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

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

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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 here 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 ealisboa.com two different regimes can be seen.