price moves

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  • Neil Shephard
  • Justin J Yang

Abstract

This article proposes a novel model of financial prices where (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve. The resulting càdlàg price process is a piecewise constant semimartingale with finite activity, finite variation, and no Brownian motion component. We use moment-based estimations to fit four high-frequency futures datasets and demonstrate the descriptive power of our proposed model. This model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals. Supplementary materials for this article are available online.
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Suggested Citation

  • Neil Shephard & Justin J Yang, "undated". "Continuous time analysis of fleeting discrete price moves," Working Paper 360986, Harvard University OpenScholar.
    • Handle: RePEc:qsh:wpaper:360986
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    File URL: http://scholar.harvard.edu/shephard/node/360986
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    2. Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
    3. Vladim'ir Hol'y & Petra Tomanov'a, 2021. "Modeling Price Clustering in High-Frequency Prices," Papers 2102.12112, arXiv.org, revised Mar 2021.
    4. Dimitriadis, Timo & Halbleib, Roxana & Polivka, Jeannine & Rennspies, Jasper & Streicher, Sina & Wolter, Axel Friedrich, 2026. "Efficient sampling for realized variance estimation in time-changed diffusion models," Journal of Econometrics, Elsevier, vol. 254(PA).
    5. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2022. "Dynamic Discrete Mixtures for High-Frequency Prices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 559-577, April.
    6. Vladim'ir Hol'y, 2022. "An Intraday GARCH Model for Discrete Price Changes and Irregularly Spaced Observations," Papers 2211.12376, arXiv.org, revised May 2024.
    7. Veraart, Almut E.D., 2019. "Modeling, simulation and inference for multivariate time series of counts using trawl processes," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 110-129.
    8. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
    9. Bennedsen, Mikkel & Lunde, Asger & Shephard, Neil & Veraart, Almut E.D., 2023. "Inference and forecasting for continuous-time integer-valued trawl processes," Journal of Econometrics, Elsevier, vol. 236(2).

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