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

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posted on 2023-06-09, 06:21 authored by Enrico Scalas, Fabio Rapallo, Tijana Radivojevic
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Physica A: Statistical Mechanics and its Applications

ISSN

0378-4371

Publisher

Elsevier

Volume

485

Page range

61-72

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-05-22

First Open Access (FOA) Date

2018-05-20

First Compliant Deposit (FCD) Date

2017-05-22

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