Low-traffic limit and first-passage times for a simple model of the continuous double auction

Scalas, Enrico, Rapallo, Fabio and Radivojević, Tijana (2017) Low-traffic limit and first-passage times for a simple model of the continuous double auction. Physica A: Statistical Mechanics and its Applications, 485. pp. 61-72. ISSN 0378-4371

[img] PDF - Accepted Version
Restricted to SRO admin only until 20 May 2018.
Available under License Creative Commons Attribution-NonCommercial No Derivatives.

Download (648kB)

Abstract

We consider a simplified model of the continuous double auction where prices are integers varying from 1 to N with limit orders and market orders, but quantity per order limited to a single share. For this model, the order process is equivalent to two M∕M∕1 queues. We study the behaviour of the auction in the low-traffic limit where limit orders are immediately matched by market orders. In this limit, the distribution of prices can be computed exactly and gives a reasonable approximation of the price distribution when the ratio between the rate of order arrivals and the rate of order executions is below 1∕2. This is further confirmed by the analysis of the first-passage time in 1 or N.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: H Social Sciences > HG Finance > HG0101 Theory. Method. Relation to other subjects > HG0106 Mathematical models
Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Enrico Scalas
Date Deposited: 22 May 2017 11:35
Last Modified: 07 Jun 2017 02:04
URI: http://sro.sussex.ac.uk/id/eprint/68176

View download statistics for this item

📧 Request an update