Price dynamics in a Markovian limit order market
File(s)
Accepted version
Author(s)
Cont, R
Larrard, AD
Type
Journal Article
Abstract
We propose and study a simple stochastic model for the dynamics of a limit
order book, in which arrivals of market order, limit orders and order
cancellations are described in terms of a Markovian queueing system. Through
its analytical tractability, the model allows to obtain analytical expressions
for various quantities of interest such as the distribution of the duration
between price changes, the distribution and autocorrelation of price changes,
and the probability of an upward move in the price, {\it conditional} on the
state of the order book. We study the diffusion limit of the price process and
express the volatility of price changes in terms of parameters describing the
arrival rates of buy and sell orders and cancelations. These analytical results
provide some insight into the relation between order flow and price dynamics in
order-driven markets.
order book, in which arrivals of market order, limit orders and order
cancellations are described in terms of a Markovian queueing system. Through
its analytical tractability, the model allows to obtain analytical expressions
for various quantities of interest such as the distribution of the duration
between price changes, the distribution and autocorrelation of price changes,
and the probability of an upward move in the price, {\it conditional} on the
state of the order book. We study the diffusion limit of the price process and
express the volatility of price changes in terms of parameters describing the
arrival rates of buy and sell orders and cancelations. These analytical results
provide some insight into the relation between order flow and price dynamics in
order-driven markets.
Date Issued
2011-04-24
Citation
SIAM Journal on Financial Mathematics, 2011, 4 (1), pp.1-25
ISSN
1945-497X
Publisher
SIAM
Start Page
1
End Page
25
Journal / Book Title
SIAM Journal on Financial Mathematics
Volume
4
Issue
1
Copyright Statement
© 2013, Society for Industrial and Applied Mathematics
Description
20.02.13 KB. Accepted version ok to add to Spiral. Sherpa/SIAM
Identifier
http://arxiv.org/abs/1104.4596v1
Subjects
limit order book
electronic markets
queueing systems
high-frequency data
diffusion limit
stochastic processes
mathematical modeling in finance
Notes
18 pages, 5 figures
Publication Status
Published
Publisher URL