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

Radivojević T, Anselmi J, Scalas E - PLoS ONE (2014)

Bottom Line: We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues.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.

View Article: PubMed Central - PubMed

Affiliation: BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain.

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.

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Related in: MedlinePlus

Mean values and error bars.Mean values and error bars of the standard deviation (a), kurtosis (b) of log-returns and the first-lag autocorrelation of absolute log-returns (c) as functions of the parameter , estimated from 1000 Monte Carlo simulations.
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pone-0088095-g003: Mean values and error bars.Mean values and error bars of the standard deviation (a), kurtosis (b) of log-returns and the first-lag autocorrelation of absolute log-returns (c) as functions of the parameter , estimated from 1000 Monte Carlo simulations.

Mentions: Figure 3 shows standard deviation, kurtosis and in more detail, namely mean values and error bars are given for these three quantities estimated from 1000 runs. One can see that these quantities increase in the non-ergodic case.


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

Radivojević T, Anselmi J, Scalas E - PLoS ONE (2014)

Mean values and error bars.Mean values and error bars of the standard deviation (a), kurtosis (b) of log-returns and the first-lag autocorrelation of absolute log-returns (c) as functions of the parameter , estimated from 1000 Monte Carlo simulations.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3928121&req=5

pone-0088095-g003: Mean values and error bars.Mean values and error bars of the standard deviation (a), kurtosis (b) of log-returns and the first-lag autocorrelation of absolute log-returns (c) as functions of the parameter , estimated from 1000 Monte Carlo simulations.
Mentions: Figure 3 shows standard deviation, kurtosis and in more detail, namely mean values and error bars are given for these three quantities estimated from 1000 runs. One can see that these quantities increase in the non-ergodic case.

Bottom Line: We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues.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.

View Article: PubMed Central - PubMed

Affiliation: BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain.

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.

Show MeSH
Related in: MedlinePlus