A statistical model of a limit order market


Hugh Luckock


Research Report 2001-9
Date: 28 September, 2001


A model of limit order market is presented, and some of its statistical properties are deduced. Given the underlying supply and demand functions, the analysis yields the stationary probability distributions for the best ask and bid prices in the order book, and for the prices of actual trades. It also predicts the existence of a clearly-defined price window within which all trades take place, thus providing a quantitative explanation for the phenomena of support and resistance. If the bid-ask spread is narrow and the elasticities of supply and demand are not strongly price-dependent, the distributions of quotes and trades within this window are completely determined by a single parameter corresponding to the proportion of market participants who own at least one unit of the asset being traded.

Key phrases

market microstructure. limit order market. continuous double auction.

AMS Subject Classification (1991)

Primary: 91B26


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