Nonlinear relationships amongst the implied volatilities of crude oil and precious metals

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Nonlinear relationships amongst the implied volatilities of crude oil and precious metals ⁎

Anupam Duttaa, Elie Bourib, , David Roubaudc a

Department of Accounting & Finance, University of Vaasa, Finland USEK Business School, Holy Spirit University of Kaslik, Lebanon c Center for Energy and Sustainable Development, Montpellier Business School Montpellier, France b

A R T I C LE I N FO

A B S T R A C T

JEL classification: C22 G11 G15

Unlike most prior studies, we rely on implied volatility data from the Chicago Board of Options Exchange to investigate the presence of cointegration and nonlinear causality between the global market of crude oil and the markets of precious metal (gold and silver) and gold-miner stocks. We apply nonlinear ARDL bound and symmetric and asymmetric nonlinear Granger causality tests to examine cointegration and short-run “lead-lag” relationships, respectively. For comparison purposes, we also apply the linear ARDL models. The results show that the nonlinear ARDL models successfully capture the long-term linkages between oil and precious metal markets, while the linear ARDL approach mostly fails to do so. Results from the nonlinear Granger causality test suggest a bidirectional and symmetric effect between crude oil and gold markets. Investment and policy implications are discussed.

Keywords: Crude oil volatility Gold and silver volatility Gold-miners volatility NARDL Nonlinear causality

1. Introduction It is well known that crude oil price shocks have a substantial impact on the precious metal markets. Baffes (2007) investigates the impact of oil price shocks on 35 internationally-traded primary commodities and show that prices of precious metals react significantly to global oil price fluctuations. Soytas et al. (2009) argue that the price transmissions between the world oil market and precious metal markets have important implications for both policymakers and investors participating in emerging markets. In addition, Sari et al. (2010) report a strong short-run association between oil and precious metal price indexes. Ewing and Malik (2013) estimate the volatility spillover effects between oil and gold futures incorporating structural breaks. The authors find a strong volatility linkage between these two markets. Furthermore, Jain and Ghosh (2013) reveal that oil and precious metal prices tend to co-move in the long run. Recently, Behmiri and Manera (2015) show that precious metal prices respond asymmetrically to oil price shocks, whereas Bildirici and Turkmen (2015) highlight the nonlinear response of precious metal price returns to oil price shocks. More recently, Dutta (2017a) analyses the influence of oil market uncertainty on the precious and industrial metal prices. The author demonstrates that gold and silver prices are sensitive to oil volatility shocks. Furthermore, Kang et al. (2017) find bidirectional return and volatility spillovers between oil and precious metal markets. The

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authors further document that the impact of spillovers increases during the global financial crises. The above-mentioned results are not surprising given that metal markets are oil-intensive (Hammoudeh et al., 2004), suggesting that oil price risk could be a driving force for the metal industry in the long-run. For instance, Dutta (2017a) argues that when the oil market is highly volatile, investment in the gold market tends to increase, leading to a potential increase in gold prices. Jain and Ghosh (2013) argue that rising oil prices increase the level of inflation in oil importing countries, which in turn leads investors to purchase long gold investment as a way to hedge inflation. A common feature of the above-mentioned articles is their reliance on return series to assess the impact of oil shocks on precious metals. However, volatility linkages between oil and precious metals markets are also important for investors and policymakers regarding risk management decisions, especially from the perspective of forward-looking measures of volatility such as the Chicago Board of Options Exchange (CBOE) implied volatility indices. The latter represents a better predictor of future volatility than historical volatility measures (Maghyereh et al., 2016; Bouri et al., 2017a; Dutta et al., 2017). Accordingly, we explore the relationship between the implied volatility index of crude oil and the implied volatilities of precious metals (gold and silver) and gold miners markets. We choose to include silver and gold-miners given mixed evidence on the similarity between these two

Corresponding author. E-mail addresses: adutta@uwasa.fi (A. Dutta), [email protected] (E. Bouri), [email protected] (D. Roubaud).

https://doi.org/10.1016/j.resourpol.2018.04.009 Received 1 November 2017; Received in revised form 31 January 2018; Accepted 16 April 2018 0301-4207/ © 2018 Elsevier Ltd. All rights reserved.

Please cite this article as: Dutta, A., Resources Policy (2018), https://doi.org/10.1016/j.resourpol.2018.04.009

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data on implied volatility indexes. Section 3 outlines the ARDL bound tests and nonlinear symmetric and asymmetric test for non-causality. The empirical findings are discussed in Section 4, whereas the concluding remarks are given in Section 5.

Table 1 Descriptive statistics. OVX Panel A: Levels Mean 34.10 Standard deviation 11.73 Skewness 0.60 Kurtosis 3.10 Jarque-Bera Test 99.64*** Panel B: 1st difference Mean − 0.008 Standard deviation 1.94 Skewness 0.62 Kurtosis 37.57 Jarque-Bera Test 81,897.92***

GVZ

VXSLV

VXGDX

18.32 4.54 1.37 5.67 1003.41***

32.01 9.36 1.55 6.59 1543.16***

39.41 8.38 0.27 2.18 67.35***

− 0.005 1.21 1.77 21.23 23,580.05***

− 0.018 1.82 2.91 34.66 70,919.25***

− 0.006 1.72 0.61 12.02 5673.29***

2. Data We use the implied volatility indexes of crude oil (OVX), gold (GVZ), silver (VXSLV), and gold miners (VXGDX). Our sample period ranges from 16 March 2011 to 30 June 2017, yielding a total of 1643 daily observations. Notably, the starting date of the sample period depends on the availability of the related CBOE data. Similar to the US equity market VIX, the four implied volatility indices considered in this empirical study are used as indicators of risk in their respective markets. All four indices were introduced and computed by the CBOE to measure the market's expectation of 30-day volatility. Each of these volatility series is obtained by applying the (US) VIX methodology to the US options markets. For example, OVX and GVZ are constructed using the options on the United States Oil (USO) Fund and SPDR gold shares, respectively. Moreover, like the US VIX, the oil and metal implied volatility indexes use options spanning a wide range of strike prices. Table 1 reports the descriptive statistics of the four volatility indexes under investigation. Panel A focuses on the level series, while Panel B focuses on the differenced series. It seems that oil market is more volatile than metal markets, as evidenced by the corresponding standard deviations. The results also indicate that each of the series used is positively skewed. Except for the gold miners index, all the indices have kurtosis higher than 3, implying a leptokurtic distribution with asymmetric tails. The Jarque-Bera test further confirms that none of the series under study follows the normality assumption. Table 2 displays the Pearson correlation coefficients between oil and metal markets. There are significant positive contemporaneous correlations between all the volatility indexes, implying that the expected changes in the oil and metal volatilities tend to move in the same direction over the sample period. Such associations suggest the existence of close linkages among those implied volatility series. Furthermore, the highest correlation is observed between the implied volatility indices of gold and silver markets.

Notes: This table presents the descriptive statistics of daily closing values of CBOE oil volatility index (OVX), CBOE gold volatility index (GVZ), CBOE silver volatility index (VXSLV), and CBOE gold miners volatility index (VXGDX), from 16 March 2011 to 30 June 2017. The data consist 1643 daily observations. *** Indicates statistical significance at the 1% level.

assets and gold and, thus, on their ability to act as a substitute for gold. We employ nonlinear ARDL bound tests (henceforth, NARDL) in order to shed further light on the relationship between crude oil volatility and the volatilities of gold, silver, and goldminers. For comparison purposes, we also use linear ARDL bound tests. Additionally, we apply a nonlinear symmetric and asymmetric test for non-causality, proposed by Kyrtsou and Labys (2006) and Varsakelis and Kyrtsou (2008), with the purpose of investigating the short-run “lead-lag” relationships. The relationship between implied volatilities of the markets under study does not receive considerable attention in the existing literature.1 Exceptions include Liu et al. (2013) and Bouri et al. (2017b), although their results are somewhat mixed. Liu et al. (2013) do not find any evidence confirming that crude oil volatility affects gold volatility, whereas Bouri et al. (2017b) indicate that uncertainty information significantly flows from crude oil market to gold market. Note that each of these studies considers the application of a linear ARDL (autoregressive distributed lag) bound test to examine whether the volatility series are co-integrated, suggesting that such contradictory results could be attributed to the nonlinear structure of the variables. Behmiri and Manera (2015), and Kumar (2017) argue that the nonlinear link between crude oil and metal markets, which could arise due to the effects of economic conditions, may lead oil and precious metals to exhibit a nonlinear behavior over time. Additionally, economic and financial time series usually exhibit nonlinear patterns due to high volatility and crises, pointing toward the need for adopting nonlinear modeling techniques. In that sense, Jain and Biswal (2016) also argue that linear models may no longer be suitable due to the increasing tendency of commodity prices to behave like financial assets. Our findings show that the application of linear ARDL models fails to capture the long-term impact of oil price uncertainty on the volatilities of gold and silver. However, the nonlinear specification provides strong evidence of the positive effect of oil volatility on the implied volatilities of gold and silver markets. Furthermore, the results of nonlinear Granger causality tests support that the association between oil and gold markets appears to be nonlinear and asymmetric. The outcomes of our empirical analyses thus lead to the conclusion that expectations of higher volatility in the crude oil market drive expectations of higher volatility in the precious metal markets. The rest of the paper is structured as follows. Section 2 explains our

3. Methods 3.1. ARDL models The ARDL bound test has several attractive features. First, it can be applied regardless of whether or not the underlying variables are stationary, that is, I(0); integrated of order one, that is I(1); or fractionally integrated (Bouri et al., 2017b; Dutta, 2017b). Therefore, the ARDL bound test is preferred over the Engle–Granger cointegration approach which requires that all series must have a unique order of integration (Khalid et al., 2016). Second, the bound test is free from the spurious regression problem (Liu et al., 2013).2 Finally, all the testing equations are allowed to have different lags. The linear ARDL model considered in our empirical analysis has the following form: n

Δyt = ω +

n

∑ αi Δyt−i + ∑ βi Δxt−i + axt−1 + byt−1 + εt i=1

i=1

(1)

where y refers to the precious metal volatility index and x represents the OVX. In order to examine whether a co-integrating relationship exists between the variables, it is adequate to test H0 :a = b = 0 . The general F-statistics are further calculated and compared with two different sets of critical values provided by Pesaran et al. (2001). One of

1 As suggested by one of the reviewers, the causal mechanism underlying the link between the implied volatility indices in the commodity markets may not be straightforward. Theoretically higher demand for commodity will lead to an increase in the price for the commodity/options. The whole mechanism largely depends on the market hype, level of uncertainty, and thus, market timing.

2 Note that the ARDL bound test has a prerequisite that the variables under study should not be integrated of order 2 or higher.

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Table 2 Correlation coefficients.

Panel A: Levels OVX GVZ VXSLV VXGDX Panel B: 1st difference OVX GVZ VXSLV VXGDX

Yt = θ21 OVX

GVZ

VXSLV

VXGDX

1.00 0.28 0.26 0.58

1.00 0.81 0.48

1.00 0.23

1.00

1.00 0.22 0.33 0.34

1.00 0.67 0.52

1.00 0.52

1.00

these sets is used as the upper bound for purely I(1) series, while the other is used as the lower bound for purely I(0) series. Cointegration or long-run association is said to be present only if the computed F-statistic exceeds the upper bound critical value. In line with Shin et al. (2013), the nonlinear version of the ARDL (NARDL) approach can be defined as: n

i=1

(2)

where, m

x− =

=

m ∑i = 1 Δx i+

max(Δx i , 0) and

m

∑ Δxi− = ∑ i=1

=

m ∑i = 1

min(Δx i , 0)

i=1

Cointegration exists between the variables if H0 : a1 = a2 = b = 0 is rejected. Moreover, the asymmetric associated long-run parameters can a a be measured as θ+ = − b1 and θ− = − b2 . Notably, the NARDL approach has received considerable attention in the existing literature. Its application is advantageous as it allows testing the long-run and short-run asymmetries in the variables and is robust to small sample sizes (Kumar, 2017). In addition, the NARDL approach is preferred to the standard cointegration technique, as the former is flexible to different orders of integrations in the time series (Shin et al., 2013). Previous studies such as Bildirici and Turkmen (2015), Raza et al. (2016), and Kumar (2017) also consider this process in their empirical research.

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4.1. Results of unit root tests and bound tests Table 3 displays the findings of different unit root tests. Panel A reports the results for volatility series (levels), and Panel B exhibits the Table 3 Unit root test results.

One of the most popular methods to assess the lead-lag associations among different variables is the Granger's linear test for non-causality (Granger, 1969). Later, Hiemstra and Jones (1994) propose a nonlinear version of this test which, however, lacks power in large samples (Diks and Panchenko, 2006). In this research, we consider the application of an extended version of nonlinear Granger causality test, developed by Kyrtsou and Labys (2006) and Varsakelis and Kyrtsou (2008), by replacing the Vector Autoregression (VAR) structure of the Granger test with a Mackey Glass model to capture the nonlinear connections among the volatility indexes under study. Such an extended version of the nonlinear causality test is advantageous, since it does not suffer from power limitations with large samples (Jain and Biswal, 2016; Bouri et al., 2017b). For a bivariate case involving two variables Xt and Yt , the model used in our empirical investigations assumes the following form:

Xt − δ1 Y − γ11 Xt −1 + θ12 t − δc 22 − γ12 Yt −1 + vt 1+Xtc−1δ1 1+Yt − δ 2

(N − nfree −1)

4. Empirical results

3.2. Kyrtsou-Labys nonlinear symmetric and asymmetric non-causality test

Xt = θ11

(SR − SUR)/ nR ~Fn , SUR/(N − nfree −1) R

where, nfree defines the number of free parameters in the model, nR −1 indicates the number of parameters set to zero while testing the constrained model, and SR and SUR denote the sum of squared residuals in the restricted and unrestricted equations. Our study examines symmetric as well as asymmetric causal relationships. The symmetric causal relationship indicates the direction of causality among the variables but fails to indicate the type or size of the effect. In this paper, the asymmetric test is employed to assess the effect of positive or negative changes in the causal variable on the dependent variable. An increase (or decrease) in the causal variable might cause an increase (or decrease) in the dependent variable, which the asymmetric test will assist us in measuring. To test whether non-negative returns in series Y cause series X, an observation ( Xi , Yi ) is included for regression only if Yt − δ2≥0 . The test is then performed in a similar way as defined before. Testing the reverse causality adopts the same procedure with the order of the series reversed. Varsakelis and Kyrtsou (2008) document that asymmetric causality testing tends to improve the common symmetric causality test. The test provides further insights into the impact of the causal variable on the dependent variable.

n

i=1

x+

T=

∑ αi Δyt−i + ∑ (βi Δxt+−i + γi Δxt−−i) + a1 xt+−1 + a2 xt−−1 + byt−1

+ εt

(4)

where, θij and γij refer to the parameters to be estimated, and the residuals vt and μt are normally distributed. Each δi denotes integer delays, and each ci is a constant to be determined prior to estimation by maximizing the likelihood of the model. In our analysis, the majority of the models have a maximum likelihood, using a delay of one and a constant exponent of two. The nonlinear Granger causality test consists of two steps. In the first step, the unconstrained model is estimated using ordinary least squares (OLS) method. To test for Y causing X, in the second step, a constrained model with ‘θ12 = 0 ’ is estimated. The Kyrtsou-Labys test statistic can be derived from the sum of squared residuals of the constrained and unconstrained models, and it follows an F distribution. If the test statistic is higher than the critical value, we can reject the null hypothesis of Y not causing X. The test statistic is as follows:

Notes: This table presents the correlation matrix between daily closing values of CBOE oil volatility index (OVX), CBOE gold volatility index (GVZ), CBOE silver volatility index (VXSLV), and CBOE gold miners volatility index (VXGDX), from 16 March 2011 to 30 June 2017.

Δyt = ω +

Xt − δ1 Y − γ21 Xt −1 + θ22 t − δc 22 − γ22 Yt −1 + μt 1+Xtc−1δ1 1+Yt − δ 2

Panel A: Levels OVX GVZ VXSLV VXGDX Panel B: 1st difference OVX GVZ VXSLV VXGDX

ADF

PP

KPSS

− 2.84** − 4.91*** − 3.92*** − 4.08***

− 2.89** − 4.42*** − 3.33** − 3.46***

0.81*** 1.16*** 2.51*** 1.03***

− 26.51*** − 31.46*** − 41.45*** − 43.38***

− 45.90*** − 47.84*** − 44.54*** − 45.55***

0.06 0.04 0.02 0.05

Notes: This table presents the results from three unit root tests for the daily closing values of CBOE oil volatility index (OVX), CBOE gold volatility index (GVZ), CBOE silver volatility index (VXSLV), and CBOE gold miners volatility index (VXGDX), from 16 March 2011 to 30 June 2017. ADF (Augmented Dickey Fuller), PP (Phillips and Perron), KPSS (Kwiatkowski-Phillips-Schmidt-Shin), *** and ** indicate statistical significance at the 1% and 5% levels. respectively.

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For example, while using gold VIX (GVZ) as the dependent variable, the estimated long-run coefficients θ+ and θ− amount to 0.25 and 0.26. That is, a 1% growth in crude oil VIX will lead to a 0.25% increase in gold VIX, and a 1% fall will result in a 0.26% decline in gold VIX. Therefore, our findings reveal the asymmetric impact for positive changes. Similar results are also observed when silver VIX (VXSLV) acts as the dependent variable. Notably, the impact of negative OVX over the VIXs of gold and silver seems to be larger than that of positive OVX. Table 5 also presents the results of the long-term asymmetry tests for the pair of oil and gold (silver) series. More specifically, we test for H0 : θ+ = θ− using the Wald test. The findings of the Wald test suggest that the null hypothesis of symmetry is rejected at the 1% significance level for gold and silver markets, further confirming that OVX has asymmetric or heterogeneous effects on the levels of implied volatility of precious metal markets. In other words, variations in crude VIX are passed through to metal VIX in the long run for positive and negative changes in OVX. These results hence reveal that the long-term linkage between oil and precious metal volatility indices are stickier towards the upper side, which provides evidence of an asymmetric co-movement. Overall, our empirical analysis reveals a long-term association amongst the implied volatility indices of oil and the two precious metal markets. The fact that the relationship is positive suggests that an upturn in oil market uncertainty could cause a rise in the expected volatility of gold and silver markets. This finding is not surprising at all, given that when the global oil market is highly volatile, international investors move into the gold market due to its safe haven status, leading to an increase in its volatility and expected future volatility (Baur, 2012; Bouri et al., 2017b). Moreover, the long-run connection between oil and gold indices could also be attributed to the fact that gold and crude oil, as the representatives of the large commodity markets, are influenced by the same eco-political events (Bildirici and Turkmen, 2015). Besides, volatile oil price impacts economic growth negatively, which in turn, leads to reduction in asset prices. As a result, investors tend to move into gold investment as an alternative choice (Reboredo, 2013). The other precious metal, silver, is highly volatile like oil and is utilized in the auto industry, which consumes a great deal of crude oil (Sari et al., 2010; Dutta, 2017a). Therefore, uncertainty in crude oil price transmits risk to the silver market as well. Our findings thus claim that global oil price uncertainty could play a significant role in predicting volatility of precious metal markets in the long run. To sum up, the results of NARDL models provide strong evidence that oil and precious metal markets interact in a nonlinear way. Such findings are also in line with previous studies such as Narayan et al. (2010), Bildirici and Turkmen (2015), and Kumar (2017).

Table 4 Linear ARDL bound tests. Dependent variable

F-test

Decision

∆GVZ ∆VXSLV ∆VXGDX

5.03 5.69 6.19**

No cointegration No cointegration Cointegration exists

Notes: The critical F-statistic at the 5% level for model with all I (1) series is 5.73. See Table CI(iii) with k = 1 on page 300 of Pesaran et al. (2001). ** Indicates statistical significance at the 5% levels.

same for their first difference. We consider applying three different unit root tests: ADF, PP and KPSS tests. The null hypothesis of both the ADF and PP tests is that the data are not stationary, while that of the KPSS test assumes the opposite. Although we have mixed unit root results when observing the findings of Panel A, after differencing, all the series appear to be stationary. Hence, none of these series is integrated of order 2. Next the results of the linear ARDL bound tests are presented in Table 4. Prior to exploring these findings, it is worth mentioning that the optimal lag order is determined on the basis of Akaike information criterion. As discussed in Section 3.1, one advantage of using the ARDL procedure is that all the testing equations are allowed to have different lags. That is, when the three different series are chosen as the dependent variables in three models, the lag structure of the model could change (Bouri et al., 2017b). Once the appropriate lags have been chosen, we test for the autocorrelation amongst the residuals to verify whether the selected model is correctly fitted. The results of the bound tests reveal that cointegration is only present when the gold miners volatility index is considered as the dependent variable. Since the F-statistics in other cases do not exceed the I (1) bound critical value, we conclude that OVX does not have any longrun associations with GVZ or VXSLV. Overall, the results of our linear ARDL models provide evidence that oil and gold miners implied volatilities co-move in the long run. Such findings clearly demonstrate that uncertainty information in the crude oil market could be utilized to improve the forecast power of expected volatility in the gold miners market. We now focus on the findings of the nonlinear ARDL specifications as presented in Table 5. The main purpose of such nonlinear analyses is to investigate if the non-appearance of the long-run association between oil and precious metals could be attributed to the nonlinear structure of the variables. Observing these outcomes indicates that cointegration is now present, as the bound tests are highly significant at the 1% level. We thus conclude that, although the linear ARDL models support the null hypothesis of no cointegration, the application nonlinear ARDL models shows evidence of a long-term connection between oil and gold/silver markets. However, the nonlinear analysis indicates that the F-test is insignificant in the case of gold miners, suggesting the non-asymmetric linkage between oil and gold miners volatility series. Regarding the estimates of long-run coefficients, we report that in all the cases considered, the signs of θ+ and θ− are found to be positive.

4.2. Results of Kyrtsou-Labys tests Table 6 exhibits the symmetric and asymmetric results from nonlinear Granger causality tests.3 We now discuss the findings of the symmetric version of the nonlinear causality tests. These outcomes indicate that a change in gold VIX causes a change in OVX, but the causality from the opposite direction is found to be insignificant. That is, we find a unidirectional causality running from gold to oil market. Interestingly, we do not find any evidence that OVX impacts gold VIX when symmetric cases are considered. In addition, both silver VIX and gold miners VIX seem to get insulated from the influence of global oil price uncertainty. It follows that precious metal markets are not sensitive to oil volatility shocks. On the flip side, the information contained in gold VIX can be utilized to predict the expected volatility of international oil prices. Next, we proceed to the results of the asymmetric version of the

Table 5 Nonlinear ARDL bound tests. Dependent variable

F-test

Decision

θ+

θ−

Test of H0 : θ+ = θ−

∆GVZ

8.95***

0.25***

0.26***

6.88***

∆VXSLV

15.69***

0.47***

0.50***

17.29***

∆VXGDX

2.54

Cointegration exists Cointegration exists No cointegration

0.16

0.15

0.16

Notes: The critical F-statistic at the 1% level for model with all I (1) series is 6.36. See Table CI(iii) with k = 2 on page 300 of Pesaran et al. (2001). *** Indicates statistical significance at the 1% level.

3 Note that, according to Diebolt and Kyrtsou (2006), when nonlinear causality is detected, there exists a strong possibility that a small variation in one variable can lead to an abnormal behavior of the others.

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Table 6 Results from the Kyrtsou-Labys nonlinear causality test. Relation

Symmetric case F-statistic

Asymmetric F-statistic

Case (P) Coefficient

Asymmetric F-statistic

Case (N) Coefficient

∆OVX → ∆GVZ ∆GVZ → ∆OVX ∆OVX → ∆VXSLV ∆VXSLV → ∆OVX ∆OVX → ∆VXGDX ∆VXGDX → ∆OVX

1.62 6.70*** 0.31 0.27 1.29 0.47

4.35** 1.46 0.03 0.16 2.11 1.75

0.31 − 0.32 0.04 0.09 0.35 − 0.31

0.11 14.06*** 0.37 0.003 0.35 0.07

− 0.05 − 1.06 0.13 0.01 0.03 0.06

Notes: *** and ** indicate that the coefficient is significant at the 1% and 5% levels, respectively. P Case indicates a causality test with positive changes in the causal variable, whereas N Case indicates a causality test with negative changes in the causal variable.

investors and policymakers. Investors could use the output of our empirical investigation to properly predict the volatility of oil and metal markets. In particular, the information content of crude oil volatility index could be used while forecasting the metal price volatility as our findings support that changes in risk levels of oil market are strongly related to that of the gold and silver markets. Financial institutions could make use of our empirical results to predict the future trends in the volatility of the oil market and thus improve their hedging performance (Dutta, 2017a). Additionally, the results could attract those investors who make use of new financial tools to hedge oil price volatility risk and who are potentially interested in futures and option trading on the oil implied volatility index (Liu et al., 2013; Dutta et al., 2017). Since volatility transmission among different financial and commodity markets has practical implications for investors and financial market participants seeking to make optimal portfolio allocation decisions, the results of this study could be useful for identifying and implementing proper investment decisions (Noor and Dutta, 2017). Moreover, since the implied volatility derivatives are widely considered as risk management tools, investors and commodity hedgers can use these volatility derivatives in hedging the risk in important commodity markets such as gold and crude oil. The information content of oil implied volatilities in particular can be utilized when predicting the risk in precious metal markets. Overall, the results of this study have important implications for market participants in reducing the risk of their portfolios. Policymakers could exercise our findings to develop appropriate strategies in order to lessen the impact of oil price uncertainty. As such, they could increase the usage of alternative energies (e.g., clean and renewable energies) in order to minimize the dependency on crude oil market. Alternatively, governments can choose to tax the fossil fuel usage (Sadorsky, 2012), which should reduce the usage of crude oil and, therefore, increase the use of alternative energies. However, a word of caution is warranted here. Economic actors should bear in mind that the relationship in terms of implied volatility may be quite unstable and easily influenced by the expectations, market timing, and other macro measures exercised by the authorities. Therefore, the unstable nature of the relationship between implied volatility indices may undermine the above-mentioned predictability, especially during stress periods and extreme market conditions, suggesting the need to explore the relationship between the examined variables more via the use of advanced modeling techniques such as copulas. Further research can also be conducted to highlight the information content of exchange rate volatility while linking between oil and precious metal markets.

Kyrtsou–Labys test. Observing the results of the asymmetric case, we document several interesting findings. First, unlike the symmetric tests, asymmetric tests now show that there is a bidirectional causal linkage between oil and gold volatility series. In particular, the causality runs from positive changes in OVX to changes in gold VIX. That is, no causality has emerged for negative case. This finding simply indicates that the positive oil volatility shocks have a more pronounced impact than negative shocks. Moreover, the positive sign of the coefficient reveals that an upsurge in crude VIX causes an increase in gold VIX. This finding imitates that found from the NARDL approach. Second, causality runs from negative changes in gold VIX to changes in OVX. We further report that increases (decreases) in gold VIX lead to decreases (increases) in OVX, suggesting a negative linkage between these two indices. Bouri et al. (2017b) also document similar findings in their empirical work. Third, when oil-silver or oil-gold miners pair is considered, no causal connection appears to be statistically significant. This finding is also consistent with the symmetric case. On the whole, the results suggest that the association between oil and gold markets appears to be nonlinear and asymmetric. Notably, our study makes a novel extension to earlier papers such as Liu et al. (2013) and Bouri et al. (2017b) in several aspects. First, unlike these two previous works, which mainly concentrate on the relationship between oil and gold volatility indexes, we consider silver VIX and gold miners VIX in our empirical analysis as well. Second, as mentioned earlier, each of these articles adopts a linear ARDL approach, although energy commodities and important precious metals usually exhibit a nonlinear behavior over time. In this paper, we employ both linear and nonlinear versions of ARDL models and show that the connection between oil and metal markets appears to be nonlinear and asymmetric. However, our findings are consistent with Bouri et al. (2017b) in that we also document an asymmetric connection between oil and gold markets using a nonlinear Granger causality test. Taken together, the results of our empirical investigation provide statistical evidence that oil and precious metal markets correlate in a nonlinear manner. Such nonlinear and asymmetric linkages between oil and metal markets should be taken into account when modeling and forecasting the commodity price volatility. 5. Conclusions Unlike most prior studies, we investigated the causal association between global oil market and the markets of precious metals and gold miners using CBOE implied volatility indexes. We employed linear and nonlinear ARDL bound tests, capable of testing cointegration relationships, and nonlinear Granger causality test, capable of exploring the short-run “lead-lag” effects. We revealed that the application of a linear ARDL approach mostly fails to detect the long-term linkages, whereas the NARDL models successfully captured such linkages. In addition, the results of a nonlinear Granger causality test suggested a bidirectional causal link between oil and gold markets. Overall, we showed that oil and precious metal volatilities interact in a nonlinear manner. The findings of this study have important implications for both

References Baffes, J., 2007. Oil spills on other commodities. Resour. Policy 32, 126–134. Baur, D., 2012. Asymmetric volatility in the gold market. J. Altern. Investig. 14 (4), 26–38. Behmiri, N.B., Manera, M., 2015. The role of outliers and oil price shocks on volatility of metal prices. Resour. Policy 46, 139–150.

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