Empirical Science of Financial Fluctuations pp 135-142 | Cite as

# Statistical Property of Price Fluctuations in a Multi-Agent Model and the Currency Exchange Market

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## Summary

We show that the price fluctuation generated in a multi-agent model of economic system driven by the positive feedback mechanism exhibits nonGaussioan (Lévy) statistics of various range of parameter α, from the Cauchy distribution (α=1) to the Gauss distribution (α=2).

Two different patterns are observed in the time series of price fluctuation, one of which is characterized by the intermittency and its probability distribution corresponds to the Cauchy distribution, and the other pattern corresponds to the Gauss distribution, within a range of 0.01 < *a,b* < 0.1, where *a* is the price denomination rate, and *b* is the price inflation constant assumed in the model. The former pattern occurs in the region of *a<b* (‘bull’ market situation), and the latter in the region of *a>b* ( ‘bear’ market situation). The boundary of the two phases roughly corresponds to a line *a = b* where the price patterns show a certain critical behavior and its probability distribution roughly fits Lévy distribution of α =1.7.

We compare this result to the real-world data. The fact that the short term currency exchange data (JPY/USD) per trade for the duration of ten days in 1998 fits the Lévy distribution of α=1.7 very well indicates that the data corresponds to the moderate market in which the price denomination rate *a* and the price inflation constant *b* are roughly equal in our model.

## Key words

Positive feedback Mechanism Lévy distribution Intermittency Anti Oscillation Cooperative Phenomena## Preview

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