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Modeling First Line Of An Order Book With Multivariate Marked Point Processes

Author

Listed:
  • Alexis Fauth

    (SAMM)

  • Ciprian A. Tudor

    (LPP)

Abstract

We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the corresponding volume of orders. The model is motivated by the fact that the "excitation" of the market is different in periods of time with low exchanged volume and high volume exchanged. We illustrate our result by numerical simulations on foreign exchange data sampling in millisecond. By checking the main stylized facts, we show that the model is consistent with the empirical data. We also find an interesting relation between the distribution of the volume of limited order and the volume of market orders. To conclude, we propose an application to risk management and we introduce a forecast procedure.

Suggested Citation

  • Alexis Fauth & Ciprian A. Tudor, 2012. "Modeling First Line Of An Order Book With Multivariate Marked Point Processes," Papers 1211.4157, arXiv.org.
    • Handle: RePEc:arx:papers:1211.4157
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    Cited by:

    1. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
    2. Simon Clinet, 2020. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Papers 2001.11624, arXiv.org, revised Aug 2021.
    3. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    4. Simon Clinet, 2022. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 189-225, July.
    5. Sobin Joseph & Shashi Jain, 2024. "Non-Parametric Estimation of Multi-dimensional Marked Hawkes Processes," Papers 2402.04740, arXiv.org.
    6. Bilodeau, Yann, 2020. "Deep limit order book events dynamics," Working Papers 20-4, HEC Montreal, Canada Research Chair in Risk Management.

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