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Stationary Distribution Of The Volume At The Best Quote In A Poisson Order Book Model

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  • IOANE MUNI TOKE

    (MICS Laboratory & Chair of Quantitative Finance, CentraleSupelec, 3 rue Joliot Curie, F-91190 Gif-sur-Yvette, France)

Abstract

We develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using applied probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms.

Suggested Citation

  • Ioane Muni Toke, 2017. "Stationary Distribution Of The Volume At The Best Quote In A Poisson Order Book Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-22, September.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:06:n:s021902491750039x
    DOI: 10.1142/S021902491750039X
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    References listed on IDEAS

    as
    1. I. Muni Toke, 2015. "The order book as a queueing system: average depth and influence of the size of limit orders," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 795-808, May.
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    19. Ioane Muni Toke & Nakahiro Yoshida, 2017. "Modelling intensities of order flows in a limit order book," Post-Print hal-01705080, HAL.
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    1. Charles-Albert Lehalle & Othmane Mounjid & Mathieu Rosenbaum, 2018. "Optimal liquidity-based trading tactics," Papers 1803.05690, arXiv.org.

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