Ergodic transition in a simple model of the continuous double auction.

• Main Authors: Tijana Radivojević, Jonatha Anselmi, Enrico Scalas
• Format: Article
• Language: English
• Published: Public Library of Science (PLoS) 2014-01-01
• Series: PLoS ONE
• Online Access: http://europepmc.org/articles/PMC3928121?pdf=render

We study a phenomenological model for the continuous double auction, whose aggregate order process is 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 a heteroskedastic behavior in the logarithmic returns. On the contrary, non-ergodicity triggers stability of prices, even if two different regimes can be seen.