Returns in futures markets and $\nu=3$ t-distribution

TL;DR

This paper demonstrates that the t-distribution with approximately 3 degrees of freedom effectively models high-frequency futures market log-returns across various datasets and sampling frequencies, providing a robust statistical description.

Contribution

It shows that the $ u hicksim 3$ t-distribution consistently fits high-frequency futures return data, a novel empirical finding across diverse financial datasets.

Findings

t-distribution with $ u hicksim 3$ fits most data series

Robustness across different financial datasets

Effective for sampling frequencies below one hour

Abstract

The probability distribution of log-returns of financial time series, sampled at high frequency, is the basis for any further developments in quantitative finance. In this letter, we present experimental results based on a large set of time series on futures. Then, we show that the t-distribution with $\nu \simeq 3$ gives a nice description of almost all data series. This appears to be a quite general result that stays robust on a large set of any financial data as well as on a wide range of sampling frequency of these data, below one hour.