title: Ergodic transition in a simple model of the continuous double auction.
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.
authors.affiliation: BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain.
authors.forename: Tijana
authors.initials: T
authors.lastname: Radivojević
authors.affiliation: BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain.
authors.forename: Jonatha
authors.initials: J
authors.lastname: Anselmi
authors.affiliation: Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, United Kingdom ; BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain.
authors.forename: Enrico
authors.initials: E
authors.lastname: Scalas
mesh_terms: D003132:Commerce; D003198:Computer Simulation; D007449:Investments / Q000191:economics; D008390:Markov Chains; D008954:Models, Biological; D018803:Models, Economic; D008962:Models, Theoretical; D009010:Monte Carlo Method; D016012:Poisson Distribution; D011336:Probability