謝 航，賴春羊，曾 宏，馬光文，陳仕軍,2，王建華

基于TGARCH-VineCopula的電價(jià)波動(dòng)分析及風(fēng)險(xiǎn)度量研究

謝 航1，賴春羊1，曾 宏1，馬光文1，陳仕軍1,2，王建華3

(1.四川大學(xué)水利水電學(xué)院/水力學(xué)與山區(qū)河流開(kāi)發(fā)保護(hù)重點(diǎn)實(shí)驗(yàn)室，四川 成都 610065；2.四川大學(xué)商學(xué)院，四川 成都 610065；3.國(guó)家能源大渡河公司，四川 成都 610041)

在市場(chǎng)化交易中，計(jì)及電價(jià)波動(dòng)信息的風(fēng)險(xiǎn)度量可以幫助市場(chǎng)利益相關(guān)者規(guī)避風(fēng)險(xiǎn)。為此，結(jié)合TGARCH與VineCopula理論，提出一種電價(jià)波動(dòng)分析及風(fēng)險(xiǎn)度量的新方法。該方法用TGARCH建立日前、實(shí)時(shí)及輔助服務(wù)交易電價(jià)邊緣分布，通過(guò)VineCopula擬合各交易電價(jià)的多維相依結(jié)構(gòu)?；诘玫降南嚓P(guān)系數(shù)與尾部關(guān)系分析各交易電價(jià)之間的動(dòng)態(tài)波動(dòng)規(guī)律，并測(cè)度電價(jià)動(dòng)態(tài)波動(dòng)風(fēng)險(xiǎn)。實(shí)證分析證明，該方法不僅可以捕捉負(fù)荷容量比和可再生能源滲透率作用下價(jià)格波動(dòng)的變化，還可以較為準(zhǔn)確地描述各交易電價(jià)的非線性關(guān)聯(lián)結(jié)構(gòu)，進(jìn)而捕獲日前、實(shí)時(shí)、輔助服務(wù)交易電價(jià)之間逐時(shí)動(dòng)態(tài)波動(dòng)特征。此外，與其他方法相比還能更有效地降低組合波動(dòng)風(fēng)險(xiǎn)。

電價(jià)分析；TGARCH；VineCopula；風(fēng)險(xiǎn)度量

0 引言

電價(jià)是電力市場(chǎng)的支點(diǎn)，是電網(wǎng)公司、發(fā)電企業(yè)、市場(chǎng)監(jiān)管部門在評(píng)估、決策、監(jiān)督時(shí)參考的關(guān)鍵指標(biāo)[1-4]。隨著國(guó)內(nèi)新一輪電力體制改革工作的推進(jìn)，國(guó)內(nèi)已有8個(gè)區(qū)域開(kāi)始現(xiàn)貨市場(chǎng)試點(diǎn)運(yùn)行[5]，電價(jià)風(fēng)險(xiǎn)管理對(duì)參與現(xiàn)貨交易的相關(guān)者顯得尤為重要?，F(xiàn)階段，國(guó)內(nèi)外針對(duì)電價(jià)風(fēng)險(xiǎn)管理的研究，按關(guān)鍵風(fēng)險(xiǎn)信息的角度可分為2類：1) 基于電價(jià)水平信息，設(shè)計(jì)風(fēng)險(xiǎn)管理機(jī)制和決策方法[6]；2) 基于電價(jià)波動(dòng)信息，進(jìn)行風(fēng)險(xiǎn)度量[7]、評(píng)估[8]與預(yù)警[9]，其中，風(fēng)險(xiǎn)度量是后兩者的基礎(chǔ)。對(duì)于風(fēng)險(xiǎn)度量，研究人員較常使用金融風(fēng)險(xiǎn)領(lǐng)域的參數(shù)法和半?yún)?shù)法計(jì)算風(fēng)險(xiǎn)的大小[10]，它們的重點(diǎn)在于選擇準(zhǔn)確的模型對(duì)電價(jià)波動(dòng)擬合，這突顯了價(jià)格波動(dòng)分析的重要性。

已有研究表明電價(jià)波動(dòng)主要呈現(xiàn)“均值回復(fù)”、“極值跳躍”和“杠桿效應(yīng)”等規(guī)律[11-13]。文獻(xiàn)[14-16]發(fā)現(xiàn)結(jié)合廣義自回歸條件異方差模型(Generalized Auto-Regressive Conditional Heteroskedasticity, GARCH)[17]與自回歸移動(dòng)平均模型(Auto-Regressive Moving Average Model, ARMA)[18]或自回歸積分滑動(dòng)平均模型(Auto-Regressive Integral Moving Average Model, ARIMA)[19]，可以較好地描述電價(jià)波動(dòng)的均值回復(fù)及異方差性。文獻(xiàn)[20-21]指出EGARCH與TGARCH模型還適合刻畫電價(jià)波動(dòng)的杠桿效應(yīng)。文獻(xiàn)[22-23]構(gòu)建了考慮電價(jià)水平與負(fù)荷容量比、可再生能源滲透率等外生因素的TGARCH模型，其比EGARCH能更合理地解釋電價(jià)波動(dòng)的杠桿效應(yīng)。但上述研究對(duì)日前或?qū)崟r(shí)交易電價(jià)的波動(dòng)特性研究的較多，較少關(guān)注輔助服務(wù)以及多個(gè)交易品種電價(jià)間的關(guān)聯(lián)性。事實(shí)上，同國(guó)外PJM、Nord Pool等電力市場(chǎng)一樣，國(guó)內(nèi)廣東、四川等試點(diǎn)省份的市場(chǎng)交易規(guī)則均指出市場(chǎng)主體有參與輔助服務(wù)交易的義務(wù)[24-25]。文獻(xiàn)[26]研究了負(fù)荷與日前、實(shí)時(shí)和輔助服務(wù)交易電價(jià)之間的波動(dòng)關(guān)系，但缺乏定量的分析。VineCopula理論廣泛應(yīng)用于多變量間非線性相關(guān)結(jié)構(gòu)的研究，比如文獻(xiàn)[7]運(yùn)用VineCopula捕獲了多個(gè)發(fā)電商損益間的尾部關(guān)聯(lián)性。

關(guān)于電價(jià)波動(dòng)風(fēng)險(xiǎn)度量方面，通常應(yīng)用風(fēng)險(xiǎn)價(jià)值(Value at Risk,VaR)作為度量風(fēng)險(xiǎn)的指標(biāo)[27]。文獻(xiàn)[20]證明了Copula-VaR模型度量風(fēng)險(xiǎn)的效果較好，并且在度量組合風(fēng)險(xiǎn)上優(yōu)勢(shì)顯著。文獻(xiàn)[7]證明了適用于Copula-VaR與電力市場(chǎng)有關(guān)的動(dòng)態(tài)風(fēng)險(xiǎn)度量。

綜上，本研究在借鑒已有研究基礎(chǔ)上，提出一種電力交易價(jià)格波動(dòng)分析與VaR度量的新方法。結(jié)合TGARCH門限模型刻畫逐時(shí)刻日前、實(shí)時(shí)與輔助服務(wù)交易電價(jià)的波動(dòng)特征，并分析各交易電價(jià)波動(dòng)特征；引入VineCopula理論構(gòu)建日前、實(shí)時(shí)和輔助服務(wù)市場(chǎng)交易電價(jià)的0～23時(shí)(h)多維相依模型，進(jìn)而定量分析不同交易價(jià)格波動(dòng)之間的關(guān)聯(lián)；計(jì)算三種置信度(即0.90、0.95、0.98)下電價(jià)與組合電價(jià)的動(dòng)態(tài)波動(dòng)風(fēng)險(xiǎn)曲線；最后通過(guò)實(shí)例證明本研究所提方法的可行性。

1 研究模型

1.1 動(dòng)態(tài)波動(dòng)分析

1.1.1邊緣分布建模

1.1.2聯(lián)合分布建模

1.2 波動(dòng)風(fēng)險(xiǎn)度量

VaR是廣泛得到應(yīng)用的風(fēng)險(xiǎn)度量指標(biāo)[31]，能有效反映價(jià)格波動(dòng)劇烈時(shí)可能導(dǎo)致的最大損失，具體數(shù)學(xué)表達(dá)式為

1.3 TGARCH-VineCopula模型的構(gòu)建

基于TGARCH-VineCopula的動(dòng)態(tài)波動(dòng)分析及風(fēng)險(xiǎn)度量模型構(gòu)建流程如圖1所示。

圖1 TGARCH-VineCopula的建模流程

建模步驟如下。

步驟6 依據(jù)1.2節(jié)所述方法估計(jì)VaR值。

2 實(shí)證分析

2.1 實(shí)證數(shù)據(jù)統(tǒng)計(jì)分析

表1 主要描述性指標(biāo)統(tǒng)計(jì)

注：上表列出的是0～23 h的各序列的平均值。

2.2 動(dòng)態(tài)波動(dòng)特征分析

圖2 LJung-Box、ARCH-LM檢驗(yàn)結(jié)果

圖3 DMP等電價(jià)序列非線性相依關(guān)系

2.3 動(dòng)態(tài)波動(dòng)風(fēng)險(xiǎn)分析

比較圖4與圖 5可知，第2)種組合(1,2,3,45)波動(dòng)VaR整體低于第1)種(2,1)組合以及RMP、RC、RP、MR波動(dòng)VaR。根據(jù)現(xiàn)有交易規(guī)則，市場(chǎng)成員不能只參與日前現(xiàn)貨交易，所以各市場(chǎng)成員可以在考慮自身容忍風(fēng)險(xiǎn)水平上，分析日前、實(shí)時(shí)、輔助服務(wù)交易的關(guān)系，結(jié)合單個(gè)或組合交易品種一天的電價(jià)波動(dòng)風(fēng)險(xiǎn)，分散交易風(fēng)險(xiǎn)，使利益最大化。

圖4 三種置信度下動(dòng)態(tài)VaR的變化曲線

圖5 三種置信水平下動(dòng)態(tài)組合VaR的變化曲線

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

圖6 三個(gè)置信度下組合VaR曲線

3 結(jié)論

附表1 0～23 h DMP序列邊緣分布模型系數(shù)估計(jì)

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

01234567891011 偏態(tài)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 偏態(tài)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序列邊緣分布模型系數(shù)估計(jì)

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

01234567891011 學(xué)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 學(xué)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序列邊緣分布模型系數(shù)估計(jì)

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

01234567891011 偏正態(tài)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 偏正態(tài)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序列邊緣分布模型系數(shù)估計(jì)

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

01234567891011 學(xué)生t分布正態(tài)分布學(xué)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 學(xué)生t分布正態(tài)分布學(xué)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序列邊緣分布模型系數(shù)估計(jì)

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

01234567891011 正態(tài)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 偏正態(tài)正態(tài)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：括號(hào)中的數(shù)值為負(fù)數(shù)

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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

謝 航(1996—)，女，碩士研究生，研究方向?yàn)樗娺\(yùn)行管理及電力市場(chǎng)；E-mail: 409367753@qq.com

王建華(1973—)，男，通信作者，高級(jí)工程師，研究方向?yàn)殡娏κ袌?chǎng)。E-mail: 1294331990@qq.com

國(guó)家重點(diǎn)研發(fā)計(jì)劃項(xiàng)目資助(2018YFB0905204)

(編輯 葛艷娜)