The order book as a queueing system: average depth and influence of the size of limit orders Ioane Muni Toke To cite this version: Ioane Muni Toke. The order book as a queueing system: average depth and influence of the size of limit orders. Quantitative Finance, Taylor & Francis (Routledge), 2015, 15 (5), pp.795-808. 10.1080/14697688.2014.963654. hal-01006410 HAL Id: hal-01006410 https://hal.archives-ouvertes.fr/hal-01006410 Submitted on 16 Jun 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The order book as a queueing system: average depth and influence of the size of limit orders Ioane Muni Toke ERIM, University of New Caledonia BP R4 98851 Noumea CEDEX, New Caledonia
[email protected] Applied Maths Laboratory, Chair of Quantitative Finance Ecole Centrale Paris Grande Voie des Vignes, 92290 Chˆatenay-Malabry, France
[email protected] Abstract In this paper, we study the analytical properties of a one-side order book model in which the flows of limit and market orders are Poisson processes and the distribution of lifetimes of cancelled orders is exponen- tial.