# A statistical model of a limit order market

## Author

**Hugh Luckock**

## Status

Research Report 2001-9

Date: 28 September, 2001

## Abstract

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

Secondary:

## Content

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Sydney Mathematics and Statistics