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Probabilistic Properties of the Continuous Double Auction

Martin Smid 

Czech Academy of Sciences, Institute of Information Theory and Automation (UTIA), Pod Vodárenskou věží 4, Prague 18208, Czech Republic

Abstract

We formulate a general model of the continuous double auction, covering the models of Maslov [2000], Luckock [2003], Smith at al. [2003] and (partially) the the model of Mike et. al. [2008]. We analytically describe the distribution of the best quotes and the (conditional) distribution of the order books. Based on these  results, we suggest a technique of a statistical inference of the order books and a procedure allowing a Monte Carlo simulation of the modes, much more efficient then a crude simulation. Finally, we study the tails of the price increments: we find them generally fat-tailed but thin-tailed if the initial order book is large enough.

 

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Presentation: Oral at International Conference on Economic Science with Heterogeneous Interacting Agents 2008, by Martin Smid
See On-line Journal of International Conference on Economic Science with Heterogeneous Interacting Agents 2008

Submitted: 2008-03-15 14:22
Revised:   2009-06-07 00:48