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Keywords = conditional Value-at-Risk (CoVaR)

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22 pages, 1111 KiB  
Article
Dependency and Risk Spillover of China’s Industrial Structure Under the Environmental, Social, and Governance Sustainable Development Framework
by Yucui Li, Piyapatr Busababodhin and Supawadee Wichitchan
Sustainability 2025, 17(10), 4660; https://doi.org/10.3390/su17104660 - 19 May 2025
Viewed by 548
Abstract
With the growing global emphasis on sustainable development goals, Environmental, Social, and Governance (ESG) factors have emerged as critical considerations in shaping economic policies and strategies. This study employs the ARMA-eGARCH-skewed t and Vine Copula models, combined with the CoVaR method, to investigate [...] Read more.
With the growing global emphasis on sustainable development goals, Environmental, Social, and Governance (ESG) factors have emerged as critical considerations in shaping economic policies and strategies. This study employs the ARMA-eGARCH-skewed t and Vine Copula models, combined with the CoVaR method, to investigate the dependence structure and risk spillover pathways across various industrial sectors in China within the ESG framework. By modeling the complex interdependencies among sectors, this research uncovers the relationships between individual industries and the ESG benchmark index, while also analyzing the correlations across different sectors. Furthermore, this study quantifies the risk contagion effects across distinct industries under extreme market conditions and maps the pathways of risk spillovers. The findings highlight the pivotal role of ESG considerations in shaping industrial structures. Empirical results demonstrate that industries such as agriculture, energy, and manufacturing exhibit significant systemic risk characteristics in response to ESG fluctuations. Specifically, the identified risk spillover pathway follows the sequence: agriculture → consumption → ESG → manufacturing → energy. The CoVaR values for agriculture, energy, and manufacturing indicate a significant potential for risk contagion. Moreover, sectors such as real estate, finance, and information technology exhibit significant risk spillover effects. These findings offer valuable empirical evidence and a theoretical foundation for formulating ESG-related policies. This study suggests that effective risk management, promoting green finance, encouraging technological innovation, and optimizing industrial structures can significantly mitigate systemic risks. These measures can contribute to maintaining industrial stability and fostering sustainable economic development. Full article
(This article belongs to the Section Economic and Business Aspects of Sustainability)
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30 pages, 736 KiB  
Article
Navigating Uncertainty in an Emerging Market: Data-Centric Portfolio Strategies and Systemic Risk Assessment in the Johannesburg Stock Exchange
by John W. M. Mwamba, Jules C. Mba and Anaclet K. Kitenge
Int. J. Financial Stud. 2025, 13(1), 32; https://doi.org/10.3390/ijfs13010032 - 1 Mar 2025
Cited by 1 | Viewed by 1112
Abstract
This study investigates systemic risk, return patterns, and diversification within the Johannesburg Stock Exchange (JSE) during the COVID-19 pandemic, utilizing data-centric approaches and the ARMA-GARCH vine copula-based conditional value-at-risk (CoVaR) model. By comparing three investment strategies—industry sector-based, asset risk–return plot-based, and clustering-based—this research [...] Read more.
This study investigates systemic risk, return patterns, and diversification within the Johannesburg Stock Exchange (JSE) during the COVID-19 pandemic, utilizing data-centric approaches and the ARMA-GARCH vine copula-based conditional value-at-risk (CoVaR) model. By comparing three investment strategies—industry sector-based, asset risk–return plot-based, and clustering-based—this research reveals that the industrial and technology sectors show no ARCH effects and remain isolated from other sectors, indicating potential diversification opportunities. Furthermore, the analysis employs C-vine and R-vine copulas, which uncover weak tail dependence among JSE sectors. This finding suggests that significant fluctuations in one sector minimally impact others, thereby highlighting the resilience of the South African economy. Additionally, entropy measures, including Shannon and Tsallis entropy, provide insights into the dynamics and predictability of various portfolios, with results indicating higher volatility in the energy sector and certain clusters. These findings offer valuable guidance for investors and policymakers, emphasizing the need for adaptable risk management strategies, particularly during turbulent periods. Notably, the industrial sector’s low CoVaR values signal stability, encouraging risk-tolerant investors to consider increasing their exposure. In contrast, others may explore diversification and hedging strategies to mitigate risk. Interestingly, the industry sector-based portfolio demonstrates better diversification during the COVID-19 crisis than the other two data-centric portfolios. This portfolio exhibits the highest Tsallis entropy, suggesting it offers the best diversity among the types analyzed, albeit said diversity is still relatively low overall. However, the portfolios based on groups and clusters of sectors show similar levels of diversity and concentration, as indicated by their identical entropy values. Full article
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23 pages, 434 KiB  
Article
Portfolio Selection Based on Modified CoVaR in Gaussian Framework
by Piotr Jaworski and Anna Zalewska
Mathematics 2024, 12(23), 3766; https://doi.org/10.3390/math12233766 - 29 Nov 2024
Viewed by 574
Abstract
We study a Mean-Risk model, where risk is measured by a Modified CoVaR (Conditional Value at Risk): [...] Read more.
We study a Mean-Risk model, where risk is measured by a Modified CoVaR (Conditional Value at Risk): CoVaRα,β(X|Y)=VaRβ(X|Y+VaRα(Y)0). We prove that in a Gaussian setting, for a sufficiently small β, such a model has a solution. There exists a portfolio that fulfills the given constraints and for which the risk is minimal. This is shown in relation to the mean–standard deviation portfolio, and numerical examples are provided. Full article
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21 pages, 557 KiB  
Article
Bidual Representation of Expectiles
by Alejandro Balbás, Beatriz Balbás, Raquel Balbás and Jean-Philippe Charron
Risks 2023, 11(12), 220; https://doi.org/10.3390/risks11120220 - 15 Dec 2023
Cited by 4 | Viewed by 2020
Abstract
Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection, pricing [...] Read more.
Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection, pricing and hedging issues, risk transference, risk sharing, etc. In contrast, expectile risk measures are not as widely used, even though they are both coherent and elicitable. This paper addresses the bidual representation of expectiles in order to prove further important properties of these risk measures. Indeed, the bidual representation of expectiles enables us to estimate and optimize them by linear programming methods, deal with optimization problems involving expectile-linked constraints, relate expectiles with VaR and CVaR by means of both equalities and inequalities, give VaR and CVaR hyperbolic upper bounds beyond the level of confidence, and analyze whether co-monotonic additivity holds for expectiles. Illustrative applications are presented. Full article
(This article belongs to the Special Issue Optimal Investment and Risk Management)
23 pages, 1540 KiB  
Article
Spatial Multivariate GARCH Models and Financial Spillovers
by Rosella Giacometti, Gabriele Torri, Kamonchai Rujirarangsan and Michela Cameletti
J. Risk Financial Manag. 2023, 16(9), 397; https://doi.org/10.3390/jrfm16090397 - 6 Sep 2023
Cited by 3 | Viewed by 3402
Abstract
We estimate the risk spillover among European banks from equity log-return data via Conditional Value at Risk (CoVaR). The joint dynamic of returns is modeled with a spatial DCC-GARCH which allows the conditional variance of log-returns of each bank to depend on past [...] Read more.
We estimate the risk spillover among European banks from equity log-return data via Conditional Value at Risk (CoVaR). The joint dynamic of returns is modeled with a spatial DCC-GARCH which allows the conditional variance of log-returns of each bank to depend on past volatility shocks to other banks and their past squared returns in a parsimonious way. The backtesting of the resulting risk measures provides evidence that (i) the multivariate GARCH model with Student’s t distribution is more accurate than both the standard multivariate Gaussian model and the Filtered Historical Simulation (FHS), and (ii) the introduction of a spatial component improves the assessment of risk profiles and the market risk spillovers. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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35 pages, 3058 KiB  
Article
The Analysis of Risk Measurement and Association in China’s Financial Sector Using the Tail Risk Spillover Network
by Can-Zhong Yao, Ze-Kun Zhang and Yan-Li Li
Mathematics 2023, 11(11), 2574; https://doi.org/10.3390/math11112574 - 4 Jun 2023
Cited by 2 | Viewed by 2646
Abstract
This study focused on analyzing the complexities and risk spillovers that arise among financial institutions due to the development of financial markets. The research employed the conditional value at risk (CoVaR) methodology to quantify the extent of tail risk spillover and constructed a [...] Read more.
This study focused on analyzing the complexities and risk spillovers that arise among financial institutions due to the development of financial markets. The research employed the conditional value at risk (CoVaR) methodology to quantify the extent of tail risk spillover and constructed a risk spillover network encompassing Chinese financial institutions. The study further investigated the characteristics, transmission paths, and dynamic evolution of this network under different risk conditions. The empirical findings of this research highlighted several important insights. First, financial institutions play distinct roles in the risk spillover process, with the securities and banking sectors as risk exporters and the insurance and diversified financial sectors as risk takers. The closest risk spillover relationships were observed between banking and insurance and between securities and diversified financial sectors. Second, in high-risk scenarios, there is significant intrasectoral risk transmission between banks and the diversified financial sector, as well as dual-sectoral risk contagion between banks and securities, with the most-common transmission occurring between diversified financial and securities sectors. Finally, the securities sector acts as the pivotal node for risk spillovers, being the main transmitter of intersectoral risks. The formation and evolution of risk spillover networks are influenced by endogenous mechanisms, in particular the convergence effect. Full article
(This article belongs to the Special Issue Advanced Research in Mathematical Economics and Financial Modelling)
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16 pages, 3404 KiB  
Article
Modelling Systemic Risk in Morocco’s Banking System
by Ayoub Kyoud, Cherif El Msiyah and Jaouad Madkour
Int. J. Financial Stud. 2023, 11(2), 70; https://doi.org/10.3390/ijfs11020070 - 21 May 2023
Cited by 5 | Viewed by 3582
Abstract
The Moroccan banking system suffered a significant impact due to the extreme market conditions caused by the COVID-19 outbreak, which led to an increase in non-performance loans. This, in turn, reduced the value of banks’ assets and their ability to meet their obligations, [...] Read more.
The Moroccan banking system suffered a significant impact due to the extreme market conditions caused by the COVID-19 outbreak, which led to an increase in non-performance loans. This, in turn, reduced the value of banks’ assets and their ability to meet their obligations, implicitly raising systemic risk. In such circumstances, the collapse of one financial institution could cause a series of bankruptcies and endanger the overall state of the economy. Given the limited attention devoted to the analysis of systemic risk in the Moroccan banking system, this paper aimed to fill this gap by analyzing the Moroccan banks’ systemic risk exposure and assessing their stability during the COVID-19 crisis, using Quantile Regression Neural Network (QRNN) optimized by Adam algorithm to calibrate the Conditional Value at Risk (CoVaR). This study revealed a significant increase in systemic risk during the pandemic crisis and highlights the suitability of more complex QRNN in assessing systemic risk. The findings emphasize the need for regulators to pay close attention to banks’ risk exposures when implementing measures to mitigate systemic risk, such as increasing banks’ capital requirements or increasing the amount of high-quality liquid assets. Full article
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21 pages, 369 KiB  
Article
Risk Measure between Exchange Rate and Oil Price during Crises: Evidence from Oil-Importing and Oil-Exporting Countries
by Mouna Ben Saad Zorgati
J. Risk Financial Manag. 2023, 16(4), 250; https://doi.org/10.3390/jrfm16040250 - 20 Apr 2023
Cited by 4 | Viewed by 2759
Abstract
This study investigates the risk spillover effect between the exchange rate of importing and exporting oil countries and the oil price. The analysis is supported by the utilization of a set of double-long memories. Thereafter, a multivariate GARCH type model is adopted to [...] Read more.
This study investigates the risk spillover effect between the exchange rate of importing and exporting oil countries and the oil price. The analysis is supported by the utilization of a set of double-long memories. Thereafter, a multivariate GARCH type model is adopted to analyze the dynamic conditional correlations. Moreover, the Gumbel copula is employed to define the nonlinear structure of dependence and to evaluate the optimal portfolio. The conditional Value-at-Risk (CoVaR) is adopted as a risk measure. Findings indicate a long-run dependence and asymmetry of bidirectional risk spillover among oil price and exchange rate and confirm that the risk spillover intensity is different between the former and the latter. They show that the oil price has a stronger spillover effect in the case of oil exporting countries and the lowest spillover effect in the case of oil importing countries. Full article
(This article belongs to the Special Issue Forecasting and Time Series Analysis)
20 pages, 1103 KiB  
Article
The Risk Contagion between Chinese and Mature Stock Markets: Evidence from a Markov-Switching Mixed-Clayton Copula Model
by Hongli Niu, Kunliang Xu and Mengyuan Xiong
Entropy 2023, 25(4), 619; https://doi.org/10.3390/e25040619 - 6 Apr 2023
Cited by 4 | Viewed by 1940
Abstract
Exploring the risk spillover between Chinese and mature stock markets is a promising topic. In this study, we propose a Markov-switching mixed-Clayton (Ms-M-Clayton) copula model that combines a state transition mechanism with a weighted mixed-Clayton copula. It is applied to investigate the dynamic [...] Read more.
Exploring the risk spillover between Chinese and mature stock markets is a promising topic. In this study, we propose a Markov-switching mixed-Clayton (Ms-M-Clayton) copula model that combines a state transition mechanism with a weighted mixed-Clayton copula. It is applied to investigate the dynamic risk dependence between Chinese and mature stock markets in the Americas, Europe, and Asia–Oceania regions. Additionally, the conditional value at risk (CoVaR) is applied to analyze the risk spillovers between these markets. The empirical results demonstrate that there is mainly a time-varying but stable positive risk dependence structure between Chinese and mature stock markets, where the upside and downside risk correlations are asymmetric. Moreover, the risk contagion primarily spills over from mature stock markets to the Chinese stock market, and the downside effect is stronger. Finally, the risk contagion from Asia–Oceania to China is weaker than that from Europe and the Americas. The study provides insights into the risk association between emerging markets, represented by China, and mature stock markets in major regions. It is significant for investors and risk managers, enabling them to avoid investment risks and prevent risk contagion. Full article
(This article belongs to the Special Issue Recent Trends and Developments in Econophysics)
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20 pages, 9131 KiB  
Article
Systemic Risk Modeling with Lévy Copulas
by Yuhao Liu, Petar M. Djurić, Young Shin Kim, Svetlozar T. Rachev and James Glimm
J. Risk Financial Manag. 2021, 14(6), 251; https://doi.org/10.3390/jrfm14060251 - 5 Jun 2021
Cited by 4 | Viewed by 4280
Abstract
We investigate a systemic risk measure known as CoVaR that represents the value-at-risk (VaR) of a financial system conditional on an institution being under distress. For characterizing and estimating CoVaR, we use the copula approach and introduce the normal tempered stable (NTS) copula [...] Read more.
We investigate a systemic risk measure known as CoVaR that represents the value-at-risk (VaR) of a financial system conditional on an institution being under distress. For characterizing and estimating CoVaR, we use the copula approach and introduce the normal tempered stable (NTS) copula based on the Lévy process. We also propose a novel backtesting method for CoVaR by a joint distribution correction. We test the proposed NTS model on the daily S&P 500 index and Dow Jones index with in-sample and out-of-sample tests. The results show that the NTS copula outperforms traditional copulas in the accuracy of both tail dependence and marginal processes modeling. Full article
(This article belongs to the Special Issue Mathematical and Empirical Finance)
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18 pages, 858 KiB  
Article
CoCDaR and mCoCDaR: New Approach for Measurement of Systemic Risk Contributions
by Rui Ding and Stan Uryasev
J. Risk Financial Manag. 2020, 13(11), 270; https://doi.org/10.3390/jrfm13110270 - 3 Nov 2020
Cited by 4 | Viewed by 3129
Abstract
Systemic risk is the risk that the distress of one or more institutions trigger a collapse of the entire financial system. We extend CoVaR (value-at-risk conditioned on an institution) and CoCVaR (conditional value-at-risk conditioned on an institution) systemic risk contribution measures and propose [...] Read more.
Systemic risk is the risk that the distress of one or more institutions trigger a collapse of the entire financial system. We extend CoVaR (value-at-risk conditioned on an institution) and CoCVaR (conditional value-at-risk conditioned on an institution) systemic risk contribution measures and propose a new CoCDaR (conditional drawdown-at-risk conditioned on an institution) measure based on drawdowns. This new measure accounts for consecutive negative returns of a security, while CoVaR and CoCVaR combine together negative returns from different time periods. For instance, ten 2% consecutive losses resulting in 20% drawdown will be noticed by CoCDaR, while CoVaR and CoCVaR are not sensitive to relatively small one period losses. The proposed measure provides insights for systemic risks under extreme stresses related to drawdowns. CoCDaR and its multivariate version, mCoCDaR, estimate an impact on big cumulative losses of the entire financial system caused by an individual firm’s distress. It can be used for ranking individual systemic risk contributions of financial institutions (banks). CoCDaR and mCoCDaR are computed with CVaR regression of drawdowns. Moreover, mCoCDaR can be used to estimate drawdowns of a security as a function of some other factors. For instance, we show how to perform fund drawdown style classification depending on drawdowns of indices. Case study results, data, and codes are posted on the web. Full article
(This article belongs to the Special Issue Risk and Financial Consequences)
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28 pages, 22213 KiB  
Article
Discovering Systemic Risks of China's Listed Banks by CoVaR Approach in the Digital Economy Era
by Huichen Jiang and Jun Zhang
Mathematics 2020, 8(2), 180; https://doi.org/10.3390/math8020180 - 2 Feb 2020
Cited by 6 | Viewed by 3941
Abstract
The world has entered the digital economy era. As a developing country, China's banking industry plays an important role in the financial industry, and its size ranks first in the world. Therefore, it is of great significance to study the systemic risks of [...] Read more.
The world has entered the digital economy era. As a developing country, China's banking industry plays an important role in the financial industry, and its size ranks first in the world. Therefore, it is of great significance to study the systemic risks of China's banks in the digital economy era. We first compare the traditional indicator approach and the market-based approach theoretically, and Conditional Value at Risk (CoVaR) model, a market-based approach, is considered to be an efficient way to discover systemic risk in different perspectives. Based on static and dynamic models, we evaluate the contributions of sixteen China's listed banks to the systemic risk. Furthermore, we model bank exposures, extend the models by considering extreme circumstance, and incorporate the effects of Fintech and non-bank financial institutions. The results show the levels of systemic risks and the corresponding systemic importance rankings vary in different time periods. We find that the contributions of some small banks to systemic risk are even higher than some big banks during the sample period. Moreover, the big banks face less risks than most of the small banks when the banking system is in distress. We make suggestions for improving financial supervision and maintaining financial stability. Full article
(This article belongs to the Section E5: Financial Mathematics)
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33 pages, 2751 KiB  
Article
Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations
by Takaaki Koike and Marius Hofert
Risks 2020, 8(1), 6; https://doi.org/10.3390/risks8010006 - 15 Jan 2020
Cited by 10 | Viewed by 7393
Abstract
In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the [...] Read more.
In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as the Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments. Full article
(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)
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15 pages, 1042 KiB  
Article
On Identifying the Systemically Important Tunisian Banks: An Empirical Approach Based on the △CoVaR Measures
by Wided Khiari and Salim Ben Sassi
Risks 2019, 7(4), 122; https://doi.org/10.3390/risks7040122 - 12 Dec 2019
Cited by 10 | Viewed by 4612
Abstract
The aim of this work is to assess systemic risk of Tunisian listed banks. The goal is to identify the institutions that contribute the most to systemic risk and that are most exposed to it. We use the CoVaR that considered the systemic [...] Read more.
The aim of this work is to assess systemic risk of Tunisian listed banks. The goal is to identify the institutions that contribute the most to systemic risk and that are most exposed to it. We use the CoVaR that considered the systemic risk as the value at risk (VaR) of a financial institution conditioned on the VaR of another institution. Thus, if the CoVaR increases with respect to the VaR, the spillover risk also increases among the institutions. The difference between these measurements is termed △CoVaR, and it allows for estimating the exposure and contribution of each bank to systemic risk. Results allow classifying Tunisian banks in terms of systemic risk involvement. They show that public banks occupy the top places, followed by the two largest private banks in Tunisia. These five banks are the main systemic players in the Tunisian banking sector. It seems that they are the least sensitive to the financial difficulties of existing banks and the most important contributors to the distress of the other banks. This work aims to add a broader perspective to the micro prudential application of regulation, including contagion, proposing a macro prudential vision and strengthening of regulatory policy. Supervisors could impose close supervision for institutions considered as potentially systemic banks. Furthermore, regulations should consider the systemic contribution when defining risk requirements to minimize the consequences of possible herd behavior. Full article
(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)
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18 pages, 1984 KiB  
Article
Risk Transmission between Chinese and U.S. Agricultural Commodity Futures Markets—A CoVaR Approach
by Yangmin Ke, Chongguang Li, Andrew M. McKenzie and Ping Liu
Sustainability 2019, 11(1), 239; https://doi.org/10.3390/su11010239 - 5 Jan 2019
Cited by 15 | Viewed by 4299
Abstract
Commodity futures markets play an important role, through risk management and price discovery, in helping firms make sustainable production and marketing decisions. An important related issue is how pricing signals between futures exchanges impact traders’ risk. We address this issue by shedding light [...] Read more.
Commodity futures markets play an important role, through risk management and price discovery, in helping firms make sustainable production and marketing decisions. An important related issue is how pricing signals between futures exchanges impact traders’ risk. We address this issue by shedding light on risk transmission between the most mature (U.S.) and the fastest growing (Chinese) commodity futures markets. Gaining greater insight of risk transmission between these key markets is vitally important to firms engaged in the efficient and sustainable trade of commodities needed to feed the world. We examine the risk transmission between Chinese and U.S. agricultural futures markets for soybean, corn, and sugar with a Copula based conditional value at risk (CoVaR) approach. We find significant upside, and to a lesser extent downside risk transmission, between Chinese and U.S. markets. We confirm the dominant pricing role of U.S. agricultural futures markets while acknowledging the increasing price discovery role performed by Chinese markets. Our results highlight that soybean markets exhibit greater risk transmission than sugar and corn markets. We argue that our findings may be explained by Chinese government policy intervention, and by the large role played by U.S. firms in the underlying cash commodity markets–both in terms of production and trade. Full article
(This article belongs to the Special Issue Application of Time Series Analyses in Business)
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