Modelling financial markets by the multiplicative sequence of trades

TL;DR

This paper presents a stochastic multiplicative point process model that captures the power-law spectral density and autocorrelation properties of trading activity in financial markets, explaining the origin of observed power-law distributions.

Contribution

It introduces a novel stochastic multiplicative point process model that reproduces key spectral and distributional properties of market trading activity.

Findings

Model exhibits 1/f^beta spectral density with beta between 0.5 and 2

Reproduces power-law autocorrelations in trading activity

Explains the origin of power-law distributions in market data

Abstract

We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autocorrelations and the origin of the power-law probability distribution of the trading activity. The model reproduces the spectral properties of trading activity and explains the mechanism of power-law distribution in real markets.