Hierarchical Cont-Bouchaud model

TL;DR

This paper extends the Cont-Bouchaud model by incorporating hierarchical agent interaction topologies, revealing that certain hierarchical structures can produce heavy-tailed distributions of market returns.

Contribution

It introduces two hierarchical models, demonstrating how specific hierarchical arrangements influence market dynamics and lead to heavy-tailed return distributions.

Findings

The first model does not produce broad return distributions outside near-critical regimes.

The second model generates heavy-tail distributions across various connection densities.

Hierarchical structures significantly impact the emergence of market-like fluctuations.

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.