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Semi-Markov Model for Market Microstructure

Author

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  • Pietro Fodra
  • Huyên Pham

Abstract

We introduce a new model based on Markov renewal processes (MRP) describing the fluctuations of a tick-by-tick single asset price. We consider a point process associated to the timestamps of the price jumps, with marks associated to price increments. By modelling the marks with a suitable Markov chain, we can reproduce the strong mean-reversion of price returns, a phenomenon known as microstructure noise. Moreover, using MRP, we can model the alternating of time intervals with high and low market activity, and consider dependence between price increments and jump times. We also provide simple parametric and nonparametric statistical procedures for the estimation of our model. We obtain closed-form formula for the mean signature plot, and show the diffusive behaviour of our model at large-scale limit. We illustrate our results by numerical simulations, and find that our model is consistent with available empirical data.

Suggested Citation

  • Pietro Fodra & Huyên Pham, 2015. "Semi-Markov Model for Market Microstructure," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 261-295, July.
    • Handle: RePEc:taf:apmtfi:v:22:y:2015:i:3:p:261-295
    DOI: 10.1080/1350486X.2015.1037963
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    Citations

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    Cited by:

    1. Alexander Barzykin & Philippe Bergault & Olivier Gu'eant, 2021. "Algorithmic market making in dealer markets with hedging and market impact," Papers 2106.06974, arXiv.org, revised Dec 2022.
    2. Fr'ed'eric Abergel & C^ome Hur'e & Huy^en Pham, 2017. "Algorithmic trading in a microstructural limit order book model," Papers 1705.01446, arXiv.org, revised Feb 2020.
    3. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    4. Riccardo De Blasis, 2023. "Weighted-indexed semi-Markov model: calibration and application to financial modeling," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-16, December.
    5. Garima Agrawal & Anindya Goswami, 2022. "A semi-Markovian approach to model the tick-by-tick dynamics of stock price," Papers 2209.04620, arXiv.org.
    6. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Marked Hawkes process modeling of price dynamics and volatility estimation," Journal of Empirical Finance, Elsevier, vol. 40(C), pages 174-200.
    7. D’Amico, Guglielmo & Petroni, Filippo, 2018. "Copula based multivariate semi-Markov models with applications in high-frequency finance," European Journal of Operational Research, Elsevier, vol. 267(2), pages 765-777.
    8. Frédéric Abergel & Côme Huré & Huyên Pham, 2019. "Algorithmic trading in a microstructural limit order book model," Working Papers hal-01514987, HAL.
    9. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    10. Antoine Jacquier & Hao Liu, 2017. "Optimal liquidation in a Level-I limit order book for large tick stocks," Papers 1701.01327, arXiv.org, revised Nov 2017.

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