Let POT and PET represent WTI international crude oil price and Euro-USD exchange rate price on T day respectively, and their statistical characteristics are shown in Table 4.23. It is not difficult to find that, firstly, the two price series (exchange rate can also be regarded as a relative price) are non-normal distribution; Secondly, the two price series have significant autocorrelation and heteroscedasticity, so there is significant fluctuation aggregation. Moreover, ADF test results show that, at the significance level of 5%, both price series are non-stationary series, but both are first-order unary series. From the standard deviation of the two, we can also find that the risk of oil price fluctuation is greater than that of exchange rate fluctuation in general.
Table 4.23 Basic statistical characteristics of international oil price and US dollar exchange rate series
4.5.3.2 Average Spillover Effect Test
(1) cointegration analysis
In order to use the concept of long-term elasticity, we first take the natural logarithm of two price series and get two new variables, 1n_PO and 1n_PE. Because the series of international oil price and US dollar exchange rate are still first-order unary after taking natural logarithm, the test results show that the two price series are still first-order unary after taking natural logarithm, which meets the basic requirements of applying cointegration theory. Specific statistical test results can be obtained from the author.
According to the co-integration theory, the regression equation is established as follows:
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Where: the t statistics of the corresponding variables are in brackets; * * means significant at the significance level of 1%. ADF method is used to test the stationarity of the residual term εt of regression equation. The results show that the residual sequence is remarkably stable at the significance level of 1%. Therefore, we believe that there is a long-term balanced cointegration relationship between the international oil price and the US dollar exchange rate. From the co-integration regression coefficient, the equilibrium relationship between them is positive. Moreover, the long-term elasticity coefficient of the international oil price about the exchange rate of the euro against the US dollar is 1.26, that is, the change of the exchange rate of the US dollar is 1%, and the long-term average change of the international oil price is 1.2607%. It can be seen that the long-term interaction between the two markets is very significant, so when analyzing and forecasting the long-term trend of international oil prices, we must consider the change of the US dollar exchange rate.
(2) Intertemporal cross-correlation test
Although the international oil price and the US dollar exchange rate are not stationary series, there is a co-integration relationship between them, which is in line with the prerequisite for establishing the VaR model. In order to confirm whether it is necessary to use VaR model to model, we first test the intertemporal correlation between the international oil price series and the US dollar exchange rate series. When it lags behind two orders, the intertemporal correlation coefficient is shown in Table 4.24. It can be seen that the cross-correlation coefficient between oil price and exchange rate series is large, which shows that there is a significant guiding and lagging relationship between the conditional mean values of the two markets. Therefore, it is necessary to establish a VaR model.
Table 4.24 Intertemporal correlation coefficient between international oil price and US dollar exchange rate
(3) average spillover effect test
By establishing the VaR model of oil price and exchange rate, according to the minimum AIC value of the whole model, the optimal lag order of Granger causality test is 1, and the results of Granger causality test are shown in Table 4.25. From the significant probability, it is found that the exchange rate of the euro against the US dollar is the Granger cause of the fluctuation of international oil prices. However, the change of international oil price is not the Granger cause of the fluctuation of US dollar exchange rate. Therefore, it can be considered that the US dollar exchange rate has a one-way average spillover effect on the international oil price, that is, the change of the international oil price is significantly affected by the change of the previous US dollar exchange rate.
Table 4.25 Granger Causality Test Results of Oil Price and Exchange Rate
Since 2002, the dollar has been depreciating for complicated reasons. The most fundamental reason is that the US government is trying to effectively boost exports and reduce the trade deficit. On the other hand, due to the comprehensive influence of market supply and demand, geopolitics and financial markets, international oil prices hit a new high since 2002. Through the above-mentioned mean spillover effect test, we can think that the depreciation of the US dollar has a significant role in promoting the rise of international oil prices. This is because crude oil futures trading is mainly denominated in US dollars. The depreciation of the US dollar has caused some foreign investors to buy crude oil futures trading contracts in large quantities to obtain higher profits. Higher crude oil futures prices will inevitably lead to higher spot prices. Of course, it also has long-term effects.
Compared with the previous results calculated by using the actual oil price and the actual exchange rate, the results obtained by using the nominal price show that although there is still a balanced interaction between the oil price and the US dollar exchange rate in the long run, the direction of interaction has changed. Therefore, it can be considered that the price level has changed the long-term interactive relationship between the two markets to some extent.
(4) Analysis of the results of impulse response function
In the VaR model, the impulse response function can be used to measure the impact of the standard deviation impact of random disturbance term on the current and future values of variables. The impulse response function based on the exchange rate between international oil price and US dollar is shown in Figure 4.27. It can be seen that the impact of a standard deviation of the US dollar exchange rate (the logarithmic value is 0. 1463, corresponding to the original exchange rate of 0. 1557) on the international oil price is slowly increasing, and it reaches the maximum value of 0.00879 US dollars/barrel after about 1 year (the specific result is 234 days) (this is right) This result further verifies the one-way average spillover effect between the international oil price and the US dollar exchange rate.
Figure 4.27 Impulse Response Function of International Oil Price and US Dollar Exchange Rate
A- the reaction after the oil price is impacted; B- the reaction after the US dollar exchange rate was hit.
4.5.3.3 volatility spillover effect test.
GARCH Effect Analysis of (1) Price Series
As can be seen from Table 4.23, there is a significant series correlation between the square series of two prices, that is, the original series has significant fluctuation aggregation, so we introduce ARCH model to describe this property. Considering the autocorrelation of the sequence, the main model adopts random walk model. By testing the residual ARCH effect, it is found that there is a significant high-order ARCH effect in the international oil price series, so GARCH model is considered, and then GARCH( 1, 1) model is adopted to describe the fluctuation aggregation of the international oil price series after many attempts according to the minimum AIC value criterion. In addition, considering that the empirical research results show that the price fluctuation caused by the rise and fall of oil prices is asymmetric, the TGARCH model is considered, and the AIC value of the model shows that this approach is also reasonable. The residual of TGARCH model is tested for ARCH effect, and it is found that ARCH effect has been filtered out. Moreover, the test results of Q( 10) and Q2( 10) statistics also show that there is no additional sequence correlation and fluctuation aggregation in the model residuals, which shows that TGARCH( 1, 1) model has a good fitting effect on the fluctuation characteristics of international crude oil prices. In the same way, we find that GARCH( 1, 1) model can better describe the fluctuation aggregation of the exchange rate of the euro against the US dollar. The estimation results of model parameters are shown in Table 4.26.
Table 4.26 Parameter Estimation Results of (T)GARCH Model for International Oil Price and US Dollar Exchange Rate
It should be noted that considering that the model residuals do not obey the normal distribution, we use the (T)GARCH model based on GED distribution to describe the peak and thick tail characteristics of the model residuals. The results in Table 4.23 show that the parameters of GED distribution are all less than 2, thus verifying the thick-tailed characteristics of the residual term obtained when using (T)GARCH model to model the oil price and US dollar exchange rate series.
The parameter estimation results of the fluctuation model show that the international oil price fluctuation has significant asymmetry, that is, leverage effect. The leverage coefficient is negative, indicating that the impact of rising oil prices in the same range on future fluctuations of oil prices is greater than that of falling oil prices. Specifically, when the oil price falls, the influence degree of α 1+ψ on ht is 0.0219; When the oil price rises, the influence degree α 1 is 0.0688, which is about 3. 1 times of that when the oil price falls. There are many reasons for this leverage effect, and the irreproducibility of oil is the most fundamental reason, which determines that the market position of oil suppliers is obviously higher than that of oil demanders. Therefore, rising oil prices will aggravate the expectation of oil shortage and make market traders tend to buy in the current period. This kind of competition has intensified the further rise of oil prices, and the fluctuation of oil prices is particularly prominent with the help of market speculation. When oil prices fell, oil producers cut production and oil dealers hoarded goods for sale, which led to a decrease in market supply and a rebound in oil prices, which prevented them from falling further. It can be seen that the asymmetric position between the long and short sides of the oil market determines that the increase of oil price is greater than the decrease of oil price when the supply is insufficient, thus causing the leverage effect of the above oil market.
From the fluctuation model, we can also find that there is a significant GARCH effect in the fluctuation of the US dollar exchange rate. The sum of the coefficients before h t- 1 in the variance equation α 1+β 1 describes the attenuation speed of fluctuation impact; The closer the value is to 1, the slower the attenuation speed is. In the GARCH( 1, 1) model in this section, the sum of these coefficients is 0.9872, which shows that the US dollar exchange rate has finite variance, that is, it belongs to a weakly stationary process. The fluctuation of the dollar exchange rate will eventually decrease, but it may last for a long time. Among them, the coefficient before ht- 1 is 0.9533, which means that 95.33% of the current variance still exists in the next period, so the half-life is 14 days.
(2) Test of volatility spillover effect
According to the test model of fluctuation spillover effect mentioned above, the estimated results of fluctuation spillover effect between international oil price and US dollar exchange rate are obtained, as shown in Table 4.27. We found that, statistically speaking, the Y coefficient of the exchange rate between the international oil price and the US dollar is not significant. It can be seen that although there is a long-term balanced cointegration relationship between the international oil price and the US dollar exchange rate, there is also a significant one-way mean spillover effect. However, the fluctuation spillover effect between them is not significant, that is, the price fluctuation information of both parties has certain independence, and the degree of price fluctuation will not be significantly transmitted to the other party. This also shows that from the perspective of price fluctuations, the impact of the US dollar exchange rate on international oil prices is quite weak.
Table 4.27 Test Results of Spillover Effect of International Oil Price and US Dollar Exchange Rate Fluctuation
4.5.3.4 Risk Spillover Effect Test
The fluctuation of the market does not mean that there must be risks, so the risk spillover effect is an extension of the fluctuation spillover effect. According to the calculation idea of VaR, this section uses the left quantile of the international oil price distribution function to measure the risk of falling oil prices, indicating that the sales revenue of crude oil producers is reduced due to the sharp drop in oil prices; The right quantile of the distribution function is used to measure the risk of rising oil prices, indicating the extra expenses brought by the sharp rise in oil prices to crude oil buyers. This comprehensive consideration of market risks is also applicable to the US dollar exchange rate market. As far as the exchange rate of Euro against USD adopted in this section is concerned, the fluctuation of exchange rate will bring different risks to different subjects in the international exchange rate market. For example, in the international import and export trade of the United States, the decline in exchange rate means the appreciation of the US dollar, and American exporters and importers in the euro zone will face greater risks; If the exchange rate rises and the dollar depreciates, then American importers and exporters in the euro zone may face obvious market risks; As far as petrodollars are concerned, the appreciation of the dollar will increase the expenses of oil importing countries (such as the euro zone); The depreciation of the dollar will hinder the oil sales revenue of major oil exporting countries (such as the Organization of Petroleum Exporting Countries).
To sum up, both the oil market and the US dollar exchange rate market need to measure the risk of price falling and rising at the same time, so as to provide decision support for different participants in the market. In this section, we will use the above TGARCH( 1, 1) model and GARCH( 1, 1) model based on GED distribution to measure the VaR risk value of international oil price and US dollar exchange rate respectively when the price rises and falls, and test the risk spillover effect between the two markets.
Quantile determination of (1)GED distribution
According to the probability density function of GED distribution, the quantile of GED distribution with degrees of freedom obtained in this section is obtained by MATLAB programming and multiple numerical calculations (Table 4.28). The results in the table show that the 95% quantile is basically consistent with the normal distribution 1.645, but the 99% quantile is obviously larger than the normal distribution of 2.326, which also shows that both the international oil price and the US dollar exchange rate price have serious fat tail characteristics.
Table 4.28 GED distribution parameters and quantiles of international oil price and US dollar exchange rate price
(2) VaR risk value calculation based on GED-(T) GARCH model.
According to the meaning of VaR risk and variance-covariance method mentioned above, we get the following two formulas to calculate VaR risk. The formula for calculating the VaR value of price rising risk is:
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Where: micron, t is the conditional average of T-day price in the m-th market (that is, the difference between actual value and residual), and zm, a is the right quantile of GED distribution that the residual of (T)GARCH( 1, 1) model in the m-th market obeys; Hm, t, t are heteroscedasticity of the m-th market price.
Similarly, the formula for calculating the VaR value of price decline risk is as follows
Risk assessment and decision support technology of foreign oil, gas and mineral resources utilization
Based on the above formula, this section calculates the rising risk and falling risk of international oil price and US dollar exchange rate with 95% and 99% confidence. After LR test (Kupiec, 1995), we found that the result of VaR risk is reliable and feasible.
(3) Risk Spillover Effect Test
After getting the VaR risk values when the international oil price and the US dollar exchange rate price rise and fall, according to the risk-Granger causality test method proposed by Hong (2003), the corresponding statistics Q 1(M) and (m) are constructed, and the values of the statistics and their significant probabilities are calculated by M B programming, thus testing the two-way and one-way risk spillover effects between the oil market and the US dollar exchange rate market. See Table 4.29 for the calculation results, where m is 10, 20 and 30 respectively.
From the risk test results, it can be seen that there is a two-way risk spillover effect between the international oil price and the US dollar exchange rate from the perspective of downside risks (that is, the oil price falls and the US dollar appreciates). Further testing the one-way risk spillover effect, we find that there is a risk spillover effect from the US dollar exchange rate market to the international oil market with 95% confidence, but there is no risk spillover effect from the international oil market to the US dollar exchange rate market. It can be seen that the risk of appreciation of the US dollar exchange rate has a significant impact on the risk of falling international oil prices. However, with 99% confidence, there is no risk spillover effect in any direction between the international oil price and the US dollar exchange rate. Therefore, as far as downside risks are concerned, the risk spillover effect between the two markets is relatively limited. When the accuracy requirement is improved to a certain extent, the risk impact of the appreciation of the US dollar exchange rate on the decline of oil prices can be ignored.
Table 4.29 Test results of price risk spillover effect between international oil price and US dollar exchange rate
On the other hand, from the perspective of rising risks (that is, rising oil prices and depreciating the US dollar), there is no risk spillover effect in any direction between the two markets with 95% or 99% confidence. It can be seen that in recent years, although the US dollar has continued to depreciate in general, as far as market risk is concerned, this depreciation has not significantly promoted the rising risk of international crude oil prices. In other words, although the high international oil price has led to a significant increase in the extra expenditure of major buyers in the international oil market (such as China and India), the continued depreciation of the US dollar is not a significant reason for the increase in expenditure in these countries.
Generally speaking, we need to pay special attention to the risk effect of dollar appreciation on the decline of international oil prices and take active measures to effectively avoid market risks. In recent years, although from the perspective of daily transactions, the exchange rate of the US dollar has fluctuated from time to time. But overall, the depreciation of the US dollar is a general trend, and the exchange rate of the euro against the US dollar has reached a record high, which has not had a significant impact on the risk of rising oil prices. Therefore, in this environment, the empirical result of risk spillover effect is a satisfactory signal for market traders.