Time-Varying Spillover Effects of Carbon Prices on China’s Financial Risks

Abstract

As China’s financial markets become increasingly integrated and the carbon market undergoes financialization, the impact of carbon emission price fluctuations on financial markets has emerged as a key area of systemic risk research. This study employs the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model and the optimal Copula function to investigate the dynamic correlation between carbon prices and China’s financial markets. Building on this, the Monte Carlo simulation and Copula CoVaR models are used to explore the spillover effects of carbon price volatility on China’s financial markets. The findings reveal the following: (1) Carbon price fluctuations generate spillover effects on all financial markets, but the intensity varies across different markets. The foreign exchange market experiences the strongest spillover effect, followed by the bond market, while the stock and money markets are relatively less affected. (2) The optimal Copula functions differ between the carbon market and China’s financial markets, indicating heterogeneous characteristics across regional markets. (3) There is a degree of interdependence between the carbon market and various sub-markets in China’s financial system. The carbon market has the strongest positive correlation with the commodity market and a relatively high negative correlation with the real estate market. These findings underscore the importance of integrating carbon price volatility into financial risk management frameworks. For policymakers, it highlights the need to consider market stability measures when crafting carbon emission regulations. Market managers can leverage these insights to develop strategies that mitigate risk spillover effects, while investors can use this analysis to inform their portfolio diversification and risk assessment processes.

1. Introduction

Over the past few decades, comprehensive human development has not only led to increasingly adverse climate change and natural disasters but has also contributed to warfare and political as well as socio-economic instability [1]. Climate change has emerged as a global issue, and reducing carbon emissions is crucial for achieving sustainable development. Research on sustainable development requires an interdisciplinary framework that not only addresses ecological and environmental factors but also considers political, economic, and institutional elements [2,3]. The Kyoto Protocol, which came into effect in 2005, identified six greenhouse gasses, with carbon dioxide having the greatest impact on global warming. Consequently, reducing carbon emissions became a top priority. Financialization is closely intertwined with the objectives of sustainable development and the Kyoto Protocol, as it pertains to the growth process of the global financial sector relative to the real economy. By fostering the development of green finance, financialization provides financial support for environmental protection and climate change mitigation, which aligns with the Kyoto Protocol’s goal of reducing greenhouse gas emissions. This not only contributes to alleviating the negative impacts of CO₂ but also represents a crucial pathway towards achieving sustainable development. The integration of financialization with environmental sustainability efforts thus emerges as a vital strategy in advancing global economic growth while minimizing ecological footprint. The European Union Emissions Trading System (EU ETS), the earliest and most mature carbon market, is highly active, with CO₂ emission allowances traded as commodities in the form of spot, futures, and options contracts. China’s carbon market has drawn lessons from the EU ETS and continues to strive for contributions to climate change mitigation within the context of carbon neutrality. Low-carbon reduction has become a dominant theme in national social development [4], with carbon pricing widely implemented as a crucial economic tool for incentivizing enterprises and individuals to reduce carbon and other greenhouse gas emissions. Current research on the development of China’s carbon emissions trading market indicates that with the expansion of market size and trading volume, the carbon trading market shows signs of restoring market efficiency [5]. Additionally, studies indicate that the carbon emissions trading policy in pilot regions has led to a reduction of 18% in CO₂ emissions and 36% in SO₂ emissions, demonstrating an immediate impact on the “decarbonization” effect [6]. Since the launch of the national carbon emissions trading market in 2021, the market has operated smoothly, exhibiting stable trading prices and a compliance rate of 99.5%, which has facilitated greenhouse gas reductions by enterprises and promoted a green, low-carbon transition. As the carbon market evolves, its financial attributes have become increasingly apparent, drawing greater scholarly attention to its connections with financial markets—particularly the spillover effects on stock, bond, and commodity markets [7,8].

The integration of carbon markets and financial markets is a complex process that involves coordination and collaboration across multiple levels. This integration faces challenges and limitations due to speculative risks, regulatory complexities, and the diversity of market participants. However, it also presents opportunities. The European Union Emission Trading System (EU ETS), one of the largest carbon markets globally, has provided a successful example of integration with financial markets. The EU ETS allows carbon emission allowances to be traded as financial assets, which not only enhances market liquidity but also attracts participation from financial institutions, including banks and investment funds. This indicates that with appropriate policy design and market mechanisms, carbon markets can effectively integrate with financial markets while achieving both environmental objectives and economic benefits.

Additionally, California has successfully attracted numerous financial institutions to participate in carbon trading by establishing a carbon market closely connected to financial markets. Through innovative financial products such as carbon credit loans and carbon futures contracts, the California carbon market has not only facilitated carbon emission reductions but has also promoted the development of green finance. As the world’s largest carbon emitter, China recorded a carbon trading volume of 263 million tons and a transaction value of CNY 17.258 billion from 1 January 2022 to 31 December 2023. By establishing a unified national carbon emissions trading market, China is gradually integrating its carbon market with financial markets. However, most studies have focused on international financial markets and EU carbon pricing, with limited research on the dependence and complex dynamic spillover effects between carbon allowance price fluctuations and the Chinese financial market [9]. There is a divergence of opinions on the impact of carbon markets on financial markets; some research suggests that they may increase market complexity and risk [10,11], while other studies emphasize their positive contribution to the sustainable development of financial markets [12,13]. The relationship between carbon markets and other financial markets is not yet fully understood, which can lead to uncertainty in decision-making for investors and policymakers. In an effort to unravel this complex interplay, our study conducts an analysis of the price volatility and spillover effects between carbon markets and other financial markets. We investigate the influence of policy shifts in carbon markets on other financial markets and evaluate the potential impact of this interrelationship on the overall stability and sustainable development of financial markets. This research offers fresh insights and evidence to shed light on this contentious issue.

Considering that the return series of financial assets often exhibit “spike” distribution characteristics, this study aims to enhance the accuracy of the CoVaR method. It begins by fitting a GARCH model based on a skewed t-distribution and generates heatmaps of rank correlation coefficients to investigate the relationship between the carbon market and the Chinese financial market. Additionally, it employs Monte Carlo simulations and the Copula–CoVaR model to explore the risk spillover effects of carbon allowance price fluctuations on the Chinese financial market. The objective is to provide theoretical insights and practical recommendations for the further improvement of the domestic carbon emissions trading system, as well as to reasonably predict the risk spillover effects of carbon allowance prices on financial markets to support stable market operations.

The main contributions of this paper are as follows: (1) From both static and dynamic perspectives, it selects multiple dimensions of the financial market to comprehensively examine the dynamic dependence and risk spillover effects of carbon allowance price fluctuations on the Chinese financial market, thereby providing theoretical support for policy implementation. (2) By adopting a skewed t-distribution for GARCH fitting and integrating the optimal Copula function with the CoVaR method, this study utilizes graphical representations to observe the structural dynamics between carbon price fluctuations and financial markets, thereby expanding the research perspectives and methodologies in this field. (3) By investigating the dynamic dependence structure and risk spillovers between the carbon market and financial markets, this research offers practical references for policymakers to consider financial market stability when formulating carbon emissions policies, assists market managers in risk avoidance and carbon price regulation, and aids investors in assessing risk processes.

2. Literature Review

In recent years, research on carbon emission trading markets by scholars both domestically and internationally primarily focuses on three aspects: the characteristics of carbon price fluctuations, the correlation between carbon markets, and the risk spillover effects between financial markets.

2.1. Characteristics of Carbon Emission Rights Price Fluctuations

Scholars worldwide have conducted extensive research on the formation of carbon emission trading prices and their fluctuation characteristics. Theoretically, researchers have mainly focused on the determinants of carbon emission rights prices, including supply and demand relationships [14], market structure [15], and energy prices [16]. Empirically, scholars have employed various econometric methods, such as GARCH models [17], VAR models [18,19], and mediation effect models [20], to deeply analyze the fluctuation characteristics of carbon emission rights prices. Li et al. [21] combined the MEPT and ICEEMDAN to propose the MEPT-ICEEMDAN-CTCN model for carbon price forecasting. Lyu et al. [22] utilized a Markov chain Monte Carlo–stochastic volatility model and wavelet multi-resolution model to analyze the price return volatility and dynamic characteristics of price fluctuations in the carbon pilot markets of Hubei, Shanghai, and Shenzhen, indicating that China’s carbon pilot markets, like the EU-ETS, have deficiencies in terms of volatility stability. Wei et al. [23] applied DMS and DMA models for comparative carbon price forecasting and analyzed the time-varying characteristics of various influencing factors’ predictive roles.

The characteristics of carbon emission rights price fluctuations mainly concentrate on the correlation between energy prices and macroeconomic indicators [24], as well as how to construct appropriate models to depict their dynamic fluctuation structures. These studies provide important theoretical foundations for the pricing mechanism, risk management, and policy formulation of carbon emission trading markets.

2.2. Correlation of Carbon Emission Rights Markets

Research on the correlation between carbon emission rights markets and financial markets primarily focuses on the mutual influence and correlation mechanisms between the two. Such research helps to reveal the intrinsic connections between carbon emission rights markets and financial markets, providing significant support for the healthy development of carbon emission rights markets and the stability of financial markets. Studies on the correlation of carbon emission rights markets cover various aspects, including the correlation between carbon emission trading mechanisms and markets [25,26], the correlation between carbon emission rights markets and financial markets [27,28], the impact of carbon emission trading on enterprises [29,30], and the risk assessment of carbon emission rights markets [31,32].

These studies not only contribute to a deeper understanding of the operational patterns of carbon emission rights markets but also provide valuable references for policymakers and enterprises. Research on the correlation between carbon emission rights markets and financial markets has often focused on the mutual influence between single financial markets, neglecting the complex interactions between markets and lacking a comprehensive and systematic perspective. Based on this, this paper categorizes the financial market into six sub-markets, systematically and comprehensively representing China’s financial market, which allows for more in-depth and extensive related research. This approach fills the gaps in the field of related research and provides strong support for addressing climate change and achieving sustainable development goals.

2.3. Financial Market Risk Spillover Effects

Research on the risk spillover effects between financial markets and carbon markets primarily focuses on the complex interconnections within financial markets and the risk transmission mechanisms between carbon markets and other markets. The risk spillover effect in financial markets is an important topic in financial research, referring to the phenomenon where a risk event in one financial market or financial institution not only affects itself but may also spill over to other related markets and institutions, potentially triggering instability in the entire financial system. This phenomenon has become increasingly prominent with the deepening of financial globalization and market integration. The main channels for financial risk spillover include price linkages, liquidity transmission, credit risk transfer, and psychological factors of market participants. These channels enable financial risks to spread and amplify rapidly between different markets and institutions.

To gain a deeper understanding of the characteristics and patterns of risk spillovers in financial markets, scholars have conducted extensive empirical research. These studies have encompassed various domains, including the stock markets of China and the United States, exchange rate markets, gold markets, and multiple equity markets. Various methodologies have been employed in these investigations, such as the Granger causality test, time-varying Copula–GARCH models, and extreme value theory (EVT). For instance, Abid et al. examined extreme dependence and risk spillover effects between Bitcoin and fiat currency markets [33], while Cevik et al. analyzed the relationship and risk spillover between Bitcoin spot and futures markets during the COVID-19 pandemic [34]. Tiwari et al. used the QVAR model to describe the conditional volatility spillover between energy, biofuels, and agricultural products [35]. Rahman et al. used the optimal Copula function to compare the risk spillover effects of oil and gas on investment-grade and high-yield bonds [36]. Chen et al. examined the linkages and dependency structures between four commodity indices and sovereign credit risks using extreme volatility risk spillover methods and quantile VAR analysis [37].

In summary, scholars have conducted empirical analyses on the price fluctuations of carbon emission rights using various econometric methods, including the GARCH model, VAR model, mediation effect model, and DMS and DMA models, among others. By comprehensively considering aspects such as volatility modeling and forecasting, capturing nonlinear relationships, volatility clustering effects, and compatibility with other models, the GARCH model demonstrates significant advantages in the field of financial time series analysis, particularly in simulating and forecasting market volatility, compared to other models. While the GARCH model holds advantages in modeling financial market volatility, it also exhibits drawbacks such as issues with nonnegative linear constraints, inadequate explanation of leverage effects, and the lack of a connection between conditional heteroskedasticity and conditional mean. In contrast, the GARCH-t model, which combines the characteristics of the GARCH model and the t-distribution, is capable of more accurately describing the “leptokurtic and fat-tailed” characteristics of financial time series data. This enhances prediction accuracy and accommodates asymmetric volatility, thereby overcoming the limitations of the standard GARCH model.

Financial markets, as the “barometers” of a country or region’s economic activity, reflect corporate wealth and real economic conditions. Volatility in financial markets can influence the carbon market by affecting real economic behavior [38]. However, the carbon market’s development lags behind that of the financial markets, and its mechanisms for influencing the financial system are not fully developed. Given the strengths and weaknesses of various models, this paper combines three models—the GARCH, Copula, and CoVaR models. This combination not only addresses the issue of asymmetrical distributions but also uses the skewed t-distribution to more accurately capture the “leptokurtic” nature of the return series, providing a fuller picture of the dynamic relationships between the carbon market and financial markets. Therefore, this study first fits a GARCH model based on the skewed t-distribution and visualizes the rank correlation heatmap to examine the relationship between the carbon market and China’s financial markets. It then applies Monte Carlo simulations and the Copula–CoVaR model to explore the risk spillover effects of carbon price volatility on China’s financial markets.

3. Model Design and Data Description

3.1. Construction of Marginal Distribution

Bollerslev (1986) extended the ARCH model and established the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, which better captures the volatility clustering and leptokurtic characteristics of both carbon emission permit prices and financial markets [39]. Through testing, this study finds that the GARCH(1,1) model effectively describes the time-varying nature of financial market returns while maintaining simplicity. The GARCH(1,1) model is expressed as

$${\mathsf{\sigma }}_{\mathrm{t}}^2={\mathsf{\alpha }}_0+{\mathsf{\alpha }}_1{\mathsf{\epsilon }}_{\mathrm{t}-1}^2+{\mathsf{\beta }}_1{\mathsf{\sigma }}_{\mathrm{t}-1}^2$$

(1)

where ${\mathsf{\epsilon }}_{\mathrm{t}}$ is the carbon emission permit price and financial market return series, ${\mathsf{\alpha }}_0$ is the parameter term, and parameters ${\mathsf{\alpha }}_1$ and ${\mathsf{\beta }}_1$ represent the impact of the squared error term and the influence of the previous conditional variance, respectively. In this paper, we intend to use the t-distribution in order to capture the heavy-tailed characteristics of the financial market. The estimated values of parameters ${\mathsf{\alpha }}_1$ and ${\mathsf{\beta }}_1$ will reflect the sensitivity of the fluctuations in the carbon emission permit price to changes in the financial market.

3.2. Time-Varying Copula Models

In the analysis of the risk spillover effects of carbon emission permit prices on financial markets, we employ time-varying Copula models to capture the dependence structure between the carbon market and financial markets. The Copula function is a widely utilized tool for correlation analysis. Essentially, it serves as a linking function that connects the marginal distribution functions of individual markets to form a new joint distribution function. It is a family of functions designed to describe the dependency structure between variables. Sklar was the first to propose the Copula function approach in 1959, and it was not until the late 1990s that it began to be applied to the field of finance [40]. The joint distribution function of N random variables ${\mathrm{X}}_1$, ${\mathrm{X}}_2$, …, ${\mathrm{X}}_{\mathrm{N}}$ is represented by H(${\mathrm{X}}_1$, ${\mathrm{X}}_2$, …, ${\mathrm{X}}_{\mathrm{N}}$), and the corresponding marginal distribution function is represented by ${\mathrm{F}}_{\mathrm{i}}$(${\mathrm{X}}_{\mathrm{i}}$) (i = 1, 2, …, n). Sklar’s theorem states that a function C(·) “connects” the joint and marginal distributions of these variables in the following way:

$$\mathrm{H}({\mathrm{X}}_1,{\mathrm{X}}_2,\dots ,{\mathrm{X}}_{\mathrm{N}})=\mathrm{C}\left[{\mathrm{F}}_1\right({\mathrm{X}}_1),{\mathrm{F}}_2({\mathrm{X}}_2),\dots {\mathrm{F}}_{\mathrm{N}}({\mathrm{X}}_{\mathrm{N}}\left)\right]$$

(2)

The expression of the Copula function can be obtained using inverse transformation of the CDF of the marginal distribution of ${\mathrm{X}}_{\mathrm{i}}={\mathrm{F}}_{\mathrm{i}}^{-1}\left({\mathrm{u}}_{\mathrm{i}}\right)$(i = 1, 2, … N):

$$\mathrm{C}({\mathrm{u}}_1,{\mathrm{u}}_2,\dots ,{\mathrm{u}}_{\mathrm{N}})=\mathrm{H}\left[{\mathrm{F}}_1^{-1}\right({\mathrm{u}}_1),{\mathrm{F}}_2^{-1}({\mathrm{u}}_2),\dots ,{\mathrm{F}}_{\mathrm{N}}^{-1}({\mathrm{u}}_{\mathrm{N}}\left)\right]$$

(3)

The models that apply to this study are Gumbel Copula, Clayton Copula, and Frank Copula because of the asymmetric features of the financial market return series. These models must be examined further in combination with the AIC to determine which model is best. The suggested Copula function has the following expression:

3.2.1. Binary Gumbel Copula Function

$${\mathrm{C}}_{\mathrm{G}}\left(\mathrm{u},\mathrm{v};\mathsf{\delta }\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left\{-{\left[{\left(-\mathrm{l}\mathrm{n}\mathrm{u}\right)}^{{\displaystyle \frac{1}{\mathsf{\delta }}}}+{\left(-\mathrm{l}\mathrm{n}\mathrm{v}\right)}^{{\displaystyle \frac{1}{\mathsf{\delta }}}}\right]}^{\mathsf{\delta }}\right\}$$

(4)

where $\mathsf{\delta }$ is the relevant parameter, $\mathsf{\delta }$ ϵ [1, +$\mathrm{\infty }$); $\mathsf{\phi }(\mathrm{t})={(-\mathrm{l}\mathrm{n}\mathrm{u})}^{\mathsf{\delta }}$ is the generating element of the Gumbel Copula function.

3.2.2. Binary Clayton Copula Function

$${\mathrm{C}}_{\mathrm{C}}\left(\mathrm{u},\mathrm{v};\mathsf{\theta }\right)={\left({\mathrm{u}}^{-\mathsf{\theta }}+{\mathrm{v}}^{-\mathsf{\theta }}-1\right)}^{-{\displaystyle \frac{1}{\mathsf{\theta }}}}$$

(5)

where $\mathsf{\theta }$ is the relevant parameter; $\mathsf{\phi }(\mathrm{t})={\mathrm{t}}^{-\mathsf{\theta }}-1$ is the generating element of the Clayton Copula function.

3.2.3. Binary Frank Copula Function

$${\mathrm{C}}_{\mathrm{F}}\left(\mathrm{u},\mathrm{v};\mathsf{\lambda }\right)=-{\displaystyle \frac{1}{\mathsf{\lambda }}}\mathrm{l}\mathrm{n}\left[{\displaystyle \frac{\left({\mathrm{e}}^{-\mathsf{\lambda }\mathsf{\mu }}-1\right)\left({\mathrm{e}}^{-\mathsf{\lambda }\mathsf{\nu }}-1\right)}{{\mathrm{e}}^{-\mathsf{\lambda }}-1}}\right]$$

(6)

where $\mathsf{\lambda }$ is the relevant parameter; $\mathsf{\phi }(\mathrm{t})=-\mathrm{l}\mathrm{n}{\displaystyle \frac{{\mathrm{e}}^{-\mathsf{\lambda }\mathrm{t}}-1}{{\mathrm{e}}^{-\mathrm{t}}-1}}$ is the generating element of the Frank Copula function. In practical applications, we will employ the marginal distribution functions of the carbon emission permit price returns and financial market returns to compute the values of u and v, subsequently estimating the parameter θ.

3.3. Risk Spillovers and CoVaR

The traditional Value at Risk (VaR) represents the maximum potential loss that a financial institution or market may incur at a specified confidence level. It is defined as a quantile of the loss distribution, expressed as

$$\mathrm{P}\mathrm{r}\left({\mathrm{X}}^{\mathrm{i}}\ll {\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}}\right)=\mathrm{q}$$

(7)

where ${\mathrm{X}}^{\mathrm{i}}$ is the loss of the asset held by the financial institution during the holding date $∆\mathrm{t}$, and VaR is the Value at Risk at confidence level 1 $-$ q. As can be seen from the above equation, VaR has two important parameters: the holding date of the asset $∆\mathrm{t}$ and the confidence level of 1 $-$ q.

Two scholars, Adrian and Brunnermeier (2011) [41], advanced the Conditional Value at Risk (CoVaR) model, which builds upon VaR to more accurately measure the risk exposure of financial institutions, factoring in the risk contagion effects between them. The CoVaR model is defined as the q-quantile of the conditional probability distribution of the loss of one financial institution, given that another institution has incurred a loss equal to its VaR:

$$\mathrm{P}\mathrm{r}\left({\mathrm{X}}^{\mathrm{i}}\ll {\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}|{\mathrm{X}}^{\mathrm{j}}={\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}}\right)=\mathrm{q}$$

(8)

where ${\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}$ contains the unconditional risk value of financial institution i and the risk spillover value of financial institution j to i. In other words, ${\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}$ is the conditional VaR value, which represents the total risk value that financial institution $\mathrm{i}$ faces when financial institution j incurs the maximum possible risk loss of VaR. We define the value of spillover risk as $∆{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}$, using the following expression to more precisely quantify the intensity of the risk spillover effect on financial institution $\mathrm{i}$ when financial institution $\mathrm{j}$ experiences a risky loss:

$$∆{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}={\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}^{\left.\mathrm{i}\right|{\mathrm{X}}^{\mathrm{i}}={\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}}}-{\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}}$$

(9)

where the risk spillover from j to $\mathrm{i}$ is represented by $∆{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}$. Nevertheless, $∆{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}$ does not sufficiently capture the magnitude of the risk spillover from financial institution j to $\mathrm{i}$ due to the wide variations in the unconditional Value at Risk (VaR) of various financial institutions. However, because the unconditional Value at Risk (VaR) of different financial institutions varies greatly, $∆{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}$ does not adequately reflect the extent of the risk spillover from financial institution $\mathrm{j}$ to $\mathrm{i}$. Therefore, it is necessary to standardize $∆{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}$ to calculate the spillover ratio between CoVaR and unconditional Value at Risk VaR with the expression

$$\%{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}=\left(∆{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}/{\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}}\right)\times 100\%$$

(10)

After the standardization of $\%{\mathrm{C}\mathrm{o}\mathrm{V}\mathrm{a}\mathrm{R}}_{\mathrm{q}}^{\mathrm{i}/\mathrm{j}}$, it can more accurately reflect the degree of risk contribution to institution $\mathrm{i}$ when institution j is in an extremely unfavorable situation, which is conducive to the comparison between different institutions. Since CoVaR is essentially VaR, it is also a quantile, so in the specific calculation, the CoVaR value can be solved through the establishment of quantile regression equations to obtain the degree of risk spillover from a single financial market to other financial markets.

3.4. Data

3.4.1. Data Selection

Since 2011, China has launched carbon trading pilot programs in eight provinces and cities, including Shenzhen, Shanghai, Beijing, Guangdong, Tianjin, Hubei, Chongqing, and Fujian. Each carbon market differs in terms of participating entities, industries, and trading mechanisms. The carbon markets in Shenzhen and Guangzhou are characterized by their technological and open nature but are relatively small in scale. Beijing and Shanghai’s carbon markets focus on policy and financial services, while Chongqing and Tianjin’s markets are more industrial. Hubei’s carbon market, the only pilot in central China, is most aligned with China’s national conditions and is more experienced, with a larger market scale. The price influencing factors in the Hubei carbon market provide valuable insights for the upcoming national carbon market.

By analyzing the trading volumes and prices in these regional markets, Hubei was found to have the highest trading activity and stability, with broad participation and good liquidity. Additionally, Hubei’s industrial structure closely matches China’s national average. Hence, this study selects the Hubei carbon emissions trading price (CARBON) as the representative of China’s carbon market.

Following the work of scholars [42,43,44], the study also selects the stock market (HS300), money market (SHIBOR), bond market (BOND), fund market (FUND), futures market (MHI), foreign exchange market (CNY), commodity markets (NHMI, NHECI, NHAI), gold market (GOLD), and real estate market (ESTATE) as proxies for China’s financial markets. The selected indicators are presented in

Table 1. Variable interpretation.

Financial System	Market Name	Description of Variables	Variable Representation
Carbon market	carbon emission trading market	Daily Closing Price	CARBON
Financial market	Stock market	Hang Seng Index	HSI
	Money market	Interbank lending weighted rate	SHIBOR
	Bond market	China Bond Composite Net Price Index	BOND
	Foreign market	US Dollar to Renminbi Exchange Rate	CNY
	Gold market	Gold Spot AU9995 Index	GOLD
	Estate market	Wind Real Estate Sector Index	ESTATE

.

Observing the time series of logarithmic returns for each market, the study found that the “leptokurtic” characteristics were less pronounced before 2019. Therefore, the sample period for this study is 1 January 2019 to 31 March 2023, with 1551 samples obtained after interpolation. The data were sourced from the Wind Database.

The daily logarithmic returns for all markets are calculated as follows:

$${\mathrm{R}}_{\mathrm{i},\mathrm{t}}=\mathrm{l}\mathrm{n}{\mathrm{P}}_{\mathrm{i},\mathrm{t}}-\mathrm{l}\mathrm{n}{\mathrm{P}}_{\mathrm{i},\mathrm{t}-1}$$

(11)

where ${\mathrm{R}}_{\mathrm{i},\mathrm{t}}$ is the natural logarithmic yield of the ith market on day t, ${\mathrm{P}}_{\mathrm{i},\mathrm{t}}$ is the closing price of the ith market on day t, and ${\mathrm{P}}_{\mathrm{i},\mathrm{t}-1}$ is the closing price of the i − 1 market on day t.

3.4.2. Descriptive Statistics

Table 2. Parameter estimation results.

	Mean	Maximum	Minimum	Std.Dev.	Skewness	Kurtosis	Jarque–Bera
CARBON	0.000487	0.429333	−0.429813	0.124266	−0.067736	5.158394	300.8881
HS300	−0.000480	0.382505	−0.385159	0.072020	−0.107834	7.577585	1351.051
SHIBOR	−0.000107	0.486677	−0.484681	0.134569	0.057037	4.780697	204.8305
BOND	2.28 × 10−5	0.024860	−0.024911	0.004921	−0.112796	8.217389	1754.501
FUND	−0.000185	0.301822	−0.299748	0.061614	−0.054365	7.808137	1488.030
MHI	−0.000433	0.452464	−0.469669	0.066713	−0.092046	12.71794	6077.711
CNY	9.52 × 10−5	0.078715	−0.073766	0.021312	0.072681	5.697864	469.6077
NHMI	−1.80 × 10−5	0.615852	−0.646346	0.155157	−0.063943	5.729317	480.2821
NHECI	0.000338	0.546713	−0.507528	0.117397	0.038226	6.171408	647.4296
NHAI	0.000147	0.338711	−0.389677	0.094622	−0.029547	5.234586	321.4652
GOLD	6.93 × 10−5	0.280443	−0.291312	0.060822	−0.037623	11.67812	4845.293
ESTATE	−0.000138	0.261786	−0.297338	0.059197	−0.017572	6.731564	895.8936

provides the descriptive statistics for the return series of the carbon emission trading market and China’s financial markets. From the data, several observations can be made: (1) The skewness of each return series is non-zero, indicating that the distributions are skewed relative to a normal distribution. The logarithmic returns of the money market, foreign exchange market, and commodity market (Nanhua Energy Index) all exhibit positive skewness, meaning the distributions have longer tails to the right compared to a normal distribution. In contrast, the skewness values for the other markets are negative, suggesting left-skewed distributions with tails extending more to the left than the normal distribution. (2) The mean of daily logarithmic returns for all markets is close to zero, with differing standard deviations across markets. This variation in standard deviation implies differing levels of volatility across markets. The commodity market has the highest range of volatility, followed by the money market and the Hubei carbon emission market. On the other hand, the bond market shows the smallest volatility, suggesting that it is relatively more stable. (3) The kurtosis values for the carbon emission trading market and all financial markets are greater than 3, indicating that the distributions exhibit “leptokurtic” characteristics, meaning they have sharp peaks and fat tails compared to a normal distribution. (4) The Jarque–Bera (J-B) test results show that none of the return series follow a normal distribution, further supporting the evidence of skewness and excess kurtosis in these markets.

4. Empirical Results

This study first applies financial time series modeling to capture the volatility characteristics of the logarithmic returns for both the carbon emission trading market and China’s financial markets. After building the GARCH model to analyze the time-varying volatility, the optimal Copula function is selected based on the Akaike Information Criterion (AIC) to link the distributions of the return series. Finally, the Monte Carlo simulation is used to calculate the Conditional Value at Risk (CoVaR) for each individual risk factor.

Figure 1 displays the time series of logarithmic returns for the carbon emission trading market and China’s financial markets. From the figure, it can be observed that the returns fluctuate around zero, demonstrating clear signs of volatility clustering and leptokurtic behavior. These characteristics indicate that the returns exhibit periods of high volatility followed by low volatility, consistent with the presence of “fat tails” and significant tail dependence—key aspects that the GARCH and Copula models are well-suited to capture.

This analysis underscores the necessity of using models capable of dealing with such nonlinear and dynamic market behaviors to accurately estimate the risk spillover effects between the carbon market and other financial markets.

4.1. Sequence Testing

An analysis of the descriptive statistics and time series plots of the logarithmic returns for the carbon emission market and China’s financial markets reveals leptokurtic behavior and volatility clustering, indicating the presence of fat tails. To ensure the appropriateness of applying a GARCH model, the stationarity of the return series must first be confirmed.

Before constructing the model, the Augmented Dickey–Fuller (ADF) test was performed to check for unit roots. As shown in

Table 3. Empirical test of return series.

Test Sequence	1% Level	ADF Test Statistic	Prob. *	Test Results	F-Statistic
CARBON	−3.434420	−11.92348	0.0000	stationary	60.90510
HS300	−3.434420	−12.03275	0.0000	stationary	17.10609
SHIBOR	−3.434417	−15.45781	0.0000	stationary	33.12426
BOND	−3.434423	−9.786999	0.0000	stationary	33.15701
FUND	−3.434420	−13.52600	0.0000	stationary	18.29496
MHI	−3.434417	−11.12796	0.0000	stationary	120.4335
CNY	−3.434420	−11.40463	0.0000	stationary	39.27381
NHMI	−3.434417	−16.06213	0.0000	stationary	56.43636
NHECI	−3.434420	−13.35186	0.0000	stationary	6.709912
NHAI	−3.434417	−16.04715	0.0000	stationary	17.29203
GOLD	−3.434423	−11.46324	0.0000	stationary	78.49289
ESTATE	−3.434401	−13.22018	0.0000	stationary	22.07776

Notes: The asterisk (*) indicates that the series are significant at the 0.1% significance level.

, the p-values for all markets are 0, indicating that the logarithmic return series of both the carbon and financial markets are stationary.

Furthermore, to test for ARCH effects, the Lagrange Multiplier (LM) test was conducted on the return series. The results show that the test statistics, at a lag order of 1, are smaller than the critical values, leading to the rejection of the null hypothesis. This confirms the presence of ARCH effects and conditional heteroskedasticity, thus justifying the use of the GARCH model for these series.

In summary, the results from both the ADF test and the ARCH effect test demonstrate that it is reasonable to employ the GARCH model to capture the volatility dynamics of the carbon market and its spillover effects on China’s financial markets.

4.2. Correlation Heatmap Analysis

To further explore the relationship between carbon market price volatility and financial markets, this study employs the Pearson correlation coefficient method to generate a heatmap of the logarithmic returns for the carbon emission trading market and China’s financial markets. The heatmap visually represents the strength and direction of the correlations between different variables using colors and numerical values.

The heatmap reveals positive, negative, and neutral correlations across various financial markets, making it easy to interpret the size and direction of these relationships. The color gradient allows for an intuitive understanding of which markets are more strongly correlated. For example, a higher correlation between the carbon market and a particular financial market would be represented by a deeper color, indicating stronger interdependence. Conversely, lighter colors would represent weaker or negative correlations.

This approach not only enriches the study of interaction mechanisms between the carbon emission trading market and financial markets but also enhances the empirical foundation and credibility of the research findings. Additionally, it facilitates the cross-disciplinary integration of environmental economics and finance, offering new perspectives for academic research in these areas and promoting opportunities for interdisciplinary collaboration. The heatmap thus serves as a valuable tool for visualizing complex datasets, providing clearer insights into the dynamics between carbon and financial markets.

As seen in Figure 2, the correlation coefficients between the carbon emission trading market and China’s financial markets are all less than 0.8, indicating that there is no significant multicollinearity between these markets. Therefore, there is no need for corrective measures to eliminate multicollinearity.

From the color variations in the heatmap, it is clear that the carbon market has the highest positive correlation with the commodity market, with correlation coefficients of 0.6, 0.8, and 0.73 for different commodity indices. This suggests that fluctuations in the carbon market are closely linked to movements in commodity prices, likely due to shared market factors such as energy consumption, resource demand, and global trading conditions.

On the other hand, the carbon market shows a moderate negative correlation with the real estate market, with a correlation coefficient of −0.61. The absolute value of this coefficient is less than 1, which indicates that the relationship between the carbon and real estate markets is neither entirely negatively correlated nor strictly linear. Other factors may be influencing this association, such as potential uncertainty in the real estate market caused by fluctuations in the carbon market, which could affect investment and development activities.

These findings suggest complex interdependencies between the carbon market and various sectors, highlighting the need for a nuanced understanding of how carbon pricing impacts different areas of the economy.

4.3. Marginal Distribution

Based on statistical tests, including but not limited to normality tests, ARCH effect tests, and model goodness-of-fit tests (the specific testing processes are omitted here), it was found that the GARCH(1,1) model adequately describes the “leptokurtic” nature of the return series. Therefore, this study employs the GARCH(1,1)-t model for fitting. As shown in

Table 4. Marginal ARMA-GARCH model parameter estimates.

	Conditional Mean Equation Parameters		Conditional Variance Equation Parameters
	C	y	$\mathbf{\omega }$	$\mathbf{\alpha }$	$\mathbf{\beta }$
CARBON	0.004771	−0.015946	0.007061	−0.070320	0.591173
HS300	−4.6 × 10−5	−0.025842	1.55 × 10−5	0.060050	0.937806
SHIBOR	−0.000252	−0.004179	6.95 × 10−5	0.057050	0.939930
BOND	3.48 × 10−6	−0.284505	1.46 × 10−5	0.150000	0.600000
FUND	0.000202	−0.010934	8.14 × 10−6	0.054194	0.942202
MHI	−0.000213	0.550395	4.38 × 10−5	0.161111	0.837249
CNY	−6.65 × 10−5	0.849324	2.39 × 10−5	0.330049	0.610042
NHMI	−0.000261	0.893061	0.001856	0.458753	0.409866
NHECI	0.000152	−0.031103	0.008980	0.150000	0.600000
NHAI	0.000205	0.005917	0.005784	0.150000	0.600000
GOLD	0.000191	0.736031	2.65 × 10−5	0.148255	0.847052
ESTATE	−0.000412	0.836025	9.29 × 10−5	0.213824	0.743706

, the model’s parameters include the ARCH coefficient and GARCH coefficient. The results indicate that the fitting process is stable, with the GARCH coefficients for the stock market, money market, and fund market all being close to 1. This suggests that earlier return volatility has a significant impact on future volatility, indicating the presence of a risk premium effect—the greater the volatility, the higher the risk, and thus the higher the expected returns.

After fitting the model, standardized residuals were obtained and transformed using a probability integral transform to generate a new sequence. This new sequence was then tested using the Kolmogorov–Smirnov (K-S) test, and the results showed that the residuals follow a normal distribution, confirming that the data meet the requirements for Copula function modeling.

4.4. Copula Function Estimation Results

Given the asymmetric distribution of the logarithmic returns in the carbon emission trading market and China’s financial markets, three different Copula functions—Gumbel Copula, Clayton Copula, and Frank Copula—were selected for parameter estimation. The goal is to capture the dependence structures between the markets under study. The estimated parameters for each Copula function are presented in

Table 5. Parameter estimates for Copulas and model selection statistics.

	Gumbel Copula	Clayton Copula	Frank Copula
CARBON-HS300	1.0648 (−7.7920 *)	1.4509 × 10−6 (0.0013)	−0.4405 (−0.3979)
CARBON-SHIBOR	1 (0.0013)	1.4509 × 10−6 (0.0013)	−1.3600 (−1.1119 *)
CARBON-BOND	1 (0.0013)	1.4509 × 10−6 (0013)	−0.3636 (−0.2978 *)
CARBON-FUND	1.3135 (−10.6680 *)	0.4930 (−3.6176)	1.5726 (−1.3653)
CARBON-CNY	1.0966 (−8.5401 *)	0.1189 (−2.6650)	0.2437 (−0.2368)
CARBON-MHI	1 (0.0013)	1.4509 × 10−6 (0.0013)	−1.5617 (−1.2486 *)
CARBON-NHMI	1.1713 (−9.5939 *)	0.2397 (−2.3501)	0.7953 (−0.7395)
CARBON-NHECI	1.7667 (−7.2843 *)	1.3225 (−6.4771)	3.8499 (−2.6345)
CARBON-NHAI	1.7110 (−7.2885 *)	1.2256 (−6.9168)	3.6392 (−2.5936)
CARBON-GOLD	1.1690 (−9.5694 *)	0.2588 (−3.3501)	0.7648 (−0.7130)
CARBON-ESTATE	1 (0.0013)	1.4506 × 10−6 (0.0013)	−0.8606 (−0.7510 *)

Notes: The first number in the table is the estimated parameter size and the AIC value is in parentheses. * denotes the Copula function with the smallest AIC value, i.e., the optimal Copula.

.

Each of these Copula functions has distinct characteristics: the Gumbel Copula is suitable for modeling stronger dependence in the upper tail, which is useful when extreme positive events in one market are likely to coincide with extreme positive events in another; the Clayton Copula is designed to model stronger lower tail dependence, capturing scenarios where extreme negative events in one market are likely to be associated with extreme negative events in another; and the Frank Copula is symmetric and suitable for modeling more balanced dependence across both the upper and lower tails, making it useful for markets that exhibit symmetrical tail dependence.

The estimation results show the specific dependence structure parameters for each market pair, which will be used to assess the risk spillover effects in the next stage of analysis. These parameters help to better understand how extreme events in one market may influence or correspond to extreme events in other markets, thus improving the risk management insights.

Using the Akaike Information Criterion (AIC) as a standard for model selection, the model with the lowest AIC value is considered to provide the best fit. Based on the results shown in Table 5, it can be observed that the Frank Copula is the optimal Copula model for the CARBON-SHIBOR, CARBON-BOND, CARBON-MHI, and CARBON-ESTATE pairs, indicating that these market pairs exhibit symmetric dependence in both tails. For the remaining market pairs, the Gumbel Copula was selected as the best model, which suggests stronger dependence in the upper tail of the distributions.

Following this selection, the distribution functions and density functions of the best-fit Copula models are visualized in Figure 3. These visualizations provide a clearer understanding of how dependence structures vary between the carbon market and different financial markets, emphasizing the tail dependence captured by each Copula function. The Frank Copula’s “U”-shaped distribution reflects symmetric tail behavior, while the Gumbel Copula’s density function highlights stronger upper tail dependence, consistent with extreme positive co-movements between these markets.

These insights from the Copula models can help in understanding risk transmission across markets, particularly during periods of extreme price fluctuations.

From the formulas and explanations in the third section, it is clear that the Frank Copula exhibits a U-shaped distribution with symmetric tail dependence. This was observed in the density function plots for the best-fit Frank Copula models between carbon emission price (CARBON) and the money market (SHIBOR), bond market (BOND), futures market (MHI), and real estate market (ESTATE). The U-shaped symmetry in these markets indicates balanced tail dependence, where extreme movements in the carbon market are mirrored by corresponding extremes in the financial markets.

In contrast, the density function plots of the Gumbel Copula—selected as the best fit for the other financial markets—show a stronger upper tail dependence. This means that extreme positive movements in the carbon market are more likely to coincide with extreme positive movements in these financial markets, while the lower tail is thinner, suggesting less dependence during extreme negative events. These results further validate the appropriateness of the selected Copula models.

4.5. Tail Dependence and Marginal Dependence

The three-dimensional Copula density plots highlight two key types of dependence between carbon prices and financial markets:

(1)

Tail Dependence: This occurs when there is strong correlation at the extremes of the distribution, meaning that when carbon prices experience extreme volatility, certain financial markets react more dramatically. For example, carbon price fluctuations show the strongest upper tail dependence with the Nanhua Energy Index (NHECI) and Nanhua Agricultural Index (NHAI) in the commodity market, with upper tail variations ranging from 0 to 10. The fund market also shows notable tail dependence, with upper tail variations between 0 and 5. As the carbon price moves from 0.8 to 1, the gold market (GOLD) exhibits an increase in upper tail thickness from 1 to 3. Similarly, the carbon market’s influence on the stock market (HS300) and foreign exchange market (CNY) is evident, though with relatively smaller upper tail changes, ranging from 1 to 2 and 1 to 2.5, respectively. Compared to other financial markets, the carbon emissions trading market exhibits relatively smaller fluctuations, which may be attributed to factors such as changes in energy prices, air quality and weather variations, the degree of development of financial markets, the regulatory framework, and the behavior of market participants. These factors interact and collectively influence the price volatility of carbon emissions allowances. In particular, the fluctuations in carbon allowance prices are closely linked to energy prices; a more developed financial market and optimized industrial structure can facilitate the implementation of emission reduction initiatives, potentially leading to a decrease in carbon allowance prices. Additionally, market speculation and misleading publicity may also contribute to price volatility, affecting market stability.

(2)

Marginal Dependence: This refers to stronger correlations in the central part of the distribution. The Frank Copula’s three-dimensional density plots show that carbon prices have the greatest impact on the futures market, followed by the money market and real estate market. The impact on the fund market is relatively stable, indicating that extreme carbon price fluctuations are more likely to spill over into the futures market and potentially spread to other financial markets, affecting overall market stability. The sensitivity of financial markets to extreme volatility in carbon emission permit prices differs significantly, with the futures market exhibiting the highest reactivity, followed by the currency and real estate markets, whereas the fund market appears to be the least impacted. This variability is likely attributable to the disparate risk management mechanisms, market architectures, participant behaviors, and responsiveness to macroeconomic indicators within each market segment. Moreover, the spillover effects of carbon emission permit price volatility underscore the potential for its extreme shifts to disrupt financial market stability, thereby highlighting the imperative for robust risk management strategies to ameliorate these influences.

5. Risk Spillover Effect of Carbon Prices on China’s Financial Markets

Based on the residuals obtained from the GARCH(1,1)-t model, the standardized residuals were transformed into a uniform distribution on the interval [0, 1] using a probability integral transform. These new series were then used in the Copula function to estimate the parameters and corresponding AIC values. The Monte Carlo simulation was applied to estimate the parameters, and the mean risk spillover effects at the 95% confidence level from carbon price volatility to China’s financial markets are summarized in

Table 6. Risk spillover level measurement.

	CoVaR	$∆$CoVaR	$\%∆$CoVaR
CARBON-HS300	−0.012491	2.7756 × 10−16	2.222258 × 10−15
CARBON-SHIBOR	−0.043419	−1.1102 × 10−16	2.556956 × 10−15
CARBON-BOND	0.0032939	3.3307 × 10−16	1.011172 × 10−13
CARBON-FUND	0.032745	−1.1102 × 10−16	3.390441 × 10−15
CARBON-CNY	0.0030717	3.3307 × 10−16	1.084318 × 10−13
CARBON-MHI	−0.040853	1.1657 × 10−15	2.853401 × 10−14
CARBON-NHMI	0.019111	1.1102 × 10−15	5.809219 × 10−15
CARBON-NHECI	0.092101	1.1102 × 10−15	1.205416 × 10−14
CARBON-NHAI	0.092101	1.1102 × 10−15	1.205416 × 10−14
CARBON-GOLD	0.016322	8.3267 × 10−16	5.101519 × 10−14
CARBON-ESTATE	−0.027253	1.1102 × 10−15	4.073679 × 10−14

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This analysis highlights the significant risk transmission between the carbon emission trading market and various financial markets, emphasizing the need for effective risk management strategies in both sectors.

From Table 6, it is evident that carbon emission price volatility has a spillover effect on various financial markets, although the intensity of these spillover effects differs across markets. Specifically, we note the following:

The commodity market, particularly in the energy and agricultural sectors, experiences the largest risk spillover effect, with values exceeding 0.09. The bond and foreign exchange markets show the smallest spillover effects, while other financial markets exhibit spillover values between 0.1 and 0.5. Despite the presence of spillover effects, the CoVaR and %CoVaR values are relatively small. This indicates that these markets are not highly sensitive to fluctuations in carbon prices. The small values also reflect the early stage of development in China’s carbon market. The market’s influence mechanisms are not fully mature, and as a result, its impact on financial markets remains limited.

These findings indicate that while the carbon market exerts an influence on China’s financial markets, this influence is still developing. In particular, the current volatility in the carbon market has had limited systemic impact, partly due to the relatively young state of the market and the complexity of its interaction with other financial systems. As the market matures, these spillover effects may become more pronounced, necessitating continued monitoring and development of mitigation strategies.

6. Conclusions and Policy Implications

With the ongoing integration of China’s financial markets and the increasing financialization of the carbon market, the impact of carbon price volatility on financial markets has become a key focus in systemic risk research. This study addresses the limitations of previous research, which has often focused on individual sub-markets and has primarily employed GARCH and VaR models, lacking comprehensiveness and dynamism. By dividing China’s financial markets into 11 sub-sectors, this paper first uses GARCH-t and Copula models to analyze the dynamic dependence between carbon prices and China’s financial markets. Additionally, the Monte Carlo simulation and Copula–CoVaR models are employed to measure the risk spillover effects of carbon price volatility. The following conclusions are drawn: (1) Carbon price fluctuations have spillover effects on all financial markets in China, but the intensity of these effects varies across markets. Overall, the spillover values remain relatively small. (2) This study leveraged the advantages of existing models by applying the GARCH–Copula–CoVaR approach. The results confirm that the GARCH-t model more accurately captures the “leptokurtic” nature of the series, aligning with the conclusions of Wang Chunfeng and other scholars. (3) There is a degree of dependency between the carbon market and sub-markets of China’s financial system. The carbon market has the highest positive correlation with the commodity market, with correlation values of 0.6, 0.8, and 0.73. The negative correlation with the real estate market (−0.61) indicates that factors beyond simple linear relationships may affect these two markets. Additionally, the optimal Copula functions differ across regions, highlighting the heterogeneity of China’s financial markets. (4) The relatively small spillover effects of carbon price volatility indicate that there are numerous influencing factors in China’s financial markets, with more complex internal structures.

The implications of this study are as follows:

(1)

Policymakers should actively leverage the guiding role of the government to continue establishing and perfecting functional mechanisms. From the perspective of risk spillover results, the introduction of carbon pricing increases the complexity and risk of financial markets, but its overall impact is relatively small and positively contributes to the sustainable development of financial markets. Therefore, policymakers should promote the establishment of a more comprehensive financial market risk management system, including risk assessment, early warning, and risk disposal. Carbon emission permit price fluctuations should be integrated into the financial risk management framework. Policymakers should guide market mechanism innovations to better equip them to address climate change and sustainable development.

(2)

Market managers should enhance the construction of price information transmission channels between the carbon market and China’s financial markets, establishing a connectivity mechanism among the various markets. Given the significant correlation between the carbon market and financial markets, particularly the highest positive correlation with the commodity market and the highest negative correlation with the real estate market, there should be increased support for financial markets. It is necessary to monitor in real-time the risk impacts of carbon emission permit price fluctuations on financial markets. Specific market stability measures can be formulated based on different degrees and directions of correlation, and coordination between markets should be strengthened to ensure stable market operations.

(3)

Supervisors must remain vigilant to carbon price fluctuations, avoiding herd mentality and inflexible trading strategies. They should be proactive in identifying market risks and implementing timely measures to mitigate them. The empirical results show that carbon price volatility affects all financial markets, so investors should consider the correlation between different markets and adjust their portfolios accordingly to effectively hedge against risks posed by carbon price fluctuations. For businesses, it is essential to understand the spillover effects of carbon price volatility in different markets and make informed decisions regarding their investments in various sectors, ensuring that they can effectively manage and mitigate potential risks.

Despite the methodological integration and comprehensive research presented in this paper, there are still some limitations. First, there are various models derived from GARCH, and this study adopts the skewed t-distribution based on the conclusions of previous scholars. Future research could explore optimal validation of GARCH models in related areas by selecting the most suitable GARCH model. Second, there are currently eight carbon emission trading markets in China. While this paper primarily focuses on the Chinese financial market and delves into the price fluctuations of the more mature Hubei carbon emission trading market, future studies could investigate price dynamics across different carbon emission trading markets. Third, this paper examines the dependence structure and risk spillover effects of carbon price fluctuations on the financial market from a dynamic perspective, utilizing the most applicable Copula function and CoVaR model. However, the modeling methods employed have certain constraints; therefore, future research should further expand the analytical methods used in this field.