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arXiv · 1502.02015

Hierarchical Cont-Bouchaud model

Robert Paluch·Krzysztof Suchecki·Janusz A. Holyst
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Abstract

We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agent's interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdos-Renyi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdos-Renyi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.

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Robert Paluch, Krzysztof Suchecki, Janusz A. Holyst. 2015-02-06. Hierarchical Cont-Bouchaud model. https://doi.org/10.12693/aphyspola.127.a-108

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