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Ergodic transition in a simple model of the continuous double auction

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  • Tijana Radivojevi'c
  • Jonatha Anselmi
  • Enrico Scalas

Abstract

We study a phenomenological model for the continuous double auction, equivalent to two independent $M/M/1$ queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior of prices and logarithmic returns are observed. In the ergodic regime, prices are unstable and one can observe an intermittent behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen.

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  • Tijana Radivojevi'c & Jonatha Anselmi & Enrico Scalas, 2013. "Ergodic transition in a simple model of the continuous double auction," Papers 1305.2716, arXiv.org.
    • Handle: RePEc:arx:papers:1305.2716
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    1. is not listed on IDEAS
    2. Gerardo-Giorda, Luca & Germano, Guido & Scalas, Enrico, 2015. "Large scale simulation of synthetic markets," LSE Research Online Documents on Economics 67563, London School of Economics and Political Science, LSE Library.
    3. Scalas, Enrico & Rapallo, Fabio & 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, Elsevier, vol. 485(C), pages 61-72.
    4. Luisanna Cocco & Michele Marchesi, 2016. "Modeling and Simulation of the Economics of Mining in the Bitcoin Market," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-31, October.

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