# An Empirical Analysis of Oil and Stock Markets’ Volatility Based on the DGC-MSV-t Model

Authors: Jing Zhang; Ya-Ming Zhuang; Jia-Bao Liu
Journal: Journal of Mathematics
 (2021)

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## Abstract

We investigate the spillover effect between crude oil future prices, crude oil spot prices, and stock index by using the multivariate stochastic volatility model. These tests between each market show the significant Granger causes of spillover effect. More and more evidences show that the crude oil price has been affected by other financial markets. The oil future played an important role in the energy market. WTI and Brent oil future have more spillover effect than INE oil future. The result shows that S&P stock market is more sensitive to the oil price than Shanghai stock market. The cross-market spillover effect we found can give some advices for the investor of oil and stock market. DIC test shows that DGC-MSV-t is considered effective and more accurate.


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## Body

## 1. Introduction

Crude oil is the blood of modern industry and the most financialized energy product. According to the report of CNPC, China’s oil dependence on foreign sources reached 70.8%, with an increase of 1.2 percentage per year. It is expected that China’s oil demand will continue to rise in the future, and its dependence on foreign sources will remain high for a long time. In addition, the report also believes that the United States has achieved energy independence through the development of domestic shale gas oilfields, and its control and influence on the global oil market are increasing. OPEC’s oil market share and influence are constantly being squeezed and keep going down. There are many unexpected factors in the crude oil price including geopolitical factors [1, 2]. WTI and Brent Crude Oil Futures are the most important pricing benchmarks for the US and European oil markets. In 2018, Shanghai International Energy Exchange (INE) established the first Chinese crude oil future trading product. After two years, the INE has surpassed the Oman and became the world’s third largest oil future product. Crude oil prices are highly related to the national economy [3, 4]. A lot of research studies show that spillover effect and co-movement between stock and oil price exist in both developed market and emerging market [5, 6]. Chen [7] has given sufficient evidence to prove US market has one-way spillover effect to China market due to the closed economic and trading relations. The commodity future market are highly corrlated [8], spillover effect still exists even in the Bitcoin market [9].The three oil crises in history have proved that the oil trading market is extremely vulnerable to emergencies, such as wars, terrorist attacks, and diseases. Clean energy also brings more spillover to the crude oil price [10]. Luo and Qin [11] have proved the oil price has a significant spillover to the Chinese stock index. In addition, Boubaker and Raza [12] have found that all BRICS stock markets have spillover or subspillover from oil price. The oil-importing and oil-exporting countries are both affected by the spillover of cross market [13–15]. A lot of work has been carried out using the OVX index to find the volatility spillover of different markets [16, 17]. Risk diversification and hedging need to clarify the relationship between markets [18]. Especially in 2020, the spot oil price and oil future are crashing in the COVID-19 pandemic [19]. The stochastic volatility model has added uncertain random disturbance into the time series. The Monte Carlo method is used to estimate the random factors [20], and the degree of random disturbance is estimated on the basis of fitting historical time series [21]. The volatility models of time series mainly include GARCH [22] and SV models [23]. MSV model is effective and performs better [24]. The time-series problem can be solved by the SV model and the MCMC method [25, 26]. Various SV models have been built to solve different problems. Ghosh et al. [27] add the nonlinear method to solve nonlinear SV problem, and Nugroho and Morimoto [28] add mean equation to solve mean-SV problem. Chib et al. [29] have improved the SV model with leverage. Omori et al. [30] and Zhongxian et al. [31] have changed the N-distribution to T-distribution, which is suitable for some problems. Jacobs and Li [32] have improved the simulation method of two-factor simulation. Based on the multivariate stochastic volatility model, this paper introduces dynamic correlation coefficients, t-distribution, and Granger causality to construct models. Using the Monte Carlo method, we try to find the volatility spillover effect among INE crude oil futures’ price and Shengli oilfield spot price of China, WTI crude oil futures and spot price of USA, BRENT crude oil futures and spot price of UK, the Shanghai Stock Index, and the S&P Index.The article consists of four sections. Section2 introduces the DGC-MSV-t model, MCMC method, and Gibbs sampling. Section 3 is empirical analysis and result of the data of stock indexes, oil spot price, and oil future price. Section 4 is the conclusion of this paper.


## 2. Multivariate Stochastic Volatility Model

### 2.1. Stochastic Volatility Model

(1)yt=expqt2ϵt,ϵt∼iidN0,Σϵ,t,qt+1=μ+ψ1qt−μ+ξt,ξt∼iidN0,σ2,where yt represents the historical logarithmic return of crude oil and stock prices. Equation (1) shows the basic model with the known yt and the unknown ψt which are unobservable variables. We combined the Ganger-MSV model and the dynamic-MSV model as Yu and Meyer [33] and replace N-distribution with T-distribution:(2)yt=expqt2ϵt,ϵt∼iidT0,Σϵ,t,o,Σϵ,t=1ρtρt1,qt+1=μ+ψpt−μ+ξt,ξt∼iidN0,diagσξa2,σξc2,rt+1=v0+vacrt−v0+σρot,ot∼iidN0,1,ρt=exprt−1exprt+1.Equation (2) has multivariate time series. Taking the WTI future (AF) and Brent future (BF) for examples, yaf represents the price volatility of WTI future and yaf represents the price volatility of Brent future ψ=ψafafψbfafψafbfψbfbf. ψafbf represents the cross-market spillover from WTI future to the Brent future. ψbfaf is the opposite. ψafaf and ψbfbf represent the autocorrelation of WTI future and Brent future. ρt represents the dynamic correlation [33]. o reflects the degree of T-distribution. qt+1, μ and ψ, and μ+ψqt−1−μ,diagσξa2,σξc2 distribution are as follows:(3)θtμ,ψ,ptN˜μ+ψqt−μ,diagσξa2,σξc2,t=1,2,…,n,ft;o=Γo+1/2Γo/21oπ1+to2−o+1/2,fptqt=exp−qt2Γo+1/2Γo/21oπ1+qt2exp−ϵto−o+1/2.Therefore,(4)Lμ,ψ,o,ϵ0:n,diagσξa2,σξc2=∏t=1nfptϵt=∏t=1n1oπΓo+1/2Γo/2exp−qt2⋅1+1opt2exp−ϵt−o+1/2=1oπn/2Γo+1/2Γo/2nexp−12∑t=1nϵt⋅∏t=1n1+1oexp−ψt−o+1/2.


### 2.2. MCMC Method and Gibbs Sampling

We use the Markov chain as follows:(5)PX0=x0,X1=x1,…,Xt=xt=PX0=x0∏t−1tPXi=xiXi−1=xi−1.Therefore, the one-step transition probability is as(6)pxt−1,xt=PXt=xtXt−1=xt−1.How to determine this conditional probability is a key issue. With further research, some powerful tool has been used to solve the N-P problem. Gibbs sampling setX=X1,X2 to follow the M-N distribution:(7)x1tx2tN˜ρ2t−1x20ρ2tx20.1−ρ4t−21−ρ4t−11−ρ4t−11−ρ4t.


## 2.1. Stochastic Volatility Model

(1)yt=expqt2ϵt,ϵt∼iidN0,Σϵ,t,qt+1=μ+ψ1qt−μ+ξt,ξt∼iidN0,σ2,where yt represents the historical logarithmic return of crude oil and stock prices. Equation (1) shows the basic model with the known yt and the unknown ψt which are unobservable variables. We combined the Ganger-MSV model and the dynamic-MSV model as Yu and Meyer [33] and replace N-distribution with T-distribution:(2)yt=expqt2ϵt,ϵt∼iidT0,Σϵ,t,o,Σϵ,t=1ρtρt1,qt+1=μ+ψpt−μ+ξt,ξt∼iidN0,diagσξa2,σξc2,rt+1=v0+vacrt−v0+σρot,ot∼iidN0,1,ρt=exprt−1exprt+1.Equation (2) has multivariate time series. Taking the WTI future (AF) and Brent future (BF) for examples, yaf represents the price volatility of WTI future and yaf represents the price volatility of Brent future ψ=ψafafψbfafψafbfψbfbf. ψafbf represents the cross-market spillover from WTI future to the Brent future. ψbfaf is the opposite. ψafaf and ψbfbf represent the autocorrelation of WTI future and Brent future. ρt represents the dynamic correlation [33]. o reflects the degree of T-distribution. qt+1, μ and ψ, and μ+ψqt−1−μ,diagσξa2,σξc2 distribution are as follows:(3)θtμ,ψ,ptN˜μ+ψqt−μ,diagσξa2,σξc2,t=1,2,…,n,ft;o=Γo+1/2Γo/21oπ1+to2−o+1/2,fptqt=exp−qt2Γo+1/2Γo/21oπ1+qt2exp−ϵto−o+1/2.Therefore,(4)Lμ,ψ,o,ϵ0:n,diagσξa2,σξc2=∏t=1nfptϵt=∏t=1n1oπΓo+1/2Γo/2exp−qt2⋅1+1opt2exp−ϵt−o+1/2=1oπn/2Γo+1/2Γo/2nexp−12∑t=1nϵt⋅∏t=1n1+1oexp−ψt−o+1/2.


## 2.2. MCMC Method and Gibbs Sampling

We use the Markov chain as follows:(5)PX0=x0,X1=x1,…,Xt=xt=PX0=x0∏t−1tPXi=xiXi−1=xi−1.Therefore, the one-step transition probability is as(6)pxt−1,xt=PXt=xtXt−1=xt−1.How to determine this conditional probability is a key issue. With further research, some powerful tool has been used to solve the N-P problem. Gibbs sampling setX=X1,X2 to follow the M-N distribution:(7)x1tx2tN˜ρ2t−1x20ρ2tx20.1−ρ4t−21−ρ4t−11−ρ4t−11−ρ4t.


## 3. Empirical Analysis

### 3.1. Data and Preprocessing

In this section, the data include INE crude oil futures (CF) and Shengli oilfield spot price (CS) of China, WTI crude oil futures (AF) and WTI crude oil spot price (AS) of USA, BRENT crude oil future (BF) and BRENT crude oil spot price (BS) of UK, the Shanghai Stock Index (SH), and the S&P Index (SP). We selected the day price from March 27, 2018, to December 31, 2019. After excluding the holidays, 8 sets of data are obtained for daily trading closing prices, each of which includes 405 common trading days. Considering the exchange rate, we obtained the logarithmic rate of return, which is abbreviated as CF, CS, AF, AS, BF, BS, SH, and SP. The data come from EIA (United States Energy Information Administration) and public database of stock market. China and USA both are the important oil importers in the world. Shengli oilfield is the largest oilfield in China and represents the spot price of China crude oil. WTI and Brent are the most important representative oil future in the world. The descriptive statistics is shown as Table1. J-B value shows that some data are different from the normal distribution.Table 1
Descriptive statistics.
CFCSAFASBFBSSHSPMean0.007066−0.016718−0.0094440.0374780.053494−0.003176−0.013046−0.016233Median0.14190.19485−0.0161660.1887390.0931340.0694780.2612940.1252Maximum7.642113.25785.4492625.6628183.37593811.8733511.7323713.50267Minimum−6.8208−8.233565−5.745464−7.801777−3.341992−6.449077−6.95906−8.724438Std. dev.1.7741792.1271981.2496912.0972120.8741982.1228891.9139112.247643Skewness−0.2004960.105674−0.267382−0.398778−0.5870870.228817−0.0969540.127722Kurtosis4.1438468.0204515.9157423.5840465.5502725.6229797.5260027.496187Jarque–Bera24.30266417.6704145.360316.16461130.3908117.2713339.4729335.4807


### 3.2. Parameter Estimation

Taking America WTI crude oil future (AF) and China INE crude oil future (CF) as example, we abandon the first 10,000 iterations. Then, we simulate the last 80,000 iterations to get the result as Table2.Table 2
The simulation results of posterior parameters of WTI and INE future.
NodeMeanSdMC error2.50%5.00%10.00%Median97.50%StartSampleμcf0.80060.18310.0079310.42130.490 20.56770.80811.1481000080002μaf0.9520.26460.011580.35490.466 50.59050.98261.4171000080002o12.634.0270.13067.017.5878.31311.8422.681000080002ψcfcf0.7440.14960.0067660.41460.474 10.53230.76480.96791000080002ψcfaf0.17510.13470.006321−0.0089070.0034720.020680.14910.46271000080002ψafaf0.78390.14580.0066010.42640.49010.57430.81510.97981000080002ψafcf0.2930.27820.01318−0.04609−0.02070.010950.22671.0171000080002σξcf0.1190.037280.0016690.065480.070370.077590.11220.20961000080002σξaf0.17410.078310.0037130.067180.074680.086970.15850.3631000080002In Table2, ψcfaf represents the volatility spillover from WTI future to INE future. As proposed by [33], if ψ is greater than 0 means significant spillover effect exists. The 2.5% quantile of ψcfaf is less than 0, but 5% quantile is greater than 0, which means the spillover from WTI to INE is significant in 95% confidence interval. The 5% quantile of ψafcf is less than 0 and the 5% quantile of ψafcf is greater than 0. Within 90% confidence interval which is greater than 0, we classify the spillover of ψafcf as subsignificant. The volatility level parameter μcf of INE future is 0.800 6. And μaf of WTI future is 0.952. The value of μcf is lower than μaf, which means the risk of the INE future is lower than the WTI future. The volatility persistence parameter ψcfcf of INE future is 0.744 and ψafaf of WTI future is 0.783 9. The INE future volatility persistence is lower than WTI future.Figure1 shows the Gelman test results of μcf and μaf. We can see the two Markov links are lower than 1.1, and it can be considered as convergent. μcf and μaf are convergent. Other parameters’ results are also convergent. In Table 3, the DIC test result shows that the DGC-MSV-t model is better than other models. Dbar reflects the difference between the model and the actual data, the smaller the better. pD reflects the complexity of the model; the larger the value, the more complicated. Dbar and pD jointly determine the DIC test value. The total DIC score is the lowest in the DGC-t-MSV model. Considering the adaptability and complexity comprehensively, it can be seen that the DGC-t-MSV model is the most suitable model for testing the volatility spillover. Figure 2 shows the dynamic correlation result between America WTI crude oil future (AF) and China INE crude oil future (CF).Figure 1
Gelman Rubin test results ofμcf and μaf.Table 3
DIC result of CC-MSV, GC-MSV, DC-MSV, and DGC-MSV-t.
DbarDhatpDDICCC-MSV3134.71308945.7123180.42GC-MSV3125.123081.4943.6293168.75DC-MSV3128.833077.9550.883179.71DGC-MSV-t2712.072688.4623.6032735.67Figure 2
Dynamic correlation result.In Table4, we can see all the spillover from each oil futures to others. ψbfaf,ψbfcf,ψbsas,ψbsas,ψcsas,ψbscs,ψbsas,ψcsas,andψbscs in 90% confidence are lower than zero. Brent oil future has significant one-way spillover to WTI oil future. WTI future has higher spillover to INE future. Also, we can see all the spillover between spot oil prices. The Brent oil spot price has one-way spillover effect to WTI and Shengli oilfield spot price. Unexpected, Shengli oilfield spot price has one-way spillover to WTI spot price. Using the same method, we can get the relationship of spillover between oil future and spot price in Table 4. It shows that WTI spot price and future price has significant two-way spillover effect. In Table 5, the Brent spot price has one-way spillover effect to Brent future and WTI future. Brent future has spillover to the price of WTI spot price. Shengli oilfield spot price has a subsignificant one-way spillover to Brent future. Three crude oil spot prices have volatility spillover to INE futures. Table 6 shows the spillover estimation result between stock and oil. There only exist a few spillover relations between the stock market and the oil market. The spillover from WTI, Brent, and INE oil future to the stock market of S&P exists. However, the Shanghai stock index has a significant one-way spillover to the Shengli oilfield spot price.Table 4
Volatility spillover parameter estimation result of different oil markets.
NodeMean2.50%5.00%10.00%Median97.50%Is it significant?ψbfaf0.06004−0.05696−0.04283−0.027760.038060.3061Not significantψafbf0.30320.090630.10760.12950.2690.6695Significantψcfaf0.1751−0.0089070.0034720.020680.14910.4627Significantψafcf0.293−0.046 09−0.02070.010950.22671.017Subsignificantψcfbf0.2184−0.02287−0.011170.0066640.19730.5731Subsignificantψbfcf0.2808−0.1651−0.1231−0.075860.17511.345Not significantψbsas0.06786−0.04367−0.03385−0.021 80.035450.338Not significantψasbs0.2809−0.0061960.018 920.067080.25480.714Significantψcsas0.1161−0.02453−0.01588−0.0057330.054010.5984Not significantψascs0.2948−0.014320.019460.070730.27180.7241Significantψcsbs0.56940.056 010.12350.22350.55081.177Significantψbscs0.02523−0.1666−0.1376−0.10760.00070.3682Not significantψbsas0.06786−0.04367−0.03385−0.02180.035450.338Not significantψasbs0.2809−0.0061960.018920.067080.25480.714Significantψcsas0.1161−0.02453−0.01588−0.0057330.054010.5984Not significantψascs0.2948−0.014320.019460.070730.27180.7241Significantψcsbs0.56940.056010.12350.22350.55081.177Significantψbscs0.02523−0.1666−0.1376−0.10760.00070.3682Not significantTable 5
Volatility spillover parameter estimation result between oil future and spot price.
NodeMean2.50%5.00%10.00%Median97.50%Is it significant?ψafas0.44850.065480.11810.19590.45060.8539Significantψasaf0.36670.028850.054080.092640.3430.8193Significantψbfbs0.2449−0.018320.0012840.029260.21370.684Significantψbsbf0.165−0.04118−0.02714−0.0098010.11510.6209Not significantψcfcs0.1284−0.0179−0.000600.017640.1150.3511Subsignificantψcscf0.2022−0.05455−0.03521−0.011470.13250.7939Not significantψafbs0.2507−0.0060170.0097450.037470.21380.7771Significantψbsaf0.146 5−0.032 99−0.02004−0.0045120.095160.5993Not significantψafcs0.2146−0.09007−0.05445−0.017260.17160.8721Not significantψcsaf0.2803−0.01483−0.0039360.01270.26750.752Subsignificantψasbf0.3341−0.031560.0056580.076480.31160.8012Significantψbfas0.1218−0.05055−0.038−0.023020.049440.7169Not significantψbfcs0.3971−0.1292−0.066350.017520.38871.007Subsignificantψcsbf0.123−0.04957−0.03826−0.023980.044340.5781Not significantψcfas0.1329−0.07335−0.04068−0.013270.098730.4624Not significantψascf0.1128−1.097−0.9743−0.66850.11651.032Not significantψcfbs0.09382−0.1008−0.07042−0.038430.070990.3969Not significantψbscf0.2786−0.07741−0.04265−0.0023240.21681.005Not significantTable 6
Volatility spillover parameter estimation result between stock and oil.
NodeMean2.50%5.00%10.00%Median97.50%Is it significant?ψshsp−0.1318−0.4226−0.3245−0.2498−0.1032−0.01694Not significantψspsh−0.02373−0.1954−0.1397−0.09121−0.0069210.04063Not significantψafsp0.05652−0.02654−0.01916−0.010820.038430.2475Not significantψspaf0.3715−0.02974−0.011220.017840.3241.173Subsignificantψafsh−0.05138−0.3714−0.2847−0.1895−0.011230.05214Not significantψshaf−0.1472−0.5502−0.4185−0.3101−0.1049−0.01055Not significantψbfsp0.05872−0.03439−0.02437−0.013810.037860.2752Not significantψspbf0.3538−0.02979−0.0062060.032270.30181.001Subsignificantψbfsh−0.004162−0.1421−0.09803−0.05940.0091450.05486Not significantψshbf−0.08078−0.2779−0.1979−0.1532−0.0599−0.0182Not significantψcfsp0.0219−0.02526−0.01954−0.012 960.013660.1205Not significantψspcf0.72180.14420.20360.27710.64261.903Significantψcfsh0.01713−0.03673−0.01401−0.0027240.01860.05428Not significantψshcf−0.07241−0.1865−0.1588−0.1307−0.06423−0.00017Not significantψassp0.06211−0.0332−0.02422−0.01320.043440.2481Not significantψspas0.3739−0.019 260.0064160.042240.32511.103Subsignificantψassh−0.00164−0.1386−0.09633−0.055490.0084640.06549Not significantψshas−0.04689−0.1528−0.1152−0.08902−0.038520.001158Not significantψbssp0.07731−0.01021−0.0014350.012420.06770.218Subsignificantψspbs0.2014−0.09414−0.07542−0.054640.055 581.115Not significantψbssh−0.02373−0.1954−0.1397−0.09121−0.0069210.04063Not significantψshbs−0.1318−0.4226−0.3245−0.2498−0.1032−0.01694Not significantψcssp0.03079−0.03393−0.0264−0.017590.021320.1511Not significantψspcs0.41050.059690.12160.1710.36710.9767Significantψcssh0.034380.0030040.0079270.012850.030560.08961Significantψshcs−0.01635−0.06732−0.05935−0.04977−0.016840.04631Not significant


## 3.1. Data and Preprocessing

In this section, the data include INE crude oil futures (CF) and Shengli oilfield spot price (CS) of China, WTI crude oil futures (AF) and WTI crude oil spot price (AS) of USA, BRENT crude oil future (BF) and BRENT crude oil spot price (BS) of UK, the Shanghai Stock Index (SH), and the S&P Index (SP). We selected the day price from March 27, 2018, to December 31, 2019. After excluding the holidays, 8 sets of data are obtained for daily trading closing prices, each of which includes 405 common trading days. Considering the exchange rate, we obtained the logarithmic rate of return, which is abbreviated as CF, CS, AF, AS, BF, BS, SH, and SP. The data come from EIA (United States Energy Information Administration) and public database of stock market. China and USA both are the important oil importers in the world. Shengli oilfield is the largest oilfield in China and represents the spot price of China crude oil. WTI and Brent are the most important representative oil future in the world. The descriptive statistics is shown as Table1. J-B value shows that some data are different from the normal distribution.Table 1
Descriptive statistics.
CFCSAFASBFBSSHSPMean0.007066−0.016718−0.0094440.0374780.053494−0.003176−0.013046−0.016233Median0.14190.19485−0.0161660.1887390.0931340.0694780.2612940.1252Maximum7.642113.25785.4492625.6628183.37593811.8733511.7323713.50267Minimum−6.8208−8.233565−5.745464−7.801777−3.341992−6.449077−6.95906−8.724438Std. dev.1.7741792.1271981.2496912.0972120.8741982.1228891.9139112.247643Skewness−0.2004960.105674−0.267382−0.398778−0.5870870.228817−0.0969540.127722Kurtosis4.1438468.0204515.9157423.5840465.5502725.6229797.5260027.496187Jarque–Bera24.30266417.6704145.360316.16461130.3908117.2713339.4729335.4807


## 3.2. Parameter Estimation

Taking America WTI crude oil future (AF) and China INE crude oil future (CF) as example, we abandon the first 10,000 iterations. Then, we simulate the last 80,000 iterations to get the result as Table2.Table 2
The simulation results of posterior parameters of WTI and INE future.
NodeMeanSdMC error2.50%5.00%10.00%Median97.50%StartSampleμcf0.80060.18310.0079310.42130.490 20.56770.80811.1481000080002μaf0.9520.26460.011580.35490.466 50.59050.98261.4171000080002o12.634.0270.13067.017.5878.31311.8422.681000080002ψcfcf0.7440.14960.0067660.41460.474 10.53230.76480.96791000080002ψcfaf0.17510.13470.006321−0.0089070.0034720.020680.14910.46271000080002ψafaf0.78390.14580.0066010.42640.49010.57430.81510.97981000080002ψafcf0.2930.27820.01318−0.04609−0.02070.010950.22671.0171000080002σξcf0.1190.037280.0016690.065480.070370.077590.11220.20961000080002σξaf0.17410.078310.0037130.067180.074680.086970.15850.3631000080002In Table2, ψcfaf represents the volatility spillover from WTI future to INE future. As proposed by [33], if ψ is greater than 0 means significant spillover effect exists. The 2.5% quantile of ψcfaf is less than 0, but 5% quantile is greater than 0, which means the spillover from WTI to INE is significant in 95% confidence interval. The 5% quantile of ψafcf is less than 0 and the 5% quantile of ψafcf is greater than 0. Within 90% confidence interval which is greater than 0, we classify the spillover of ψafcf as subsignificant. The volatility level parameter μcf of INE future is 0.800 6. And μaf of WTI future is 0.952. The value of μcf is lower than μaf, which means the risk of the INE future is lower than the WTI future. The volatility persistence parameter ψcfcf of INE future is 0.744 and ψafaf of WTI future is 0.783 9. The INE future volatility persistence is lower than WTI future.Figure1 shows the Gelman test results of μcf and μaf. We can see the two Markov links are lower than 1.1, and it can be considered as convergent. μcf and μaf are convergent. Other parameters’ results are also convergent. In Table 3, the DIC test result shows that the DGC-MSV-t model is better than other models. Dbar reflects the difference between the model and the actual data, the smaller the better. pD reflects the complexity of the model; the larger the value, the more complicated. Dbar and pD jointly determine the DIC test value. The total DIC score is the lowest in the DGC-t-MSV model. Considering the adaptability and complexity comprehensively, it can be seen that the DGC-t-MSV model is the most suitable model for testing the volatility spillover. Figure 2 shows the dynamic correlation result between America WTI crude oil future (AF) and China INE crude oil future (CF).Figure 1
Gelman Rubin test results ofμcf and μaf.Table 3
DIC result of CC-MSV, GC-MSV, DC-MSV, and DGC-MSV-t.
DbarDhatpDDICCC-MSV3134.71308945.7123180.42GC-MSV3125.123081.4943.6293168.75DC-MSV3128.833077.9550.883179.71DGC-MSV-t2712.072688.4623.6032735.67Figure 2
Dynamic correlation result.In Table4, we can see all the spillover from each oil futures to others. ψbfaf,ψbfcf,ψbsas,ψbsas,ψcsas,ψbscs,ψbsas,ψcsas,andψbscs in 90% confidence are lower than zero. Brent oil future has significant one-way spillover to WTI oil future. WTI future has higher spillover to INE future. Also, we can see all the spillover between spot oil prices. The Brent oil spot price has one-way spillover effect to WTI and Shengli oilfield spot price. Unexpected, Shengli oilfield spot price has one-way spillover to WTI spot price. Using the same method, we can get the relationship of spillover between oil future and spot price in Table 4. It shows that WTI spot price and future price has significant two-way spillover effect. In Table 5, the Brent spot price has one-way spillover effect to Brent future and WTI future. Brent future has spillover to the price of WTI spot price. Shengli oilfield spot price has a subsignificant one-way spillover to Brent future. Three crude oil spot prices have volatility spillover to INE futures. Table 6 shows the spillover estimation result between stock and oil. There only exist a few spillover relations between the stock market and the oil market. The spillover from WTI, Brent, and INE oil future to the stock market of S&P exists. However, the Shanghai stock index has a significant one-way spillover to the Shengli oilfield spot price.Table 4
Volatility spillover parameter estimation result of different oil markets.
NodeMean2.50%5.00%10.00%Median97.50%Is it significant?ψbfaf0.06004−0.05696−0.04283−0.027760.038060.3061Not significantψafbf0.30320.090630.10760.12950.2690.6695Significantψcfaf0.1751−0.0089070.0034720.020680.14910.4627Significantψafcf0.293−0.046 09−0.02070.010950.22671.017Subsignificantψcfbf0.2184−0.02287−0.011170.0066640.19730.5731Subsignificantψbfcf0.2808−0.1651−0.1231−0.075860.17511.345Not significantψbsas0.06786−0.04367−0.03385−0.021 80.035450.338Not significantψasbs0.2809−0.0061960.018 920.067080.25480.714Significantψcsas0.1161−0.02453−0.01588−0.0057330.054010.5984Not significantψascs0.2948−0.014320.019460.070730.27180.7241Significantψcsbs0.56940.056 010.12350.22350.55081.177Significantψbscs0.02523−0.1666−0.1376−0.10760.00070.3682Not significantψbsas0.06786−0.04367−0.03385−0.02180.035450.338Not significantψasbs0.2809−0.0061960.018920.067080.25480.714Significantψcsas0.1161−0.02453−0.01588−0.0057330.054010.5984Not significantψascs0.2948−0.014320.019460.070730.27180.7241Significantψcsbs0.56940.056010.12350.22350.55081.177Significantψbscs0.02523−0.1666−0.1376−0.10760.00070.3682Not significantTable 5
Volatility spillover parameter estimation result between oil future and spot price.
NodeMean2.50%5.00%10.00%Median97.50%Is it significant?ψafas0.44850.065480.11810.19590.45060.8539Significantψasaf0.36670.028850.054080.092640.3430.8193Significantψbfbs0.2449−0.018320.0012840.029260.21370.684Significantψbsbf0.165−0.04118−0.02714−0.0098010.11510.6209Not significantψcfcs0.1284−0.0179−0.000600.017640.1150.3511Subsignificantψcscf0.2022−0.05455−0.03521−0.011470.13250.7939Not significantψafbs0.2507−0.0060170.0097450.037470.21380.7771Significantψbsaf0.146 5−0.032 99−0.02004−0.0045120.095160.5993Not significantψafcs0.2146−0.09007−0.05445−0.017260.17160.8721Not significantψcsaf0.2803−0.01483−0.0039360.01270.26750.752Subsignificantψasbf0.3341−0.031560.0056580.076480.31160.8012Significantψbfas0.1218−0.05055−0.038−0.023020.049440.7169Not significantψbfcs0.3971−0.1292−0.066350.017520.38871.007Subsignificantψcsbf0.123−0.04957−0.03826−0.023980.044340.5781Not significantψcfas0.1329−0.07335−0.04068−0.013270.098730.4624Not significantψascf0.1128−1.097−0.9743−0.66850.11651.032Not significantψcfbs0.09382−0.1008−0.07042−0.038430.070990.3969Not significantψbscf0.2786−0.07741−0.04265−0.0023240.21681.005Not significantTable 6
Volatility spillover parameter estimation result between stock and oil.
NodeMean2.50%5.00%10.00%Median97.50%Is it significant?ψshsp−0.1318−0.4226−0.3245−0.2498−0.1032−0.01694Not significantψspsh−0.02373−0.1954−0.1397−0.09121−0.0069210.04063Not significantψafsp0.05652−0.02654−0.01916−0.010820.038430.2475Not significantψspaf0.3715−0.02974−0.011220.017840.3241.173Subsignificantψafsh−0.05138−0.3714−0.2847−0.1895−0.011230.05214Not significantψshaf−0.1472−0.5502−0.4185−0.3101−0.1049−0.01055Not significantψbfsp0.05872−0.03439−0.02437−0.013810.037860.2752Not significantψspbf0.3538−0.02979−0.0062060.032270.30181.001Subsignificantψbfsh−0.004162−0.1421−0.09803−0.05940.0091450.05486Not significantψshbf−0.08078−0.2779−0.1979−0.1532−0.0599−0.0182Not significantψcfsp0.0219−0.02526−0.01954−0.012 960.013660.1205Not significantψspcf0.72180.14420.20360.27710.64261.903Significantψcfsh0.01713−0.03673−0.01401−0.0027240.01860.05428Not significantψshcf−0.07241−0.1865−0.1588−0.1307−0.06423−0.00017Not significantψassp0.06211−0.0332−0.02422−0.01320.043440.2481Not significantψspas0.3739−0.019 260.0064160.042240.32511.103Subsignificantψassh−0.00164−0.1386−0.09633−0.055490.0084640.06549Not significantψshas−0.04689−0.1528−0.1152−0.08902−0.038520.001158Not significantψbssp0.07731−0.01021−0.0014350.012420.06770.218Subsignificantψspbs0.2014−0.09414−0.07542−0.054640.055 581.115Not significantψbssh−0.02373−0.1954−0.1397−0.09121−0.0069210.04063Not significantψshbs−0.1318−0.4226−0.3245−0.2498−0.1032−0.01694Not significantψcssp0.03079−0.03393−0.0264−0.017590.021320.1511Not significantψspcs0.41050.059690.12160.1710.36710.9767Significantψcssh0.034380.0030040.0079270.012850.030560.08961Significantψshcs−0.01635−0.06732−0.05935−0.04977−0.016840.04631Not significant


## 4. Conclusion

The cross-market spillover effect we found can give some advice to correctly diversify investment and reduce risks. (1) The empirical results show that WTI and Brent oil future have more spillover to both spot price and future price. The oil future played an important role in the energy market and economic. INE oil future is a fast-growing product of China. However, INE oil future still lacks international influence. (2) S&P stock market is more sensitive to the oil price than Shanghai stock market. After experiencing three oil crises, the investors of USA fully understand the impact of crude oil prices on the market. The investor in China does not pay attention to the volatility of crude oil price. S&P includes many oil company, which is not included in the Shanghai stock market. (3) The volatility of the Chinese and American stock markets is not highly correlated and suitable for diversified investment. DIC test shows that DGC-MSV-t is considered effective and more accurate. Our possible future studies will be focus on the difference when market volatility increases and decreases based on regime-switching method of stochastic volatility.



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*Source: 6270525-2021-12-31.xml*