3.1 Bivariate EGARCH Model with Error Correction Term

Pursuant to the literature, the presence of asymmetrical effects in volatility has been amply confirmed in the stock markets of industrialized and emerging countries. However, the evidence for the oil markets needs to be verified. For that reason, this study extends the ^{Nelson (1991)} EGARCH model to a multivariate structure to analyze the nature of mean and volatility transmission mechanisms between oil markets.

To analyze the price information transmission patterns and the performance of the physical and futures oil markets, the model considered whether they are affected by their own terms and the terms of other performances, with delay, as well as an error correction term.

The conditional mean equations are specified using error correction vector models as follows:

where R_S,t and R_F,t are the yields of the physical oil and oil futures markets, meaning S= Maya, Istmo, Olmeca and F= WTI, Brent P_S,t and P_F,t are the logarithmic prices of S and F on date t, respectively. Moreover, and are the coefficients of the own effects of the delayed yields. and measure the indirect effects of the mean on physical and futures yields. and are the coefficients measuring the speed of price adjustment across the physical oil and oil futures market or the speed at which the difference in the long-term balance is corrected. Ψ _t-1 is the set of information available at time t-1 ε _t = (ε _S,t , ε _F,t ) are the residuals of the conditional means, such that ε _t ׀ Ψ _t-1 ~N(0,H _t ) H _t {h _s,t , h _F,t , h _SF,t } is defined as the conditional variance-covariance matrix.

Given that volatility is important to better understanding the information transmission process between the physical oil and oil futures markets when there are asymmetry effects, the conditional variance equations are defined as follows:

where j = S,F and ξ _j,t-1 = ε _j,t-1 = ε _j,t-1 ׀h _j,t-1 are standardized residuals. Moreover, ϕ _S1 y ϕ _F1 measure the short-term persistence or own direct effects of shock transmission. The parameters ϕ _S3 and ϕ _F3 measure the short-term cross-market volatility transmission effects on the yields of physical oil and oil futures prices, respectively. As such, the conditional volatility will not only be affected by shocks in the past residuals of the own market, but also by shocks from other markets. ϕ _S2 ϕ _F2 and quantify the degree of long-term persistence in the volatility. A value close to one indicates that high volatility is followed by even stronger volatility in the same direction.

For their part, ϕ _S4 and ϕ _F4 measure the long-term cross-market volatility transmission effects on each of the physical and futures markets. The parameters β _S0 and β _F0 represent the effects of temporary deviations from the equilibrium, which affect the conditional variance because an increase in the differential between the two variables generates uncertainty and drives up volatility (^{Lee, 1994}).

The presence of the asymmetry effect in conditional volatility is determined by equation (5) when the parameter δ _j is significantly different from 0. If the partial derivatives of the function g(ξ _j,t ) are taken with respect to ξ _j,t , the following results:

The terms and δ _j ξ _j,t measure the size and sign effects, respectively. If δ _j < 0, negative innovation⁷ strengthens the size effect, but the size effect is neutralized when δ _j < 0. This means that negative innovations increase the volatility more than positive innovations of the same magnitude. Likewise, the evaluation of the importance of asymmetry or leveraging factors is measured by .

The covariances are determined as follows:

where ρ is the constant conditional correlation.

Finally, the quasi-maximum likelihood method is used to estimate the parameters of the logarithmic likelihood function:

where θ is the vector of model parameters and T indicates the number of observations.

5.1 Transmission of Information Through Yields and Volatility

Using the physical prices yields series and the future prices yields series, this study estimated 12 bivariate VEC-EGARCH specifications to analyze the information on the mean and volatility transmission mechanisms across the Mexican physical oil and oil futures markets.

In Table 2, pursuant to the specification of the conditional mean, the statistical significance of the estimated parameters reveals that the current yields on Maya, Istmo, and Olmeca oil are directly affected by their own performance delayed on period. The number of lags in the mean equation was chosen pursuant to the Akaike information criterion.

Table 2 Parameters Estimated from the Bivariate VEC-EGARCH Model 

Note: Q(18) and Q²(18) indicate the Ljung-Box test statistics for simple and squared residuals with 18 lags and p-values in parentheses. The terms *,**, and *** indicate significance at levels 1,5 and 10%, respectively. Standard errors reported in parentheses.

Source: Created by the author with information from the Bloomber database.

In terms of the transmission of information on the indirect effects of the mean, the Mexican oil yields were positively affected by the futures yields of the WTI and Brent, except where the WTI → Olmeca relationship was concerned. The strongest market reaction to a change in futures prices was found in the WTI→Istmo, WTI→Maya, and Brent→Istmo relationships with values of 0.7824, 0.7605, and 0.5258, respectively. The weakest factor was in the WTI→Olmeca relationship with a value of -0.1847. The results indicate that the information generated in the WTI and Brent futures markets is rapidly transmitted to the Mexican oil markets. This is fueled by the major role the futures markets play in assimilating market expectations and reflecting them efficiently in the formation and prediction of futures prices. Moreover, the inefficiency and lack of liquidity in the Mexican oil market obliges it to act as a taker of prices rather than a setter, prompting rising dependency on the international markets to set the prices from abroad, despite being an oil producing country with high production capacity.

The estimated coefficients in the VEC model determine the speed of price adjustment to reach the long-term equilibrium relationship between the physical oil and oil futures markets. The lack of significance in the results reveals the absence of adjustment between the Maya and Istmo prices and the deviations from the long-term equilibrium relationship, except for the Brent→Olmeca (1.0214) and WTI→Olmeca (1.0159) relationships at a level of 1% and 5%, respectively. The reason for this finding rests on the similar physical and chemical traits of the Olmeca crude and the international reference oils, because Olmeca prices are adjusted and react to imbalances in the physical and futures prices when the price system exhibits narrow differentials. On another note, the Istmo and Maya oil prices generally do not react to the presence of temporary deviations in the long-term equilibrium relationship in the period prior when the coefficients of the error correction term are negative or close to zero, because physical prices require a significant increase to maintain market equilibrium.

For the case of the conditional variance equation estimates reported in Panel B, the significance of the estimated parameters reveal the existence of ARCH effects in the Mexican oil markets. This result means that past innovations have a positive and significant effect on current volatility of Mexican oil prices. For the cross-effects of short-term volatility transmission, the significance of the parameters only indicates volatility propagation effects in the WTI→Maya, WTI→Olmeca, and Brent→Olmeca relationships at 1 and 5%, with strong positive impacts running from WTI and Brent to Olmeca. This result shows that the Maya and Olmeca oil markets are evidently vulnerable, not only due to news in the own market, but also due to unexpected shocks in the international oil futures markets. This finding can be attributed to the mechanism adopted by the governmental authorities to set regulated Mexican oil prices, because Mexico as a producer of oil is a taker of prices by nature rather than the position of setter.

With respect to the direct long-term effects, all of the estimated coefficients are statistically significant at 1%, showing strong evidence for persistence in the volatility. The past volatility of the physical oil markets has a significant effect on the current volatility and requires a lot of time to decay. This fact is reflected most in the Brent→Maya (0.9973) and WTI→Maya (0.9942) relationships, and can be attributed to the different physical and chemical properties between Maya (22 API degrees and 3.3% sulfur) and the WTI (40 API degrees and 0.2% sulfur) and Brent (38 API degrees and 0.4% sulfur). So the highest prices are found in the international markets and the price differentials are widest there, too.

Looking at the long-term cross-market effects, the significance of the estimated coefficients at conventional levels reveals the existence of volatility transmission from the WTI and Brent futures markets to the Maya and Olmeca physical markets. In absolute terms, the strongest effects run from WTI and Brent to Olmeca, followed by the Brent→Maya relationship. This finding reveals the presence of high volatility in combination with the short- and long-term cross-market effects, prompting burgeoning uncertainty in current physical oil prices, especially for Olmeca crude, despite the fact that the sign of the coefficient is negative. This is because the value of the coefficient of the short-term cross-market effects is relatively larger than that of the coefficient of the long-term cross-market effects in the respective oil markets, meaning that the indirect ARCH effects are more important for predicting the future volatility of physical prices than the indirect GARCH effects.

Likewise, the direct asymmetry effect and that of the futures markets toward the physical oil markets, measured by the parameters δ _S and is significantly different than zero. This finding means that negative news will have a greater impact on volatility than good news. The asymmetry effect of bad news from the WTI futures market is 1.86, 3.77, and 3.11 times stronger than the impact of good news on the Maya, Istmo, and Olmeca oil markets, respectively. The effects of leveraging from the Brent futures market on the physical oil markets amounts to values of 1.67, 1.87, and 1.62 in the same order. This finding explains why energy policy designers in Mexico are concerned when the positive price trend does a drastic about-face in the short term.

Pursuant to the magnitude and statistical significance of the parameters, which measure the effects of short-term deviations in the equilibrium on the conditional variance of the physical oil markets, the error correction term only has a significant negative effect for the WTI→Olmeca relationship at a level of 10%. The negative value of the coefficient indicates that as the deviations between physical and futures prices climb to high values, volatility in the Olmeca oil market will decline at a slow pace and price behavior will be slightly less volatile over time.

Looking at the results estimated for the futures markets reported in Table 3, it appears that just as in the case of the physical markets, the current yields on WTI and Brent oil are affected by their own yields delayed by one period. In the case of the mean information transmission mechanism, the majority of the coefficients are positive and significant at 1%, indicating the existence of bilateral effects between the physical oil and oil futures markets. Comparing their coefficients, it emerges that . For example, the coefficient of the WTI→Istmo reltionship is 0.7824 compared to 0.4346 for the Istmo→WTI relationship. This is evidence of stronger and faster effects flowing from the futures markets to the Istmo and Maya physical markets, so they provide more information, which is transmitted from one market to the other. By contrast, changes in the Olmeca oil market have a stronger effect on the futures market pursuant to the size of their estimated coefficient, meaning more information for setting futures prices in the respective markets.

Table 3 Parameters Estimated from the Bivariate VEC-EGARCH Model 

Note: Q(18) and Q²(18) indicate the Ljung-Box test statistics for simple and squared residuals with 18 lags and p-values in parentheses. The terms *,**, and *** indicate significance at levels 1,5 and 10%, respectively. Standard errors reported in parentheses.

Source: Created by the author with information from the Bloomber database.

There are two external factors that could explain these results. The first is that Mexico was ranked twelfth in oil production worldwide in 2015, with a volume of approximately 2.3 billion barrels a day pursuant to the global ranking published by the Organization of Petroleum Exporting Countries (OPEC). The second justification is that Mexican oil exports rose to 427.9 million barrels with a customs value of 18.524 billion dollars approximately, placing Mexico in fourth place as a net supplier of crude to the United States measured in volume, after Canada, Saudi Arabia, and Venezuela. These figures are relevant to domestic economic growth because Mexico exercises some degree of control over international oil prices, at least in the short term, and, at the same time, has the ability to directly and significantly influence lower-quality oil prices.

The coefficient of the error correction term is negative and statistically significant at 1% for all futures yields with the exception of the Olmeca→WTI and Olmeca→Brent relationships. The reason for these results is attributed to the far-reaching difference in the physical and chemical characteristics of Maya and Istmo and international reference crudes. In this context, the WTI and Brent oil futures prices are adjusted and react to imbalances between physical and futures prices when the price system displays a big gap, because the futures prices are overvalued and require a significant increase to keep the long-term equilibrium.

Likewise, the findings do not support the hypothesis that the physical oil and oil futures markets following a progressive integration trend. There are various causes that could explain this outcome, such as the small transaction volumes in the Mexican oil market, transaction costs, and the price differential. Other important domestic factors relate to the fact that the structure of the Mexican oil industry market is completely monopolized by Petróleos Mexicanos (Pemex) and there is no futures and options market that could serve as a transparent hedging mechanism against exposure to the Mexican oil price risk.

The results of the conditional variance equations for the WTI and Brent futures yields are outlined in Panel B of Table 3. The estimators of the ARCH effects are all significant at 1% and positive, meaning that past innovations have a positive and significant effect on the current volatility of futures prices. Likewise, the statistical significance of the estimators reveals the presence of a high degree of persistence in volatility. The justification for this finding is in line with the high volumes moving in the respective futures markets. These financial instruments have not only been added to investment portfolios as an option diversify risk, but have also been added for speculative purposes, which has spurred increasing volatility in recent years.

In terms of the short-term cross-market effect, the results or the coefficients reveal that unexpected shocks from the physical oil markets can have a positive impact on the evolution of the current volatility in the futures markets, which can prompt price instability for the futures, in particular in the Istmo→WTI, Maya→Brent, and Istmo→Brent relationships. The existence of bilateral volatility transmission effects is only attained in the WTI↔Olmeca and Brent↔Olmeca relationships with stronger spillover effects, in terms of value, running from WTI and Brent to Olmeca, although the results are weak due to the specification error in the conditional variance of the futures yields. These findings are explained by the capacity of the futures markets to assimilate rapidly information from external events related to the Mexican energy reform.

Looking at the long-term cross-market effects, the coefficients indicate that the bilateral volatility transmission effect only occurs in the WTI↔Olmeca and Brent↔Olmeca relationships. In absolute terms, the volatility transmission process is strongest in the WTI→Olmeca and Olmeca→Brent relationships than the opposite effect. This fact confirms the significant function of the futures markets in the area of information transparency in the oil market, as well as the integration of the Olmeca oil market via platforms to negotiate futures on international reference crude. The explanation for these findings can be found in the liberalization of the energy sector approved by the Mexican congress to allow foreign investment in to explore deepwater and ultra-deepwater wells in the Gulf of Mexico; Mexico's joining to the International Energy Agency in 2015, in an attempt to initiate the process to improve the oil and tax regime for extraction.

Just as in the physical oil markets, the direct and indirect asymmetry effects on the volatility of futures yields are statistically significant at 1%. The leverage effects of the physical markets Maya, Istmo, and Olmeca on the futures markets amount to 1.91, 1.90, and 3.06 for the WTI and 2.33, 4.73, and 3.26 for the Brent, respectively, pursuant to the magnitude and statistical significance of the parameters of the error correction term in the conditional variance of the futures markets. The results reveal a mixed effect. For example, it is positive for the WTI→Maya, WTI→Istmo, and Brent→Maya relationships and negative for the WTI→Olmeca and Brent→Olmeca relationships. The positive value of the coefficients indicates that as the deviations between the physical and futures oil prices become smaller, volatility in the futures markets will rise at an accelerated pace, meaning that price behavior will become more volatile over time, and, as a result, it will be more difficult to predict, and vice versa.

The findings may hold relevance for the federal government and industrial consumers of Mexican oil, as they provide important information or develop cross-hedging strategies to help mitigate exposure to the oil price risk in times of extreme volatility. Moreover, these financial transactions will be more transparent and performed at lower transaction costs than hedging with sales options, characterized for having a riskier structure exacerbated by the risk of default from the counterparties. Likewise, the analysis of price and volatility transmission patterns may offer useful information for energy policy, in terms better understanding the vulnerability of the market to the opening of the oil sector to foreign investment. The availability of this information could also help energy policy designers to enact effective policies and a solid regulatory framework that guarantees the security of production and net exports in the Mexican crude basket, and, therefore, fosters competitiveness and sustainability in the country by ramping up its presence in international markets.

However, stakeholders in the futures and physical oil markets should be careful, because the results are too weak to explain the cross-market short- and long-term volatility effects. This is because several of the conditional variances did not manage to eliminate the autocorrelation in the standardized squared residuals as shown in Panel C in Tables 2 and 3. The Ljung-Box statistics with 18 lags indicate the presence of non-linear dependence on standardized squared innovations for the Brent→Maya, Brent→Istmo, Olmeca→WTI, and Olmeca→Brent relationships. This phenomenon characteristic of the financial series could be perhaps relaxed if structural changes were made to the bivariate VEC-EGARCH model.