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

*Enrico Scalas* (),
*Fabio Rapallo* and
*Tijana Radivojević*

*Physica A: Statistical Mechanics and its Applications*, 2017, vol. 485, issue C, 61-72

**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 behavior 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.

**Keywords:** Double auction; Markov chains; Queueing theory; Low-traffic limit (search for similar items in EconPapers)

**Date:** 2017

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**Related works:**

Working Paper: Low-traffic limit and first-passage times for a simple model of the continuous double auction (2016)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:phsmap:v:485:y:2017:i:c:p:61-72

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