Phase Transition of Dynamical Herd Behaviors in Financial Markets

TL;DR

This paper investigates the phase transition in herd behaviors in the Japanese financial market, revealing a critical time lag at 30 minutes where the return distribution shifts from crash-prone to stable, characterized by power-law scaling.

Contribution

It identifies a phase transition in herd behavior at a specific time lag, linking it to changes in the return distribution's power-law exponent.

Findings

Power-law distribution of returns with different exponents at various time lags.

Crash regime observed for time lags less than 30 minutes.

Phase transition point identified at 30-minute time lag.

Abstract

We study the phase transition of dynamical herd behaviors for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior with three different values of the scaling exponent 3.11 (one time lag $\tau$ = 1 minute), 2.81 (30 minutes), and 2.29 (1 hour). The crash regime in which the probabilty density increases with the increasing return appears in the case of $\tau$ < 30 minutes, while it occurs no financial crash at $\tau$ > 30 minutes. it is especially obtained that our dynamical herd behavior exhibits the phase transition at one time lag $\tau$ = 30 minutes.