Self-organized model of cascade spreading

TL;DR

This paper introduces a self-organized model of cascade spreading in stock markets that reproduces power-law distributions of price drops and other empirical features like volatility clustering, using a probabilistic and mean-field approach.

Contribution

It presents a minimal, analytically solvable model that captures critical behavior and cascade dynamics observed in real stock market data.

Findings

Power-law distribution of stock price drops for high thresholds

Model reproduces volatility clustering and cascade phenomena

System operates near a critical state across various parameters

Abstract

We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a power-law distribution. To reproduce these collective downturns, we propose a minimal self-organized model of cascade spreading based on a probabilistic response of the system elements to stress conditions. This model is solvable using the theory of branching processes and the mean-field approximation. For a wide range of parameters, the system is in a critical state and displays a power-law cascade-size distribution similar to the empirically observed one. We further generalize the model to reproduce volatility clustering and other observed properties of real stocks.