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

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  • Enrico Scalas
  • Fabio Rapallo
  • Tijana Radivojevi'c

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 transformed into 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 $N$.

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  • Enrico Scalas & Fabio Rapallo & Tijana Radivojevi'c, 2016. "Low-traffic limit and first-passage times for a simple model of the continuous double auction," Papers 1603.09666, arXiv.org.
    • Handle: RePEc:arx:papers:1603.09666
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    References listed on IDEAS

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    1. Tijana Radivojević & Jonatha Anselmi & Enrico Scalas, 2012. "A stylized model for the continuous double auction," Lecture Notes in Economics and Mathematical Systems, in: Andrea Teglio & Simone Alfarano & Eva Camacho-Cuena & Miguel Ginés-Vilar (ed.), Managing Market Complexity, edition 127, chapter 0, pages 115-125, Springer.
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