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Multi-dimensional queue-reactive model and signal-driven models: a unified framework

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  • Emmanouil Sfendourakis

Abstract

We present a Markovian market model driven by a hidden Brownian efficient price. In particular, we extend the queue-reactive model, making its dynamics dependent on the efficient price. Our study focuses on two sub-models: a signal-driven price model where the mid-price jump rates depend on the efficient price and an observable signal, and the usual queue-reactive model dependent on the efficient price via the intensities of the order arrivals. This way, we are able to correlate the evolution of limit order books of different stocks. We prove the stability of the observed mid-price around the efficient price under natural assumptions. Precisely, we show that at the macroscopic scale, prices behave as diffusions. We also develop a maximum likelihood estimation procedure for the model, and test it numerically. Our model is them used to backest trading strategies in a liquidation context.

Suggested Citation

  • Emmanouil Sfendourakis, 2025. "Multi-dimensional queue-reactive model and signal-driven models: a unified framework," Papers 2506.11843, arXiv.org.
    • Handle: RePEc:arx:papers:2506.11843
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    References listed on IDEAS

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    1. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach To Order Book Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-40.
    2. Rüdiger Frey & Wolfgang J. Runggaldier, 1999. "Risk-minimizing hedging strategies under restricted information: The case of stochastic volatility models observable only at discrete random times," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 339-350, October.
    3. Christian Y. Robert & Mathieu Rosenbaum, 2011. "A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 344-366, Spring.
    4. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach to Order Book Modelling," Post-Print hal-00621253, HAL.
    5. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
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