The Distribution of Commodity Futures: A Test of the Generalized Hyperbolic Process

ABSTRACT

Using daily closing price data spreading over 3 April 1990, to 5 May 2020, this study explores the skewness and excess kurtosis behaviour across energy, metals, and agricultural commodity futures. Subsequently, it compares the fitting of an empirical distribution under normal distribution assumption with those under the Generalized Hyperbolic distribution. The generalized hyperbolic distribution includes Hyperbolic distribution, Variance-Gamma distribution, and Normal Inverse Gaussian distribution. The results show that the Normal Inverse Gaussian distribution for natural gas, gold, platinum, copper, sugar, and feeder cattle futures captures skewness as well as excess kurtosis of the daily logarithmic returns. The findings are robust to the sub-sample analysis.

KEYWORDS:

• Heavy-tailed distribution
• asymmetry
• leptokurtosis
• commodity futures

JEL CLASSIFICATION:

• C46
• Q11
• Q41

Acknowledgments

The author acknowledges the detail and collegiate review received from the Editor and two anonymous referees that led to the considerable improvement of this paper. This is a significantly modified version of a paper presented at the 96^th Annual Conference of the Western Economic Association. The author is thankful to the session participants, especially Jeff Nugent. The valuable insights and remarks of David Scott, Arnab Laha, Manojit Chattopadhyay, Anshul Sinha, and Jaime Mosquera Gutierrez are thankfully acknowledged.

Disclosure statement

The author declares no conflict of interest.

Data availability statement

The data that support the findings of this study are available from the author upon reasonable request.

Human/animal rights

This article does not contain any studies with human or animal subjects performed by the author.

Supplemental data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/00036846.2023.2177598

Notes

¹ The r package ‘nortest’ of Gross and Ligges (2015) is used to generate normal Quantile-Quantile plots.