Stochastic model of financial markets reproducing scaling and memory in volatility return intervals

TL;DR

This paper presents a stochastic agent-based model that reproduces key statistical features of volatility return intervals in financial markets, emphasizing herding behavior over efficient market assumptions.

Contribution

It introduces a herding-based microscopic model that explains scaling and memory in volatility return intervals across multiple markets and assets.

Findings

Model reproduces empirical scaling laws and memory effects.

Herding interactions explain universal properties of volatility intervals.

Model matches statistical features of NYSE, FOREX, and S&P500 data.

Abstract

We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce various stylized facts of different markets and different assets with the same set of model parameters. We show that the power-law properties and the scaling of return intervals and other financial variables have a similar origin and could be a result of a general class of non-linear stochastic differential equations derived from a master equation of an agent system that is coupled by herding interactions. Specifically, we find that this approach enables us to recover the volatility return interval statistics as well as volatility probability and spectral densities for the NYSE and FOREX markets, for different assets, and for different time-scales. We find also that the historical S\&P500 monthly series exhibits the same volatility return interval properties recovered by our proposed model. Our statistical results suggest that human herding is so strong that it persists even when other evolving fluctuations perturbate the financial system.