On anomalous distributions in intra-day financial time series and Non-extensive Statistical Mechanics

TL;DR

This paper analyzes intra-day financial log-returns in the Lisbon stock market, demonstrating they follow a distribution derived from non-extensive statistical mechanics, specifically a generalized power-law form.

Contribution

It introduces a novel distribution model based on non-extensive statistical mechanics to describe intra-day financial returns.

Findings

Distribution fits well with empirical data

Power-law behavior observed in log-returns

Supports non-extensive statistical mechanics in finance

Abstract

In this paper one studies the distribution of log-returns (tick-by-tick) in the Lisbon stock market and shows that it is well adjusted by the solution of the equation, {$\frac{dp_{x}}{d| x|}=-\beta_{q^{\prime }}p_{x}^{q^{\prime}}-(\beta_{q}-\beta_{q^{\prime}}) p_{x}^{q}$}, which corresponds to a generalization of the differential equation which has as solution the power-laws that optimise the entropic form $S_{q}=-k \frac{1-\int p_{x}^{q} dx}{1-q}$, base of present non-extensive statistical mechanics.