# Modeling the Risk of Extreme Value Dependence in Chinese Regional Carbon Emission Markets

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## Abstract

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## 1. Introduction

_{2}emissions. The success of China’s national plan of greenhouse gas emission will determine whether the climate change issue can be solved at the global level. Therefore, China assumes the responsibility of reducing greenhouse gas emissions and plays a vital role in coping with global climate change, reducing carbon emission, and achieving sustainable economic development. Studying the risks of China’s regional carbon emission market and their interdependence will help to comprehensively analyze the development of the global carbon emission market. Identifying and measuring the risks of the carbon market is essential to successfully developing a healthy market. We investigate the risk-dependent relationship between China’s regional carbon emissions trading markets, which is of great significance to integrating China’s carbon emissions market with global carbon emissions markets. Many countries are paying more and more attention to carbon emission markets and their risk monitoring systems. China’s carbon emission markets still face challenges and risks, and many risk characteristics reflect the universality of the international carbon market. Through developing and managing its carbon trading markets, the Chinese government has accumulated valuable experiences that can be applied to other countries. A global and healthy development of the carbon emission market will help to mitigate global climate change, develop a low-carbon economy, and achieve sustainable development.

## 2. Literature Review

**POT**). According to the analysis of McNeil et al. [10], extreme value distribution is more powerful than most parametric distributions. It has been considered a better way to measure extreme value risk in financial markets, and a number of previous studies have used it to analyze financial markets, including Longin and Solnik [11], Longin and Pagliardi [12], Liu et al. [13], and Sobreira and Louro [14]. For empirical analysis, previous studies generally adopt a Value-at-Risk (VaR) or conditional Value-at-Risk (CoVaR) to better estimate extreme value risk in financial markets [15,16,17]. Since market prices are affected by many factors, the introduction of these factors could result in a more comprehensive exploration of the degree of extreme value risk in the markets, caused by these risk factors. Hammoudeh et al. [18] analyze the short-term dynamics of CO

_{2}emission price changes with oil, coal, natural gas, and electricity prices, using a Bayesian structure VAR (BSVAR).

## 3. Models and Methodology

#### 3.1. AR-GARCH Model

#### 3.2. Extreme Value Theory (EVT)

#### 3.3. Copula Function

## 4. Data and Empirical Analysis

#### 4.1. Data

#### 4.2. Empirical Analysis

#### 4.2.1. Autocorrelation Analysis

#### 4.2.2. Evaluation of EVT Model

#### 4.2.3. VaR Calculation

## 5. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The daily index of the six regional Carbon emission trading markets, and the figure plots the daily index of the six regional Carbon emission trading markets for the whole sample period of April 1, 2014 to April 12, 2018. It consists of 1134 daily observations after deleting the missing data and the data without a corresponding trading day. The source is from TANKQIAM (http://k.tanjiaoyi.com/).

**Figure 2.**Normal Q-Q plot of the daily logarithm returns for each regional carbon emission trading market. HB, BJ, SH, GZ, TJ, and SZ respectively represent the carbon emission markets of Hubei, Beijing, Shanghai, Guangzhou, Tianjin, and Shenzhen. It is shown that the curves exist as tails, which means the data have more extreme values than would be expected. This indicates that it is misaligned with normal distribution.

**Figure 3.**Daily logarithmic returns of the six regional carbon emission trading markets from the period of April 1, 2014 to April 12, 2018. HB, BJ, SH, GZ, TJ, and SZ respectively represent the carbon emission markets of Hubei, Beijing, Shanghai, Guangzhou, Tianjin, and Shenzhen. The figure provides the evidence of volatility clustering in the returns of the six markets.

**Figure 4.**Autocorrelation functions (ACF) of returns in the six markets. HB, BJ, SH, GZ, TJ, and SZ respectively represent the carbon emission markets of Hubei, Beijing, Shanghai, Guangzhou, Tianjin, and Shenzhen. The figure reveals some mild serial correlations in the markets.

**Figure 5.**Autocorrelation functions (ACF) of the squared returns in the six regional markets. HB, BJ, SH, GZ, TJ, and SZ respectively represent the carbon emission markets of Hubei, Beijing, Shanghai, Guangzhou, Tianjin, and Shenzhen. The figure reveals the degree of persistence in variance and implies that GARCH models could be used in fitting the characteristics of the returns.

**Figure 6.**Autocorrelation functions (ACF) of the standardized residuals in the six regional markets. HB, BJ, SH, GZ, TJ, and SZ respectively represent the carbon emission markets of Hubei, Beijing, Shanghai, Guangzhou, Tianjin, and Shenzhen. The figure reveals that the standardized residuals are now approximately i.i.d.

**Figure 7.**Cumulative Distribution Function (CDF) of the exceedance of the residuals, along with the CDF from GPD for the six regional markets. HB, BJ, SH, GZ, TJ, and SZ respectively represent the carbon emission markets of Hubei, Beijing, Shanghai, Guangzhou, Tianjin, and Shenzhen. These Pareto tails show the estimates of the parametric generalized Pareto lower tail, the non-parametric kernel-smoothed interior, and the parametric generalized Pareto upper tail, to build a composite semi-parametric CDF for the residuals. The lower and upper tail regions are respectively displayed in red and blue, while the kernel-smoothed interior is black.

**Figure 8.**Cumulative Distribution Function (CDF) of the exceedance of the residuals for the upper tail, along with the CDF from GPD for the six regional markets. HB, BJ, SH, GZ, TJ and SZ respectively represent the carbon emission markets of Hubei, Beijing, Shanghai, Guangzhou, Tianjin and Shenzhen. The fitted generalized Pareto CDF and empirical CDF are respectively displayed in blue and red. 10% of the standardized residuals are used, and the fitted distribution is closely following the most exceedance data.

HB | BJ | SH | GZ | TJ | SZ | |
---|---|---|---|---|---|---|

Mean | −0.0004 | 0 | 0 | −0.0012 | −0.0012 | −0.0005 |

Std. | 0.043 | 0.0581 | 0.063 | 0.0515 | 0.0646 | 0.0634 |

Kurtosis | 16.8556 | 25.3499 | 55.4872 | 7.6041 | 131.0534 | 7.2871 |

Skewness | −0.3211 | −0.6705 | 2.1326 | −0.1766 | 0.3916 | 0.3409 |

Jarque-Box | 9082.4 | 23666 | 130910 | 1006.6 | 77414 | 889.5997 |

Freedom | Maximum Simulated Loss | Maximum Simulated Revenue | VaR | ||
---|---|---|---|---|---|

90% | 95% | 99% | |||

23.1829 | 0.4689% | 0.2437% | −0.2141% | −0.2486% | −0.3116% |

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**MDPI and ACS Style**

Qiu, H.; Hu, G.; Yang, Y.; Zhang, J.; Zhang, T.
Modeling the Risk of Extreme Value Dependence in Chinese Regional Carbon Emission Markets. *Sustainability* **2020**, *12*, 7911.
https://doi.org/10.3390/su12197911

**AMA Style**

Qiu H, Hu G, Yang Y, Zhang J, Zhang T.
Modeling the Risk of Extreme Value Dependence in Chinese Regional Carbon Emission Markets. *Sustainability*. 2020; 12(19):7911.
https://doi.org/10.3390/su12197911

**Chicago/Turabian Style**

Qiu, Hong, Genhua Hu, Yuhong Yang, Jeffrey Zhang, and Ting Zhang.
2020. "Modeling the Risk of Extreme Value Dependence in Chinese Regional Carbon Emission Markets" *Sustainability* 12, no. 19: 7911.
https://doi.org/10.3390/su12197911