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Integer-valued L�vy processes and low latency financial econometrics

Author

Listed:
  • Ole E. Barndorff-Nielsen
  • David G. Pollard
  • Neil Shephard

Abstract

Motivated by features of low latency data in financial econometrics we study in detail integer-valued L�vy processes as the basis of price processes for high-frequency econometrics. We propose using models built out of the difference of two subordinators. We apply these models in practice to low latency data for a variety of different types of futures contracts.

Suggested Citation

  • Ole E. Barndorff-Nielsen & David G. Pollard & Neil Shephard, 2012. "Integer-valued L�vy processes and low latency financial econometrics," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 587-605, January.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:4:p:587-605
    DOI: 10.1080/14697688.2012.664935
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    References listed on IDEAS

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    1. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    2. Peter Reinhard Hansen & Guillaume Horel, 2009. "Quadratic Variation by Markov Chains," CREATES Research Papers 2009-13, Department of Economics and Business Economics, Aarhus University.
    3. Bruce Lehmann, 2008. "Arbitrage-free Limit Order Books and the Pricing of Order Flow Risk," NBER Working Papers 13848, National Bureau of Economic Research, Inc.
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    Citations

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    Cited by:

    1. Mikkel Bennedsen & Asger Lunde & Neil Shephard & Almut E. D. Veraart, 2021. "Inference and forecasting for continuous-time integer-valued trawl processes," Papers 2107.03674, arXiv.org, revised Feb 2023.
    2. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    3. Siem Jan Koopman & Rutger Lit & André Lucas, 2015. "Intraday Stock Price Dependence using Dynamic Discrete Copula Distributions," Tinbergen Institute Discussion Papers 15-037/III/DSF90, Tinbergen Institute.
    4. 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.
    5. Paul Doukhan, 2012. "Comments on: Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 447-450, September.
    6. Jonas Hallgren & Timo Koski, 2016. "Testing for Causality in Continuous Time Bayesian Network Models of High-Frequency Data," Papers 1601.06651, arXiv.org.
    7. 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.
    8. Ole E. Barndorff-Nielsen & Asger Lunde & Neil Shephard & Almut E.D. Veraart, 2014. "Integer-valued Trawl Processes: A Class of Stationary Infinitely Divisible Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 693-724, September.
    9. Baena-Mirabete, S. & Puig, P., 2020. "Computing probabilities of integer-valued random variables by recurrence relations," Statistics & Probability Letters, Elsevier, vol. 161(C).
    10. Vladim'ir Hol'y & Petra Tomanov'a, 2021. "Modeling Price Clustering in High-Frequency Prices," Papers 2102.12112, arXiv.org, revised Mar 2021.
    11. Shota Gugushvili & Ester Mariucci & Frank van der Meulen, 2020. "Decompounding discrete distributions: A nonparametric Bayesian approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 464-492, June.
    12. Vladim'ir Hol'y, 2022. "An Intraday GARCH Model for Discrete Price Changes and Irregularly Spaced Observations," Papers 2211.12376, arXiv.org, revised Sep 2023.
    13. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    14. Zhang, Huiming & Liu, Yunxiao & Li, Bo, 2014. "Notes on discrete compound Poisson model with applications to risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 325-336.
    15. Michael Grabchak, 2022. "Discrete Tempered Stable Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1877-1890, September.
    16. Fry, John & Serbera, Jean-Philippe, 2017. "Modelling and mitigation of Flash Crashes," MPRA Paper 82457, University Library of Munich, Germany.
    17. Siem Jan Koopman & Rutger Lit & André Lucas, 2014. "The Dynamic Skellam Model with Applications," Tinbergen Institute Discussion Papers 14-032/IV/DSF73, Tinbergen Institute, revised 06 Jul 2015.
    18. Xiaofei Hu & Beth Andrews, 2021. "Integer‐valued asymmetric garch modeling," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 737-751, September.
    19. Mikkel Bennedsen & Asger Lunde & Neil Shephard & Almut E.D. Veraart, 2021. "Inference and forecasting for continuous-time integer-valued trawl processes and their use in financial economics," CREATES Research Papers 2021-12, Department of Economics and Business Economics, Aarhus University.
    20. Zhanyu Chen & Kai Zhang & Hongbiao Zhao, 2022. "A Skellam market model for loan prime rate options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 525-551, March.

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