Exact and asymptotic solutions of the call auction problem

Ioane Muni Toke ()
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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

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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.

Date: 2015-03-25
Note: View the original document on HAL open archive server: https://hal.science/hal-01061857v1
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Published in Market microstructure and liquidity, 2015, 1 (1), pp.1550001. ⟨10.1142/s238262661550001x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01061857

DOI: 10.1142/s238262661550001x

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