IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v22y2015i3p261-295.html
   My bibliography  Save this article

Semi-Markov Model for Market Microstructure

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/1350486X.2015.1037963
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/1350486X.2015.1037963?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Frédéric Abergel & Côme Huré & Huyên Pham, 2019. "Algorithmic trading in a microstructural limit order book model," Working Papers hal-01514987, HAL.
    4. 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.
    5. 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.
    6. 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.
    7. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    8. 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.
    9. Luca Lalor & Anatoliy Swishchuk, 2024. "Algorithmic and High-Frequency Trading Problems for Semi-Markov and Hawkes Jump-Diffusion Models," Papers 2409.12776, arXiv.org.
    10. 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.
    11. Garima Agrawal & Anindya Goswami, 2022. "A semi-Markovian approach to model the tick-by-tick dynamics of stock price," Papers 2209.04620, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:22:y:2015:i:3:p:261-295. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.