Co‐Jump Dependency and Transmission Across US Commodity Futures: A Network Analysis

• Published date: 01 December 2024
• Author: Lei Zhang,Yan Chen,Elie Bouri
• Date: 01 December 2024
• DOI: http://doi.org/10.1002/fut.22547

Journal of Futures Markets

RESEARCH ARTICLE

Co‐Jump Dependency and Transmission Across US

Commodity Futures: A Network Analysis

Lei Zhang

1

| Yan Chen

1,2

| Elie Bouri

3

1

Business School, Hunan University, Changsha, China |

2

Key Laboratory of High‐Performance Distributed Ledger Technology and Digital Finance (Hunan

University), Ministry of Education, Changsha, China |

3

School of Business, Lebanese American University, Beirut, Lebanon

Correspondence: Yan Chen (chenyan15153@hotmail.com) | Elie Bouri (elie.elbouri@lau.edu.lb)

Received: 20 January 2024 | Revised: 10 June 2024 | Accepted: 15 July 2024

Funding: This study is partially supported by the MOE Layout Foundation of Humanities and Social Sciences (Grant No. 22YJA790007), the Science and

technology innovation Program of Hunan Province (Grant No. 2021RC3057), and the Fundamental Research Funds for the Central Universities.

Keywords: co‐jump network | co‐jump transmission| COVID‐19 and Russia–Ukraine war | US commodity futures| volatility forecasting implications

ABSTRACT

This paper examines the co‐jump transmission in 20 commodity futures returns in the United States using co‐jump network

models. Specifically, it reveals co‐jumping behavior in both static and time‐varying settings, considering the overall commodity

markets and various commodity groups separately, which helps us understand the dynamic changes in co‐jump dependencies

at the overall and sector levels. The main results reveal that co‐jump heterogeneity exists among commodities but is generally

more apparent within each commodity group, and co‐jumps vary over time. Gold exerts the strongest influence, with many

commodity futures being influenced by the jumps behavior in gold returns. During the COVID‐19 outbreak and the Russia–

Ukraine war, the energy group ranks highest in terms of co‐jump network centrality. Our empirical analysis highlights the

portfolio performance and risk reduction, and an additional examination shows that centrality information from the co‐jump

network contains a highly and statistically forecasting power for US stock market volatility.

JEL Classification: C52, G14

1 | Introduction

Discontinuous variations of the asset price process, called

jumps, are rare events in financial markets and encompass a

multitude of crucial insights for asset pricing and risk man-

agement. Bates (1991) argues that jumps incorporate the risk of

financial market crashes, and later research emphasizes the

significance of jumps in various domains, such as volatility

forecasting (Andersen, Bollerslev, and Diebold 2007; Clements

and Liao 2017), risk premium explanation (Bollerslev and

Todorov 2011), return modeling (Cremers, Halling, and

Weinbaum 2015; Bollerslev, Todorov, and Xu 2015), diversifi-

cation (Bollerslev, Law, and Tauchen 2008), and options pricing

(Bates 2019). Notably, the simultaneous occurrence of jumps in

two or more stocks or assets, called co‐jumps, is broadly

accepted. Previous studies (see, Gilder, Shackleton, and

Taylor 2014; Caporin, Kolokolov, and Renò 2017) examine co‐

jumps in the stock market, showing that the simultaneous

occurrence of large jumps in individual stocks is associated with

market‐level news, including Fed Funds target rate announce-

ments,

1

and suggesting that co‐jumps imply short‐term pre-

dictability of stock returns and have an influence on the risk

premia (Caporin, Kolokolov, and Renò 2017).

Much less attention has been given to the presence of co‐jumps

in commodities, despite the emergence of commodities as an

asset class highly appreciated by market participants. The

importance of commodity markets has been widely recognized

over the past two decades as an instrument useful for hedging

and the portfolio choice, and the dynamic behavior of

© 2024 Wiley Periodicals LLC.

1851 of 1922Journal of Futures Markets, 2024; 44:1851–1868

https://doi.org/10.1002/fut.22547

commodities has been prominently examined (Christoffersen,

Lunde, and Olesen 2019), especially during stress periods such

as the 2008 global financial crisis, the COVID‐19 outbreak, and

the Russian–Ukrainian war (Wang et al. 2022). Various groups

of commodities exist, such as energy, metals, agricultural, and

grains, offering diversification and hedging possibilities

(Rehman et al. 2019; Abid et al. 2020). The relationship across

various commodities is shown to be time varying and tends to

increase under crisis periods (Zhang and Broadstock 2020;

Bouri et al. 2021), reducing and hedging diversification

possibilities.

The prices of commodity futures tend to experience violent

fluctuations, especially during crisis periods, which lead to en-

ormous volatility. Jumps in returns differ from jumps in vola-

tility, although they can serve complementary purposes (Bandi

and Renò 2016), and existing studies typically focus on jumps in

returns. Several studies indicate the presence of jumps in the

commodity futures returns (Chatrath and Song 1999; Diewald,

Prokopczuk, and Wese Simen 2015; Sévi 2015; Chevallier and

Ielpo 2014; Prokopczuk, Symeonidis, and Wese Simen 2016;

Nguyen and Prokopczuk 2019; Bouri and Gupta 2020; Zhang,

Chen, and Bouri 2024). However, the literature on co‐jumps in

the commodity markets is limited. Laurini, Mauad, and Aiube

(2020) examine jump and co‐jumps in oil prices and stock prices

of integrated oil companies using a new multivariate stochastic

volatility model with jumps. Jawadi et al. (2019) study the role

of co‐jump to forecast the volatility in commodity futures

markets. Other studies examine the co‐jump behavior of com-

modity futures markets with different markets such as energy

spot and futures markets (Maslyuk‐Escobedo, Rotaru, and

Dokumentov 2017), the US interest rates, and precious metals

markets (Semeyutin and Downing 2022). Bouri and Gupta

(2020) study the presence of jumps in the volatility of energy

and nonenergy commodity markets, showing that jumps tend to

occur more with the energy group than across the commodity

groups, and that jumps are associated with macroeconomic

news surprises, especially in crude oil. Semeyutin et al. (2021)

find that three commodity futures (crude oil, gold, and copper)

exhibit co‐jumping behavior, which can trigger jumps in the

next periods. They provide evidence that, despite the significant

influence of jump risks on commodities correlations, the

potential for diversification benefits remains intact, indicating

that investors can exploit market‐specific price jump in the

copper and oil markets to enhance diversification strategies.

The related literature on jumps and co‐jumps lacks a compre-

hensive analysis of the co‐jump transmission in commodity

futures returns within a co‐jump network model in both static

and time‐varying settings and their feasible implications. Spe-

cifically, there is no empirical evidence and model on how

commodity futures return co‐jump and how their co‐jump

behaviors evolve over time and during crisis periods, which if

addressed could help to understand the mechanisms of jump

transmission in the commodity futures markets and the port-

folio implications, both of which should provide useful infor-

mation to market participants. In fact, the transmission of co‐

jump in commodity futures returns have received very limited

attention at both the aggregate and industry‐group levels, and

the following questions remain unanswered: Which commodity

futures act as bridges for cross‐industry group jumps? Which

commodity futures hold the highest ranking in the co‐jump

network during the full sample period and crisis periods? How

does the dynamics of interrelated jumps in commodity futures

returns change during crisis events? What are the feasible

implications of significant of co‐jumps in commodity markets?

Our study provides answers to these important research ques-

tions in commodity markets. Our study addresses the above‐

mentioned research gap by explicitly identifying the co‐jump

transmission in 20 commodity futures returns using co‐jump

network models. We examine the co‐jump dependency in

commodity futures returns within the overall commodity mar-

ket and across different industry groups, from the perspective of

network analysis. We are particularly interested in under-

standing the dynamic changes in these co‐jump dependencies

over time. The co‐jump network model can reflect the depen-

dent feature of edges in the real‐world network and discover

pairwise jump dependency among a large number of com-

modity futures returns. This approach allows us to examine not

only the occurrence of co‐jumps in commodity future markets

but also the intensity of co‐jumps between pairs of commodity

futures returns from a network visualization perspective. Tra-

ditional co‐jump methods often focus on the co‐jumps between

two commodity futures returns, whereas the co‐jump network

model can simultaneously consider the jump dependency

among multiple pair of commodity futures returns. This com-

prehensive consideration helps to reveal the co‐jump relation-

ships between different commodity futures returns and provides

a more holistic understanding of commodity market dynamics.

Furthermore, the co‐jump network model captures more com-

plex commodity futures market jump relationships by con-

structing a network of co‐jump dependency among commodity

futures returns, which can reveal the co‐jump transmission

paths across and within commodity groups. This should provide

more refined understandings of jump risk and practical insights

into the feasible implications of co‐jumps in commodities.

The main contributions of this paper are summarized as fol-

lows: First, following the approach proposed by Ding et al.

(2024) and adopted by Zhang, Bouri, and Chen (2023) in the

cryptocurrency markets, we apply the co‐jump network

framework to study co‐jump dependency among 20 commodity

futures returns, offering a comprehensive understanding of how

co‐jumps in commodity futures returns are transmitted across

time. The co‐jump network model can identify important nodes

in the commodity future markets, which help reveal the com-

modity futures that have the largest impact on market jumps.

Specifically, unlike the work of Laurini, Mauad, and Aiube

(2020) and Semeyutin et al. (2021), we assess the intensity of co‐

jumps between commodity futures returns based on the co‐

jump network, which helps us understand which commodity

futures have stronger impacts on others through jumps, and

which have a weaker influence from other commodity futures

returns’jumps. Second, we compare and analyze the similari-

ties and differences between whole commodity future markets’

co‐jump network and different industry groups’co‐jump net-

work to explore time‐varying nature of co‐jumps. Third, we

compare the structure of co‐jump networks during the COVID‐

19 crisis and Russia–Ukraine conflict to assess the diverse co‐

jump impact of these crises on commodity futures markets.

Fourth, we emphasize the role of co‐jump dependence in

1852 of 1922 Journal of Futures Markets, 2024