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Exact and asymptotic solutions of the call auction problem

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  • Ioane Muni Toke

    (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, ERIM - Equipe de Recherche en Informatique et Mathématiques - UNC - Université de la Nouvelle-Calédonie)

Abstract

The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution F, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of orders statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.

Suggested Citation

  • Ioane Muni Toke, 2015. "Exact and asymptotic solutions of the call auction problem," Post-Print hal-01061857, HAL.
    • Handle: RePEc:hal:journl:hal-01061857
    DOI: 10.1142/s238262661550001x
    Note: View the original document on HAL open archive server: https://hal.science/hal-01061857
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    References listed on IDEAS

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    Cited by:

    1. M. Derksen & B. Kleijn & R. de Vilder, 2019. "Clearing price distributions in call auctions," Papers 1904.07583, arXiv.org, revised Nov 2019.
    2. Mike Derksen & Bas Kleijn & Robin de Vilder, 2020. "Effects of MiFID II on stock price formation," Papers 2003.10353, arXiv.org, revised Aug 2020.
    3. Twu, Mia & Wang, Jianxin, 2018. "Call auction frequency and market quality: Evidence from the Taiwan Stock Exchange," Journal of Asian Economics, Elsevier, vol. 57(C), pages 53-62.

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