Market laws

TL;DR

This paper investigates financial data for power law behaviors, confirming known exponents and discovering new ones, and proposes a universal model based on Maxwell-Boltzmann distributions to explain these phenomena.

Contribution

It identifies multiple power law behaviors in financial data and introduces a novel model using Maxwell-Boltzmann distributions with random exponents to explain them.

Findings

Confirmed power law with exponent around -4 in relative returns

Discovered new power law behaviors with various exponents

Proposed a universal model based on Maxwell-Boltzmann distributions

Abstract

More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was detected in the empirical distributions of the relative returns. Moreover, a number of new power law behaviors with various power exponents were explored in the same data. Further on, a model based on finite sums over numerous Maxwell-Boltzmann type distribution functions with random (pseudorandom) multipliers in the exponent were proposed to deal with the empirical distributions involving power laws. The results indicate that the proposed model may be universal.