基于TGARCH-VineCopula的电价波动分析及风险度量研究

谢 航，赖春羊，曾 宏，马光文，陈仕军,2，王建华

基于TGARCH-VineCopula的电价波动分析及风险度量研究

谢 航1，赖春羊1，曾 宏1，马光文1，陈仕军1,2，王建华3

(1.四川大学水利水电学院/水力学与山区河流开发保护重点实验室，四川 成都 610065；2.四川大学商学院，四川 成都 610065；3.国家能源大渡河公司，四川 成都 610041)

在市场化交易中，计及电价波动信息的风险度量可以帮助市场利益相关者规避风险。为此，结合TGARCH与VineCopula理论，提出一种电价波动分析及风险度量的新方法。该方法用TGARCH建立日前、实时及辅助服务交易电价边缘分布，通过VineCopula拟合各交易电价的多维相依结构。基于得到的相关系数与尾部关系分析各交易电价之间的动态波动规律，并测度电价动态波动风险。实证分析证明，该方法不仅可以捕捉负荷容量比和可再生能源渗透率作用下价格波动的变化，还可以较为准确地描述各交易电价的非线性关联结构，进而捕获日前、实时、辅助服务交易电价之间逐时动态波动特征。此外，与其他方法相比还能更有效地降低组合波动风险。

电价分析；TGARCH；VineCopula；风险度量

0 引言

电价是电力市场的支点，是电网公司、发电企业、市场监管部门在评估、决策、监督时参考的关键指标[1-4]。随着国内新一轮电力体制改革工作的推进，国内已有8个区域开始现货市场试点运行[5]，电价风险管理对参与现货交易的相关者显得尤为重要。现阶段，国内外针对电价风险管理的研究，按关键风险信息的角度可分为2类：1) 基于电价水平信息，设计风险管理机制和决策方法[6]；2) 基于电价波动信息，进行风险度量[7]、评估[8]与预警[9]，其中，风险度量是后两者的基础。对于风险度量，研究人员较常使用金融风险领域的参数法和半参数法计算风险的大小[10]，它们的重点在于选择准确的模型对电价波动拟合，这突显了价格波动分析的重要性。

已有研究表明电价波动主要呈现“均值回复”、“极值跳跃”和“杠杆效应”等规律[11-13]。文献[14-16]发现结合广义自回归条件异方差模型(Generalized Auto-Regressive Conditional Heteroskedasticity, GARCH)[17]与自回归移动平均模型(Auto-Regressive Moving Average Model, ARMA)[18]或自回归积分滑动平均模型(Auto-Regressive Integral Moving Average Model, ARIMA)[19]，可以较好地描述电价波动的均值回复及异方差性。文献[20-21]指出EGARCH与TGARCH模型还适合刻画电价波动的杠杆效应。文献[22-23]构建了考虑电价水平与负荷容量比、可再生能源渗透率等外生因素的TGARCH模型，其比EGARCH能更合理地解释电价波动的杠杆效应。但上述研究对日前或实时交易电价的波动特性研究的较多，较少关注辅助服务以及多个交易品种电价间的关联性。事实上，同国外PJM、Nord Pool等电力市场一样，国内广东、四川等试点省份的市场交易规则均指出市场主体有参与辅助服务交易的义务[24-25]。文献[26]研究了负荷与日前、实时和辅助服务交易电价之间的波动关系，但缺乏定量的分析。VineCopula理论广泛应用于多变量间非线性相关结构的研究，比如文献[7]运用VineCopula捕获了多个发电商损益间的尾部关联性。

关于电价波动风险度量方面，通常应用风险价值(Value at Risk,VaR)作为度量风险的指标[27]。文献[20]证明了Copula-VaR模型度量风险的效果较好，并且在度量组合风险上优势显著。文献[7]证明了适用于Copula-VaR与电力市场有关的动态风险度量。

综上，本研究在借鉴已有研究基础上，提出一种电力交易价格波动分析与VaR度量的新方法。结合TGARCH门限模型刻画逐时刻日前、实时与辅助服务交易电价的波动特征，并分析各交易电价波动特征；引入VineCopula理论构建日前、实时和辅助服务市场交易电价的0～23时(h)多维相依模型，进而定量分析不同交易价格波动之间的关联；计算三种置信度(即0.90、0.95、0.98)下电价与组合电价的动态波动风险曲线；最后通过实例证明本研究所提方法的可行性。

1 研究模型

1.1 动态波动分析

1.1.1边缘分布建模

1.1.2联合分布建模

1.2 波动风险度量

VaR是广泛得到应用的风险度量指标[31]，能有效反映价格波动剧烈时可能导致的最大损失，具体数学表达式为

1.3 TGARCH-VineCopula模型的构建

基于TGARCH-VineCopula的动态波动分析及风险度量模型构建流程如图1所示。

图1 TGARCH-VineCopula的建模流程

建模步骤如下。

步骤6 依据1.2节所述方法估计VaR值。

2 实证分析

2.1 实证数据统计分析

表1 主要描述性指标统计

注：上表列出的是0～23 h的各序列的平均值。

2.2 动态波动特征分析

图2 LJung-Box、ARCH-LM检验结果

图3 DMP等电价序列非线性相依关系

2.3 动态波动风险分析

比较图4与图 5可知，第2)种组合(1,2,3,45)波动VaR整体低于第1)种(2,1)组合以及RMP、RC、RP、MR波动VaR。根据现有交易规则，市场成员不能只参与日前现货交易，所以各市场成员可以在考虑自身容忍风险水平上，分析日前、实时、辅助服务交易的关系，结合单个或组合交易品种一天的电价波动风险，分散交易风险，使利益最大化。

图4 三种置信度下动态VaR的变化曲线

图5 三种置信水平下动态组合VaR的变化曲线

Fig.5 Performance of dynamic portfolio VaR curvesunder three confidence levels

图6 三个置信度下组合VaR曲线

3 结论

附表1 0～23 h DMP序列边缘分布模型系数估计

Attached Table 1 Estimation of marginal distribution model coefficients of 0～23 hrs DMP

01234567891011 偏态分布 0.310.120.100.090.080.100.080.080.100.160.060.05 0.090.780.900.900.920.830.920.920.850.260.940.95 (1.00)(1.00)(1.00)(0.99)(0.58)(1.00)(1.00)(1.00)(1.00)(1.00)(1.00)(1.00) 0.0000.000.000.000.000.000.000.000.000.000.000.00 121314151617181920212223 偏态分布 0.060.110.060.240.270.190.130.150.160.170.320.27 0.940.760.940.720.000.270.830.850.840.830.100.08 (0.99)(1.00)(1.00)(1.00)(0.56)(1.00)(1.00)(1.00)(1.00)(1.00)(1.00)(1.00) 0.000.000.000.000.000.000.000.000.000.000.000.00

附表2 0～23 h RMP序列边缘分布模型系数估计

Attached Table 2 Estimation of marginal distribution model coefficients of 0～23 hrs RMP

01234567891011 学生t分布 0.350.650.300.250.270.100.490.200.080.280.970.68 0.030.060.700.710.570.880.510.770.860.000.000.32 (1.00)(1.00)(0.70)(0.76)(0.14)(0.85)(0.62)(1.00)(0.99)(1.00)(0.48)(0.07) 0.000.000.130.000.000.000.000.000.000.000.000.00 121314151617181920212223 学生t分布 0.230.030.040.030.480.410.470.500.300.160.640.34 0.770.970.960.850.000.420.120.500.700.810.150.66 (0.74)(1.00)(1.00)(0.94)(1.00)(1.00)(0.81)(1.00)(1.00)(1.00)(1.00)(1.00) 0.000.000.000.000.000.000.000.000.000.000.000.00

附表3 0～23 h RC序列边缘分布模型系数估计

Attached Table 3 Estimation of marginal distribution model coefficients of 0～23 hrs RC

01234567891011 偏正态分布 0.060.040.050.500.490.400.190.030.020.070.080.10 0.020.850.870.500.510.600.720.870.980.870.720.90 (1.00)1.000.61(0.78)(0.78)(0.46)(1.00)1.00(1.00)(1.00)(0.86)(0.80) 0.000.000.000.050.050.690.000.000.000.000.410.33 121314151617181920212223 偏正态分布 0.090.000.050.050.030.010.000.000.200.200.140.02 0.900.590.910.900.900.990.000.960.800.800.000.16 (1.00)0.250.020.271.00(1.00)(1.00)(1.00)0.790.79(1.00)(1.00) 1.540.000.000.000.000.000.001.880.000.000.000.00

附表4 0～23 h RP序列边缘分布模型系数估计

Attached Table 4 Estimation of marginal distribution model coefficients of 0～23 hrs RP

01234567891011 学生t分布正态分布学生t分布 0.360.430.64(0.90)0.330.100.270.180.270.210.090.00 0.600.290.36(0.06)0.570.840.630.720.400.790.891.00 0.280.06(0.09)(0.37)0.410.810.25(0.25)(0.02)(0.21)0.481.00 0.000.030.000.000.000.060.000.020.400.000.000.00 121314151617181920212223 学生t分布正态分布学生t分布 0.150.250.030.040.020.070.030.910.901.000.380.40 0.810.410.940.870.890.900.870.080.100.190.500.35 (1.00)(0.49)(0.82)1.001.000.02(1.00)(0.35)(0.24)(0.15)(0.03)(0.23) 0.000.010.020.010.000.000.010.000.000.000.030.00

附表5 0～23 h MR序列边缘分布模型系数估计

Attached Table 5 Estimation of marginal distribution model coefficients of 0～23 hrs MR

01234567891011 正态分布 0.050.050.000.010.560.000.050.050.020.330.000.00 0.950.950.970.960.120.990.950.950.980.151.000.95 (0.87)1.000.19(0.90)0.730.54(0.10)1.001.00(0.35)1.00(1.00) 0.000.000.000.000.000.000.000.000.000.000.000.00 121314151617181920212223 偏正态正态分布 0.150.000.100.021.000.000.020.060.010.000.040.07 0.811.000.920.970.830.960.980.940.990.990.950.93 (1.00)(0.15)0.86(1.00)1.000.64(1.00)(0.06)1.00(1.00)(1.00)(1.00) 0.000.000.000.000.000.000.000.000.000.000.040.00

注：括号中的数值为负数

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Fluctuation analysis and risk measurement of electricity pricing using TGARCH and VineCopula

XIE Hang1, LAI Chunyang1, ZENG Hong1, MA Guangwen1, CHEN Shijun1, 2,WANG Jianhua3

(1.College of Water Resources and Hydropower/State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China; 2.Business School, Sichuan University, Chengdu 610065, China; 3.Dadu River Company, China Energy Corporation, Chengdu 610041, China)

In a market-oriented transaction, risk measurement of electricity price fluctuation contributes to conduct risk management for market stakeholders.This paper proposes a new method for analyzing electricity price fluctuation and measure risk.It combines TGARCH and Vinecopula.This method applies TGARCH to establish the margin distribution of day-ahead, real-time and ancillary service transaction electricity prices, and uses Vinecopula to fit the multi-dimensional dependent structure of each transaction electricity price.Based on the Kendall rank correlation and tail correlation calculated from the method, the dynamic fluctuation characteristic between each transaction price is analyzed, and its risk is measured.Empirical analysis shows that this method can not only capture the change of price fluctuation under the combined action of load/capacity ratio and renewable energy penetration rate, but can also accurately describe the nonlinear correlation structure of each transaction price.This can capture the dynamic fluctuation characteristics of day-ahead, real-time and ancillary service transaction price.Also, it can more effectively reduce portfolio volatility risk in comparison to other methods.This work is supported by the National Key Research and Development Program of China (No.2018YFB0905204).

analysis of electricity price; TGARCH; VineCopula; risk measurement

10.19783/j.cnki.pspc.210504

2021-04-29；

2021-07-02

谢 航(1996—)，女，硕士研究生，研究方向为水电运行管理及电力市场；E-mail: 409367753@qq.com

王建华(1973—)，男，通信作者，高级工程师，研究方向为电力市场。E-mail: 1294331990@qq.com

国家重点研发计划项目资助(2018YFB0905204)

(编辑 葛艳娜)