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.
Ergodic transition in a simple model of the continuous double auction / Radivojević, Tijana; Anselmi, Jonatha; Scalas, Enrico. - In: PLOS ONE. - ISSN 1932-6203. - 9:2(2014). [10.1371/journal.pone.0088095]
Ergodic transition in a simple model of the continuous double auction
Scalas, Enrico
2014
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.