Price dynamics in a Markovian limit order market

TL;DR

This paper introduces a Markovian queueing model for limit order book dynamics, providing analytical formulas for key market quantities and insights into how order flow influences price movements.

Contribution

It presents a simple, analytically tractable stochastic model for limit order book dynamics, linking order flow parameters to price behavior.

Findings

Derived distributions for price change durations and autocorrelations.

Expressed price volatility in terms of order arrival and cancellation rates.

Provided analytical insights into order flow and price dynamics relationship.

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.