Spillover effects of geopolitical risks on global energy markets: Evidence from CoVaR and CAViaR-EGARCH model

This study investigated the spillover effects of geopolitical risks on energy (crude oil, coal and natural gas) markets. The empirical evidence is based on the CoVaR index and the CAViaR-EGARCH model. Results demonstrate that the spillover effects of geopolitical risks on the global energy market are nonlinear, asymmetric and time-varying. With each 1% rise in global geopolitical risks, the left tail risks in the crude oil, coal, and natural gas markets decreased by 0.179%, 0.119% and 0.113%, while the right tail risks increased by 0.144%, 0.135% and 0.097%, respectively. In addition, the magnitude of energy crises triggered by different geopolitical events varies. Lastly, the spillover effects of GPR on energy markets vary considerably across nations, with more substantial effects observed on average in BRICS than in G7 countries. The primary implication is to provide references for government and energy investors to avoid energy market risks timely.


Introduction
Energy resources are the fundamental driving force behind modern economic development, which is pivotal in safeguarding national economic and social well-being.The smooth operation of markets to geopolitical risk spillovers (Abdel-Latif et al., 2020;Amineh and Crijns-Graus, 2018;Banya, 2022).Specifically, the decent objectives of this paper can be stated as follows: • This article constructs a CAViaR-EGARCH model incorporating geopolitical risk to examine the transmission of tail risk spillover from geopolitics to the energy market to make a marginal contribution.• Within the global landscape characterized by a rise in localized conflicts, social upheaval, and heightened tensions, clarifying the ramifications of geopolitical risks on the energy market becomes imperative.This study offers a pragmatic framework for protecting global energy security and the interests of international energy investors.
The rest of the paper is organized as follows.Section "Literature review" clarifies the underlying mechanisms of geopolitical risk spillovers to energy markets and reviews existing research on the relationship between geopolitical risk and energy market volatility.Section "Methodology and data" presents the model constructed in this paper and describes the sources and characteristics of the data.Section "Results and discussion" provides the results of our tests, encompassing four parts: parameter estimation, spillover effect assessment, spillover effect simulation, and risk spillovers from GPR in different countries.The last section reports the findings of this paper.

Literature review
The mechanisms by which geopolitical risks affect energy markets are multifaceted and intricate.First, the emergence of heightened geopolitical risks will force energy-exporting nations to modify their energy supply policies, resulting in a notable level of uncertainty regarding the quantity and price of global energy commodity supplies (Cunado et al., 2020;Liu et al., 2019Liu et al., , 2021;;Sharma et al., 2021).For instance, when the fourth Middle East war broke out in 1973, the Arab nations within the Organization of Petroleum Exporting Countries (OPEC) initiated an oil embargo against select countries.This action resulted in a substantial escalation of the international oil price, surging from under $3/barrel in 1973 to over $13/barrel, triggering the 1973 oil crisis.Secondly, geopolitical risk can potentially induce volatility in global economic activities, affecting energy demand (Ersin and Bildirici, 2023;Song et al., 2022;Yatsenko et al., 2018).Li et al. (2021) found that the rise of geopolitical risk will lead to the lower prices of coal and crude oil and the higher price of natural gas, inhibiting the total amount of energy imports and exports.Furthermore, the stability of the energy market is also significantly influenced by expectations regarding the trend in the evolution of energy supply and demand.These expectations are projected onto the overall sentiment of global investors and their trading decisions, subsequently impacting the current levels of energy inventories and prices (Balcilar et al., 2018;Bouoiyour et al., 2019;Kilian and Murphy, 2014;Su et al., 2019;Wang and Liao, 2022).Among them, changes in supply and demand expectations exert a more immediate influence, whereas modifications in actual supply and demand exert a longer-term impact on energy prices.Finally, geopolitical uncertainty will disrupt energy markets through the indirect mechanism of financial linkage networks (Li and Umair, 2023;Ouyang et al., 2021;Shahzad et al., 2023).Based on the above theoretical analysis, it can be concluded that geopolitical risk exists objectively in the formation mechanism of energy supply demand and price.Therefore, this study considers evaluating the marginal explanatory power of geopolitical risk for volatility in energy markets.
The impact of geopolitical risk on the global economy is apparent.However, due to the inherent challenges in quantifying geopolitical risk, initial studies primarily focused on examining the consequences of particular geopolitical occurrences, such as the impact of terrorist events on commodity and stock markets (Ramiah et al., 2019), and the effects of geopolitical events on oil prices (Noguera-Santaella, 2016).In recent years, certain scholars have clearly defined and quantified geopolitical risk (Hu and Li, 2023;Liu and Tao, 2023;Neacşu, 2016).Among them, the GPR index proposed by Caldara and Iacoviello (2022) is quite notable.This index is derived from news reports about geopolitical circumstances and effectively portrays various geopolitical occurrences, including acts of terrorism, military provocations, and regional instabilities.Several studies have demonstrated the scientific validity of the GPR index (Aysan et al., 2019;Mei et al., 2020), which has thus been widely used in the empirical literature (Alam et al., 2023;Bossman et al., 2023;Bussy and Zheng, 2023;Zheng et al., 2023).This study employs the measure developed by Caldara and Iacoviello (2022) to investigate the influence of the time-series monthly GPR index on volatility within the energy market.
With the maturity of measurement methods, scholars have extensively discussed the correlation between geopolitical risks and energy market fluctuations.Qin et al. (2020) examined the asymmetric effects of geopolitical risk on energy returns and volatility using a quantile regression model.Aslam et al. (2022) employ the multifractal detrended cross-correlation analysis to investigate the nonlinear structure and multi-component behavior between geopolitical risks and energy markets.Shahbaz et al. (2023) analyzed to examine the causal association between oil price movements and geopolitical risks through the Granger causality within quantiles.Hence, further analysis from a time-varying perspective is necessary.Lau et al. (2023) employed the variational mode decomposition-based copula method to identify the dependency structure between crude oil prices and geopolitical risks, exhibiting both time-varying and frequency-varying characteristics.Additionally, Jin et al. (2023) investigated the dynamic relationship particularly pronounced at high frequencies among geopolitical risk, energy risk, and climate risk using the BEKK-GARCH and BK models.
Although the existing literature fills the research gap in examining the dynamic influence of geopolitical risk on energy markets, it falls short in identifying tail risk spillovers between the two.The global financial crisis in 2008 has underscored the necessity and urgency of capturing market tail risks and their correlations.Adrin and Brunnermeier constructed the conditional value-at-risk (CoVaR) model in 2008, which has gained widespread usage in empirical research as it better reflects the impact of extreme losses suffered by a particular institution (market) on other institutions (markets).For example, Keilbar and Wang (2022) calibrated the CoVaR of global systemically important financial institutions from the USA based on neural network quantile regression.The estimation results showed that their methodology accurately quantified the interbank risk spillover effect in the nonlinear and multivariable context.Tian and Ji (2022) proposed a CoVaR model based on GARCH copula quantile regression-based and proved it could capture nonlinear tail correlations at different risk levels and is more manageable than the time-varying copula model.However, the model has the drawback of being unable to calculate the upward risk spillover effect.Given the above, this paper uses CoVaR to quantify the tail risk of geopolitical and energy market.
In summary, the preceding research findings provide a substantial theoretical groundwork for this study and inspire research ideas, but aspects remain to be deepened.On the one hand, few literatures examine whether geopolitical risks trigger violent fluctuations in the energy market and the characteristics of such effects.On the other hand, studies testing the risk spillover effects of geopolitics on the energy market from a dynamic nonlinear, and asymmetric perspective are scarce, and the research needs to be improved.
The academic innovation of this paper lies in the following aspects: In terms of research perspectives, this paper focuses on the tail risk spillover of geopolitical to the energy market, and the findings will help the countries and investors to guard against extreme risks.In terms of research methodology, this paper uses CoVaR index to characterize tail risks and uses Cornish-Fisher method to calculate them, and constructs CAViaR-EGARCH model to test the tail risk spillover effect of geopolitical risks on energy markets, which can depict time-varying, asymmetric and nonlinear characteristics.In terms of research content, this paper selects three primary energy sources as the object and further explores the impact of different geopolitical events and geopolitical risks of different countries on the international energy market.This dramatically distinguishes this paper from the present research and is innovative.

Methodology
VaR is the maximum loss faced by assets at a specific confidence level q.Specifically, VaR is defined in terms of the 1-q percentile of the yield distribution.
F is the cumulative distribution function of the rate of return r.Equations ( 1) and ( 2) define VaR from the left tail and right tail of the return distribution, respectively.The spillover effect of geopolitical risks on the energy market in this study is expressed by the conditional value at risk (CoVaR).CoVaR j|i q refers to the maximum possible loss of the transaction in energy market j when the geopolitical risk reaches a certain level of VaR i q at a certain probability level q.The values of j are 1, 2 and 3, denoting Brent crude oil market, South African coal market and Netherlands TTF natural gas market, respectively.The conditional value at risk is expressed as the following quantile regression model: According to the definition of Adrian and Brunnermeier (2016), the marginal risk of energy markets generated by geopolitical risk is denoted by equation ( 4), where VaR i 0.5 denotes the median of geopolitical risk.
The percentile q of the normalized sequence is approximated by the Cornish-Fisher expansion: C(q) is the q percentile of the standard normal distribution.μ, σ, s and k are the return series' mean, variance, skewness and kurtosis, respectively.
We construct the CAViaR-EGARCH model and add the geopolitical risk index to it to measure the VaR value.The model is stated as follows: Where r t denotes energy returns; x t denotes global geopolitical risks; h t is the conditional variance of energy revenue series; ϵ 1t and ϵ 2t are residual series.
present the parameters to be estimated.Among them, q is the confidence level.The CAViaR-EGARCH model considers the leverage effect of global geopolitical risks in the energy market when measuring CoVaR.

Data source and descriptive statistics
The International Geopolitical Risk Index (GPR) was published by Caldara and Iacoviello (2022). 1 Brent crude oil, South African coal and Netherlands TTF natural gas prices are obtained from the IMF's commodity price database. 2The data were sampled by monthly frequency from January 1990 to September 2022, with 393 sets of data.Figure 1 reports the variation characteristics of energy market returns and the geopolitical risk index.The trend chart of the geopolitical risk index shows that the global geopolitical risks and threats increased after 9-11 compared to before 9-11.In addition, Figure 1 shows that after the events of the U.S. invasion of Afghanistan, the Iraq War, and the Russia-Ukraine conflict, major energy markets such as crude oil, coal, and natural gas all experienced significant volatility.Especially after the outbreak of the Russian-Ukrainian conflict, the coal and gas market has experienced historic shocks.Table 1 reports the descriptive statistical results of each variable.The statistical characteristics of the energy return data show that the average rates of returns of the three energy sources are all positive, but the fluctuation range of the crude oil and natural gas market is greater than that of the coal market; the skewness of crude oil yield is negative, while the skewness of natural gas and coal yield is positive.These indicate a greater probability of negative returns in the crude oil market, i.e. companies are more exposed to the depreciation of crude oil assets than to asset appreciation after purchasing crude oil.The natural gas and coal markets have a higher probability of positive returns, i.e. companies are less exposed to asset depreciation after purchasing natural gas and coal.The kurtosis of the return series is greater than 3, indicating more extreme values in the data compared to the normal distribution.From the perspective of skewness and kurtosis, the minimum value of crude oil price appears more than the maximum value, while coal and natural gas prices have fewer minima than maxima.In addition, the ADF unit root test indicates that all four series are stationary sequences.

Parameter estimation results
MATLAB was used to estimate the parameters of the CAViaR-EGARCH model.Table 2 reports the results of parameter estimation for equations ( 7)-( 9).The estimation results of the conditional expectation equation indicate that the return series of Brent crude oil and South African coal have first-order positive correlation characteristics, while geopolitical risks have a positive effect on the average return.For each 1% increase in global geopolitical risk, South African coal's average rate of returns increases by 0.012 units, and the average rate of returns of Dutch natural gas increases by 0.002 units.Moreover, the estimation results of the conditional variance equation indicate a firstorder positive correlation in return volatility.The "leverage effect" exists in all three energy markets.In the Brent crude oil market, good news will bring 0.371 times the impact, while bad news will bring 0.705 times the impact; in the South African coal market, good news will bring 0.307 times the impact, while bad news will bring 0.177 times the impact; in the Dutch natural gas market, good news will bring 0.220 times the impact, while bad news will bring 0.294 times the impact.Meanwhile, the estimation results of the VaR 0.05 and VaR 0.95 equation suggest that the impacts of global geopolitical risk on the energy market's left and right tail risks are asymmetric.When the global geopolitical risk increases by 1%, the Brent crude oil market's left tail risk VaR 0.05 decreases by 0.179%, while the right tail risk VaR 0.95 increases by 0.144%; the South African coal market's left tail risk VaR 0.05 decreases by 0.119%, while the right tail risk VaR 0.95 increases by 0.135%; the Dutch natural gas market's left tail risk VaR 0.05 decreased by 0.113%, while right tail risk VaR 0.95 increased by 0.097%.
Further, the estimation results of the VaR 0.05 equation and the VaR 0.95 equation also indicate that the tail risk of the energy markets is significantly influenced by the volatility and the tail risk of the previous period, in addition to the geopolitical risk.Figure 2 reports the energy market volatility and geopolitical risk quantile.The results show that global geopolitical risks have increased significantly in recent years.At the same time, the energy market has fluctuated violently and has reached the highest level in history.

Assessment of global GPR spillover effects
According to the three methods of historical simulation, Monte Carlo simulation and Cornish-Fisher, the tail risk value of the three energy markets is calculated, respectively.The results are as follows: the 0.95 quantiles of the geopolitical risk index are 127.546, 135.293, and 148.143,   respectively, and the 0.5 quantiles are 75.005,80.821 and 65.032, respectively.As measured by equation ( 8), the mean values of conditional variance for the three markets are 0.008, 0.005, and 0.009, respectively.CoVaR 0.95 , CoVaR 0.05 , ΔCoVaR 0.95 , ΔCoVaR 0.05 , % ΔCoVaR 0.95, and % ΔCoVaR 0.05 of the three energy markets from January 1990 to September 2022 can be calculated according to equation ( 9).Tables 3 and 4 report the relevant calculation results.The results in Tables 3 and 4 show that when geopolitical risk changes from the median to the 0.95 quantiles, the Brent crude oil market increases right tail risk by approximately 11.515% and left tail risk by approximately 22.805%; the South African coal market increases right tail risk by approximately 22.225% and left tail risk by approximately 10.095%; and the Dutch natural gas market increases right tail risk by approximately 10.336% and left tail risk by approximately 9.518%.The above results support the view that geopolitical risks have asymmetric spillover effects on energy markets.6) and ( 9).According to the simulation results, the CoVaR values of the three energy markets are significantly higher than the VaR values.Over the period January 2000 to September 2022, the mean CoVaR 0.95 values of the Brent crude oil, South African coal, and Dutch natural gas markets are 0.173, 0.362, and 0.283, respectively; the mean VaR 0.95 values are 0.125, 0.112 and 0.121, respectively; the mean CoVaR 0.05 values are −0.306,−0.157 and −0.208; the mean VaR 0.05 values are −0.156,−0.090 and −0.088, respectively.Figure 3 shows the nonlinear, asymmetric, and timevarying characteristics of the spillover effects of geopolitical risk on energy markets.The left tail risk of the crude oil market is higher than the right tail risk, while the right tail risk of coal and natural gas markets is higher than the left tail risk.Since the Russia-Ukraine conflict, the risk exposure of the crude oil market has not changed much; the risk exposure of the coal market increased first and then decreased; the risk exposure of the natural gas market has continued to expand.

Simulation of global GPR spillover effects
Table 5 reports the main events corresponding to the local peaks of the geopolitical risk index since the beginning of the 21st century, as well as the CoVaR values of energy markets after being affected by geopolitical risks.The results show that the impact of major geopolitical events on the tail risk of the Brent crude oil market differs little over time, while the natural gas market has seen a significant increase in condition risk since the deterioration of USA-Iran relations in 2020, and then the Russia-Ukraine conflict in 2022 has further pushed upmarket risks.Moreover, we find that major geopolitical events induce significantly more upside than downside risk in coal and natural gas markets, while in crude oil markets they induce significantly less upside than downside risk.

Spillover effects of GPR on energy markets in major countries
The spillover effects of Country-specific GPR indexes on energy markets are further measured and compared using equation ( 9) for a sample of Group of Seven, BRICS countries. 3As shown in Table 6, the Country-specific GPR indexes have a significant spillover effect on the energy market.Except for a few countries such as Germany, the geopolitical risk indexes for most of the Group of Seven and BRICS countries have greater left-tail spillover effects on the crude oil market than the right-tail spillover effects, and more minor left-tail spillover effects on the coal and natural gas markets than the right tail spillover effects.It reaffirms that after 2000, the downside risk is greater than the upside risk in crude oil prices when hit by geopolitical risks, while the upside risk is greater than the downside risk in coal and natural gas markets.Taking the USA as an example, for every 1% increase in the GPR indexes, CoVaR 0.95 in the crude oil market increases by 0.122%, and CoVaR 0.05 decreases by 0.139%; the coal market CoVaR 0.95 increases by 0.095% and CoVaR 0.05 decreases by 0.089%; the natural gas market CoVaR 0.95 increases by 0.081%, CoVaR 0.05 decreased by 0.092%.On average, the spillover effect of BRICS countries ' geopolitical risks on the energy market is higher than that of Group of Seven countries.Antonakakis et al. (2017) and Plakandaras et al. (2019) found that geopolitical risk negatively affected crude oil returns.Qin et al. (2020) suggested that geopolitical risk significantly negatively affected oil market returns at the lower quantiles but had no impact on gas returns in any quantile.These findings corroborate the argument of this paper to some extent.However, they do not consider whether geopolitical risk affects the return of energy commodities at the extreme (0.05 and 0.95 quantiles) situations.Additionally, Gong et al. (2023) showed a significant risk spillover effect between crude oil spot prices and geopolitical risk.Li et al. (2023) found that GPR had timevarying and heterogeneous characteristics on the volatility of crude oil and natural gas prices.The results of these studies are similar to this paper.Furthermore, the results of this paper show that geopolitical risk has time-lag characteristics in the energy market.

Conclusion
This paper employs the CoVaR and the CAViaR-EGARCH models to examine the dynamic spillover effects and tail characteristics of geopolitical risks on major global energy markets from 1990 to 2022.The empirical analysis results show that: First, the spillover effect of geopolitical risk on energy markets is nonlinear, asymmetric, and time-varying.In the crude oil market, geopolitical risk spillovers generate higher left tail risk than right tail risk, while the opposite is true for coal and natural gas markets.Second, major geopolitical risk events will lead to greater tail risk.Since 2020, the deteriorating relationship between the USA and Iran and the Russia-Ukraine conflict have pushed up energy market risk, with the upside risk induced by the two events being significantly greater than the downside risk in the coal and natural gas markets, but the opposite being true in the crude oil market.Third, the spillover effects of national GPRs on energy markets are comparable to those of global GPRs, but the spillover effects of GPR on energy markets vary significantly across nations.On average, the spillover effects of geopolitical risks on energy markets are generally higher in BRICS countries than in Group of Seven countries.
The findings of this paper provide valuable insights for countries to solidify their energy security and for energy investors to avoid market tail risks.On the one hand, given the heterogeneity of the and change patterns of the spillover effects of geopolitical risks on the three major energy markets are identified.The limitations are as follows.First, the GPR is derived from the frequency of geopolitical risk phrases in the U.S. media and does not reflect the media coverage in other nations, which may lead to the neglect of some critical geopolitical events.Second, the EGARCH model presupposes a priori that residual terms adhere to a particular distribution, which may result in an incomplete depiction of the return features of the energy market.Third, the work solely examined the impact of geopolitical risk events on energy market risk and did not assess the cumulative excess returns from geopolitical risk events, which is also a topic for future research.

Figure 1 .
Figure 1.Energy market returns and geopolitical risk index.

Figure 2 .
Figure 2. Energy market volatility and geopolitical risk quantiles.

Figure 3 reports
Figure 3 reports VaR and CoVaR simulation results in the energy market based on equations (6) and (9).According to the simulation results, the CoVaR values of the three energy markets are significantly higher than the VaR values.Over the period January 2000 to September 2022, the mean CoVaR 0.95 values of the Brent crude oil, South African coal, and Dutch natural gas markets are 0.173, 0.362, and 0.283, respectively; the mean VaR 0.95 values are 0.125, 0.112 and 0.121, respectively; the mean CoVaR 0.05 values are −0.306,−0.157 and −0.208; the mean VaR 0.05 values are −0.156,−0.090 and −0.088, respectively.Figure3shows the nonlinear, asymmetric, and timevarying characteristics of the spillover effects of geopolitical risk on energy markets.The left tail risk of the crude oil market is higher than the right tail risk, while the right tail risk of coal and natural gas markets is higher than the left tail risk.Since the Russia-Ukraine conflict, the risk exposure of the crude oil market has not changed much; the risk exposure of the coal market increased first and then decreased; the risk exposure of the natural gas market has continued to expand.Table5reports the main events corresponding to the local peaks of the geopolitical risk index since the beginning of the 21st century, as well as the CoVaR values of energy markets after being affected by geopolitical risks.The results show that the impact of major geopolitical events on the tail risk of the Brent crude oil market differs little over time, while the natural gas market has seen a significant increase in condition risk since the deterioration of USA-Iran relations in 2020, and then the Russia-Ukraine conflict in 2022 has further pushed upmarket risks.Moreover, we find that major geopolitical events induce significantly more upside than downside risk in coal and natural gas markets, while in crude oil markets they induce significantly less upside than downside risk.

Figure 3 .
Figure 3. VaR and CoVaR of energy market simulation results.

Table 3 .
Right tail risk assessment values for energy markets.

Table 4 .
Left tail risk assessment values for energy markets.