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Energy sector uncertainty decomposition: New approach based on implied volatilities
Applied Energy 248 (2019) 141–148
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Energy sector uncertainty decomposition: New approach based on implied volatilities Jussi Nikkinen1, Timo Rothovius
T
⁎
School of Accounting and Finance, University of Vaasa, Finland
HIGHLIGHTS
sector companies’ market uncertainty consists of two main components. • Energy oil uncertainty component (OUC) and stock market uncertainty component (SUC). • Crude crude oil uncertainty component is more important, and it is enhanced with Internet interest in crude oil. • The • The level of oil price and implied volatilities of oil or stock markets affect the weights. ARTICLE INFO
ABSTRACT
Keywords: Crude oil Energy company Uncertainty Volatility Risk
The source(s) of uncertainty for energy sector companies is of interest for managers and investors, both trying to manage the uncertainty. In this paper, we suggest decomposing this uncertainty into crude oil and stock market uncertainty components. Using time-series data on implied volatility indexes, we estimate the weights of the components (55% and 45%, respectively) by applying a maximum likelihood method. We find that the model accounts for 69% of the variability in the changes of energy sector uncertainty. Furthermore, we report that during high public interest in crude oil, measured by internet interest using crude oil related search terms, the weight of the crude oil (stock market) component increases (decreases), but when the price of oil or implied volatilities of crude oil or stock markets are high, it decreases (increases). Thus, we contribute by showing how energy sector companies’ market uncertainty can be divided into separate components; by suggesting how the weights of the components can be estimated using implied volatilities; and by providing empirical evidence on the effects of public interest and general crude oil and stock market conditions on the obtained weights.
1. Introduction Many of the World’s largest companies lie in the energy sector, such as China Petroleum & Chemical Corporation, Royal Dutch Shell, China National Petroleum Corporation, BP Plc and Exxon Mobil, of which even the smallest is included in the top 20 of the Fortune 500 companies. Given their importance, as well as the importance of oil price uncertainty in general for the economy, as explained for example in Eyden et al. [1], understanding the sources and dynamics of uncertainty associated with these companies is important for the companies themselves, but also for investors in managing the uncertainty and hedging against risks in the sector. For decades, the risks in the energy sector have been in the interest of research, because of their fundamental value for markets, societies and environment. For example, Chen et al. [2] report that political risk
of OPEC countries affects crude oil prices and their fluctuations. Tulloch et al. [3] claim that legislative changes aimed at liberalization, increase systematic risk exposure of the sector and reduce it as a defensive investment asset. Spada et al. [4] in turn discuss the usefulness of different risk measures in the evaluation of accident risks in the energy sector, whereas Restrepo et al. [5], explore the volatility spillovers and directional connectedness of oil firms and finds shock transmitters and receivers among them. Some previous research finds only weak evidence of relationship between oil price shocks and stock markets, for example Cong et al. [6] in Chinese stock market. Lopez [7] investigates the effect of scheduled news announcements on two implied volatility indexes, including the energy sector, concluding that news resolve market’s uncertainty. In contrast to previous research, we look at the risks of energy sector companies from another angle: What are the sources and dynamics of
Corresponding author at: University of Vaasa, Dept. of Accounting and Finance, P.O. Box 700, FIN-65101 Vaasa, Finland. E-mail addresses: [email protected] (J. Nikkinen), [email protected] (T. Rothovius). 1 University of Vaasa, Dept. of Accounting and Finance, P.O. Box 700, FIN-65101 Vaasa, Finland. ⁎
https://doi.org/10.1016/j.apenergy.2019.04.095 Received 22 December 2018; Received in revised form 10 April 2019; Accepted 16 April 2019 Available online 24 April 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.
Applied Energy 248 (2019) 141–148
J. Nikkinen and T. Rothovius
their market uncertainty. For this purpose, we employ implied volatility indexes, deduced from option markets. They measure energy and stock market’s view of the future volatility (uncertainty) during the maturity of the options. In this respect, our study is related to several recent papers using implied volatility indexes, among others Liu et al. [8], Dutta [9], and Nikkinen and Rothovius [10].2 In order to extend the existing literature, we investigate energy sector companies’ market uncertainty by postulating that it consists of two main components: the crude oil uncertainty component, OUC, and the market wide uncertainty, or the stock market component, SUC. Thus, the purpose of our paper is first, to show how the uncertainty of energy sector companies can be decomposed, second, to empirically measure their weights, and third, to investigate how these weights are affected by public interest in the sector. The basis for the decomposition is solid. Given that the stock market performance of energy sector companies is influenced by crude oil prices, the energy sector uncertainty must have a crude oil dependent component. Similarly, the performance of the energy companies is affected by the performance of business enterprises in general, so the energy sector uncertainty should depend on a stock market component. Thus, in order to understand the energy sector uncertainty fundamentally, it is important to realize this decomposition and overall dynamics of the phenomenon. The magnitudes of the OUC’s and SUC’s weights is an empirical question, which we address from a novel perspective as well, thus providing also methodological contribution to the existing energy literature.3 To estimate the weights, we propose utilizing timeseries data on changes in the corresponding implied variances. Furthermore, on top of decomposing energy sector uncertainty and calculating the weights, we extend the existing literature by studying the effect of public attention towards crude oil market. Previous studies on the subject, for example Guo and Ji [16], or recently Qadan and Nama [17] and Nikkinen and Rothovius [10], using measures inferred from internet searches, suggest that high search volumes manifest high interest in oil market at the time and highlight market participants’ need for new, meaningful information. This, along with variables describing general market conditions, such as oil price or volatility levels, will enable us to study dynamic changes in the weights of the uncertainty components. Our approach is completely novel, but related to the existing literature in the following way. Many of the previous studies, such as Tjaaland et al. [18], study the risk factors driving oil company stocks, and others, like Liu et al. [8] utilize the implied volatility series like crude oil (OVX), stock market (VIX), gold (GVZ), and euro vs. dollar exchange rate (EVZ) to examine the association of uncertainty across these markets. Dutta et al. [14] in turn use the OVX to investigate its’ impact on stock market volatilities in the Middle East and Africa. Dutta [9] investigates the lead lag relationships of the OVX and VIX pair-wise against energy sector uncertainty using Toda-Yamamoto test, and finds on a weekly basis that only the OVX causes energy sector uncertainty. Unlike Dutta [9], our perspective is to decompose the energy sector uncertainty directly into two uncertainty components. This enables us to assess the weights of the crude oil and general stock market uncertainty simultaneously, and on top of that, to show how the market conditions affect these weights. Furthermore, the results of Dutta [9] are contradictory to, for example, Liu et al. [8]. According to Dutta [9], the reason for this may be due to either using different causality tests, or the fact that the results are sample period sensitive. The conflicting evidence suggests that it might be advantageous to study the contemporaneous relationships instead, which we are able to do. Most recently, Nikkinen and Rothovius [10] model the behavior of the OVX
and VIX indexes at the Energy Information Administration (EIA) Weekly Petroleum Status Report (WPSR) release at the times of high and low internet attention in crude oil. Overall, these recent studies, along with many others, point out the relevance of examining various research questions on energy market related uncertainty. In order to measure the uncertainty of the energy sector companies, and the uncertainties of the crude oil and stock markets, we utilize the Chicago Board Option Exchange (CBOE) implied volatility indexes VXXLE, OVX and VIX. The VXXLE implied volatility index is based on the market prices of options on Energy Select Sertor Index (XLE) Exchange Traded Fund (ETF), which contains large energy sector companies, such as Exxon Mobil Corporation, Chevron Corporation, Schlumberger NV and Conoco Phillips. Thus, the VXXLE implied volatility index represents the future stock price uncertainty of the companies in the energy sector. The OVX is the crude oil ETF Volatility Index (also called the Oil VIX), which measures the market's expectation of future volatility of crude oil prices. The first official index of implied volatilities, the VIX, is a 30-day expected volatility of the U.S. stock market, derived from options on one of the most used stock market indexes, the S&P 500. All the other indexes are calculated in the similar manner as the VIX. While various implied volatility indexes and their relationships have attracted researchers’ attention for years,4 studies utilizing the VXXLE index are scarce, with only few above-cited exceptions, Dutta [9] and Lopez [7]. This provides also practical motivation to investigate the VXXLE index and provide further analysis based on it. The main implications of the paper are as follows. Because of the better understanding of energy sector uncertainty, its components and relevant sources, policy makers can benefit in managing economic risks, energy company managers can identify and hedge financial risks, and investors can model volatility in energy sector and thus, benefit in option pricing and cross-hedging volatility risks of energy sector companies. The same applies also for managers and investors in other sectors, especially in banking, where the financial risks are an important source of total risk. The reminder of the paper is organized as follows. Section 2 presents the model for energy sector uncertainty. Section 3 presents the data used, after what the results of the empirical analyses are provided in Section 4. Finally, Section 5 concludes the paper. 2. Model for energy sector uncertainty We postulate that energy sector uncertainty consists of two components, first, the crude oil uncertainty component (OUC) and second, the stock market uncertainty component (SUC). Both components are assumed to be linearly related to the energy sector uncertainty in the following way: 2 Energy, t
=
2 Crude _oil, t
+ (1
)
2 Stock _market , t
(1)
where represents the energy sector uncertainty expected by the 2 2 market participants at time t, and Crude _oil, t and Stock _market , t are the uncorrelated OUC and SUC, respectively, expected at time t. The terms and (1 ) are the weights of the OUC and SUC, respectively. In order to model the impact of the changes in the OUC and SUC on the energy sector uncertainty, the weights of the components needs to be estimated. Given that the implied volatility indexes VXXLE, OVX and VIX describe the expected uncertainty of the energy sector, crude oil and stock market, constant weights and (1 ) are estimated by applying the following empirical equation: 2 Energy, t
VXXLEt2 = where OVXt2
2
Other related studies are, among others, Maghyereh et al. [11], Campos et al. [12], Luo and Qin [13] and Dutta et al. [14]. 3 A similar type of approach is used by Hasanhodzic and Lo [15] to obtain linear clones to replicate risk exposures of hedge funds.
4
142
+
OVXt2 + (1
¯ t2 + ) VIX
t
(2)
VXXLEt2 log(VXXLEt2) log(VXXLEt2 1) , and ¯ t2 is obtained as a residual from log(OVXt2) log(OVXt2 1). VIX
See, e.g. [19] for early evidence.
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J. Nikkinen and T. Rothovius
a regression in which VIXt2 is explained by OVXt2 , implying that ¯ t2 are uncorrelated. This removes the effect of the OVXt2 and VIX crude oil uncertainty from the stock market uncertainty, since they are documented to be correlated (see, e.g., [8]). Similar restriction of the sum of the regression coefficients to unity is used by Hasanhodzic and Lo [15], for example, in constraining the beta coefficients of risk factors to obtain linear clones when replicating risk exposures of hedge funds. In our case, the weights and (1 ) multiplied by the respective percentage changes in OUC and SUC, determine the percentage change in the energy sector’s uncertainty. It is assumed that, i, t = i, t i i, t 1, where i is an autoregressive parameter and i, t is an error term modeled using the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle [20] and Bollerslev [21]. According to the model, the conditional variance, hi, t , is expressed as a function of past errors and the lagged conditional variances hi, t = i + i i2, t 1 + i hi, t 1, where i, t is then given by i, t = hi, t z i, t . The term z i, t is i.i.d. (independent and identically distributed) and modelled with the generalized error distribution (GED) as suggested by Nelson [22] and later used also in energy related research, for example by Fan, Zhang, Tsai and Wei [23] to estimate Value at Risk of crude oil price and its spillover effects. This specification is flexible, enabling wide range of shapes for the error distribution. The GED, normalized to have zero mean and unit variance, is defined by
ve
f ( t )=
2
The data consist of time series of the West Texas Intermediate (WTI) and Brent crude oil prices, and implied volatility indexes,6 the VXXLE, OVX and VIX, all from 16/3/2011 to 30/6/2017, yielding 1644 daily observations per each series. These data are sourced from the Thomson Reuters DataStream. Monthly Google Search Volume Indexes (SVI) for search terms “WTI” and “Brent” are used to measure the internet interest in crude oil market.7 The SVIs are obtained from the Google Trends, readily available on the Google web page.8 Fig. 1 illustrates the development of the crude oil price during the sample period. Price was at a relatively high level following the financial crisis, until the end of year 2013, when the oil market experienced a clear change in price regime. After that, the market can be characterized as a low price era. Fig. 2 presents the development of the Chicago Board Options Exchange (CBOE) implied volatility indexes used in the study. These are the VXXLE, OVX and VIX indexes, which represent energy sector, crude oil and stock market uncertainty, respectively. Of these indexes, the CBOE Volatility Index (VIX) was introduced already in 1993, and is based on the prices of the S&P 500 stock index options. It may be the most cited measure of risk in the equity markets, sort of “fear gauge”, around the world. The other two volatility indexes, the Oil Volatility Index (OVX) and Energy Sector ETF Volatility Index (VXXLE), were introduced in 2008 and 2013, respectively.9 The OVX and VXXLE measure the price uncertainty of their underlying markets in the similar manner to the VIX. The crude oil implied volatility index, OVX, also called the Oil VIX, is based on the price of options on the United States Oil Fund (USO), which is an Exchange Traded Fund (ETF) that follows the WTI light, sweet crude oil futures contracts. The USO itself has been under examination as well, for example by Agbeyegbe [31]. The VXXLE is calculated similarly, using the option prices on the energy sector ETF (XLE ETF). A visual inspection of Figs. 1 and 2 suggests that, the VXXLE, OVX and VIX indexes are correlated more with each other when the price of crude oil is relatively high, and the inter-dependence has been lower during low oil price era, starting from 2014. Overall, these indexes seem to develop in a similar manner, at least to some extent. Interestingly, the behavior of the VXXLE seems to reflect the behavior of the OVX and VIX indexes, but when the crude oil prices are low, the OVX is at a relatively higher level than the VIX, compared to high crude oil price era. All in all, the volatilities of energy sector companies, crude oil and stock markets have varied considerably during the past years. Table 1 presents the descriptive statistics of the three uncertainty measures used in the paper. Panel A reports the implied volatility indexes VXXLE, OVX, and VIX. Of these, the OVX has both the highest values and highest standard deviation. Interestingly though, the same variable is also closest to the normal distribution, meaning that the implied oil volatility does not have as many extreme values as the other series, and at the same time it is not as concentrated around the mean value. Panel B provides the corresponding logarithmic changes of implied VXXLEt2 log(VXXLEt2) log(VXXLEt2 1) , variances, defined as
(3)
(1/v )
where (·) is the gamma function and
=
3. Data used in the study
1 | / |v 2 t
2(v + 1)/ v
2/ v
changes in the uncertainty components OUC and SUC (ceteris paribus) on call and put option values, as well as the corresponding delta values.
(1/ v ) (3/ v )
is given by
1/2
(4)
and v is a parameter that determines the fatness of the tails [24,p. 668]. Furthermore, the GJR-GARCH type of variance specification with the GED is applied to test possible asymmetric consequences of positive and negative innovations.5 In the second step of our analyses, we relax the assumption of the constant weights and (1 ), by allowing to be some function t = f (·) . Specifically, we test the hypotheses that t is linearly related to certain Google search terms regarding crude oil market, reflecting the crude oil related internet interest (see, e.g. [10]), as well as a set of variables, which are the crude oil price and volatility levels, and the stock market volatility level, that characterize general market conditions. Hence, the dependence of the weights on the general market conditions takes the following form: t
=
0
+
(SVI VARIABLES)t (5)
+ (MARKET CONDITION VARIABLESti )
where SVI variables are based on the Google Search Volume Index and the market condition variables are as explained above. The variables and their empirical counterparts are defined in details in the following data section. The parameter values are obtained via maximum likelihood estimation. We present also practical implications of the estimation results for the market participants illustrated via simulations, based on the BlackScholes-Merton option pricing model. According to the model, the theoretical value for a European call option is given by ct = St N (d ) Xe r (T t ) N [d t )], where N (·) is a cumulative t (T normal distribution function and d = [ln
( ) + (r + St X
2 t
2
) (T
6 A comprehensive explanation of various implied volatility indexes can be found in Christoffersen et al. [26]. 7 Several studies use the Google Search Volume Index (SVI) as a measure of demand for information. It is used, for example, by Guo and Ji [16], Ji and Guo [27], Yao et al. [28] and Campos et al. [12], or most recently, Nikkinen and Rothovius [10], focusing on in crude oil markets and, Klemola et al. [29], focusing the stock markets and Wang et al. [30] focusing on the futures markets.. 8 http://www.google.com/trends. 9 The VXXLE data are available from 16/3/2011.
t )]/[ t
(T t )], and the call delta is equal to N (d ) . The corresponding values for European put options are obtained via the put-call parity condition. The following hypothetical examples illustrate the effects of percentage 5 Glosten et al. [25] suggest a GJR-GARCH model that can incorporate the asymmetric consequences of positive and negative innovations.
143
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J. Nikkinen and T. Rothovius
120
WTI crude oil price in $
100 80 60 40 20 0 2011
2012
2012
2013
2014
2015
2016
2017
2015
2016
2017
Year Fig. 1. WTI crude oil price.
90 80 70
Index value
60 50 40 30 20 10 0 2011
2012
2012
2013
2014
Year VXXLE
OVX
VIX
Fig. 2. Implied volatility indexes.
that the changes in implied oil variance are further away from the mean, and has more extreme (positive) changes. However, these differences are quite small. In the empirical analyses VXXLEt2 , OVXt2 , ¯ t2 are used. The VIX ¯ t2 is obtained as a residual from a reand VIX gression in which VIXt2 is explained by OVXt2 .
Table 1 Descriptive statistics of uncertainty measures. Panel A. CBOE implied volatility indexes (%)
Mean Median Std Dev Skewness Kurtosis Minimum Maximum
VXXLE
OVX
VIX
23.53 21.64 7.37 1.40 1.93 13.53 57.47
34.00 32.77 11.61 0.63 0.18 14.50 78.97
16.53 14.97 5.63 2.11 5.32 9.36 48.00
4. Empirical analysis Table 2 reports the empirical results on the weights of percentage changes in the crude oil uncertainty component OUC and the stock market uncertainty component SUC. The weight for the OUC is denoted ). by and the weight for the SUC can be simply calculated by (1 The estimates are provided for both GARCH(1,1)-GED and GJR-GARCH (1,1)-GED specifications. Both models are estimated with an autoregressive term. The results for the GARCH-GED show that the weights for the OUC and SUC are 0.55 and 0.45, respectively. This finding suggests that, regarding the energy sector uncertainty, the percentage change of the OUC has a slightly higher weight than that of the SUC. Thus, assuming equal-sized percentage changes in the uncertainty components, oil related uncertainty is more important for energy sector companies than stock market related uncertainty. However, the total effect on energy sector uncertainty is determined by both of these weights and the sizes of the percentage changes in the OUC and SUC. The R2 of the model is 0.69, indicating that these two components alone are able to explain quite a large proportion, more than two thirds, of the variability in the energy sector uncertainty.
Panel B. Logarithmic changes of implied variances (%)
Mean Median Std Dev Skewness Kurtosis Minimum Maximum
VXXLE
OVX
VIX
−0.07 −0.40 10.84 0.52 2.49 −42.77 58.54
−0.04 −0.39 9.62 0.86 12.09 −87.98 84.99
0.00 0.09 13.27 0.39 4.00 −76.10 74.40
OVXt2 log(OVXt2) log(OVXt2 1) , VIXt2 log(VIXt2) and log(VIXt2 1) . Contrary to Panel A, the change in implied oil variance is further away from the normality than that of the other series, meaning 144
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The results are shown in Table 3 for the search term “WTI”. The weight for the OUC range from 0.518 to 0.573 throughout the estimations. As expected, when the internet interest towards crude oil is high, the weight for the OUC is higher and that for the SUC lower. The statistically highly significant coefficient estimates for the dummy variable “WTI” vary between 0.062 and 0.127. However, extreme market conditions, characterized by the remaining explanatory variables, lowers the weight of the OUC, and the negative relationship is statistically highly significant. This means that during periods of high oil and stock market volatilities and high crude oil prices, the oil related uncertainty becomes less important. The R2s are quite stable and high, ranging from 0.69 to 0.70. Table 4 reports corresponding results for the search term “BRENT” instead of the “WTI”. The results for 0 are very close to the ones reported in Table 3. Depending on the specification, the coefficient estimate lies between 0.523 and 0.582. In all cases, the p-values are highly significant with values less than 0.001. Regarding the other variables, the results are well in line with the findings reported in Table 3, showing how the weight of the crude oil component is lowered by high volatilities and high oil price. To further elaborate our results, we implement an example on how the results can be used for the real applications by an experiment. Based on our estimations in Table 2, we assume that the change in energy ¯ t2 . sector volatility is determined by VXXLEt2 = 0.55 OVXt2 + 0.45 VIX We further assume that the options are 15% out-of-the money (i.e. the difference between the underlying asset price and the exercise price is 15%) and with one month time-to-maturity. The initial VXXLE volatility level is 23.53%, the mean of the sample. The continuously compounded risk-free interest rate is assumed to be one percent. Fig. 3 illustrates the effects of various combinations of percentage ¯ t2 (ceteris paribus) changes in the uncertainty components OVXt2 and VIX on a call option value. In the figure, the horizontal axis represents ¯ 2 , while the vertical axis provides percentage changes in OVX 2 and VIX the call values. As can be seen from the figure, an increase in either uncertainty component increases (ceteris paribus) the call value. However, for small percentage changes, the impact is relatively small in absolute terms, but even moderate changes can be substantial in relative terms. An increase in option value is further magnified if both uncertainty components increase at the same time, and for large changes in the components, the joint effect can be substantial. On the other hand, opposite changes in the components may also offset each others’ effect so that the total effect remains negligible. The effects of similar changes on call delta are important, since it is the key statistic in the delta-hedging scheme. The purpose of the delta
Table 2 Components of energy sector uncertainty. The reported results are estimated ¯ t2 + t , where OVXt2 + (1 ) VIX using the following model: VXXLEt2 = + VXXLEt2 log(VXXLEt2) log(VXXLEt2 1) , and OVXt2 log(OVXt2) log(OVXt2 1) . ¯ t2 is obtained as a residual from a regression in which VIXt2 is explained VIX by OVXt2 . i, t = i, t i i, t 1, where i is an autoregressive parameter and i, t is the error term which is modeled using a (GJR)-GARCH(1,1)-GED model. GARCH-GED
GJR-GARCH-GED
Variable
Estimate
t-value
Pr > |t|
Estimate
t-value
Pr > |t|
Intercept
−0.106 0.550 0.089 4.808 0.083 0.787
−1.07 63.70 3.82 2.74 3.52 12.63
0.2837 < 0.0001 0.0001 0.0062 0.0004 < 0.0001
1.310
−0.121 0.551 0.088 5.254 0.108 0.771 −0.041 1.311
−1.14 59.61 3.89 2.86 3.01 12.07 −1.01 20.46
0.2557 < 0.0001 0.0001 0.0044 0.0026 < 0.0001 0.3138 < 0.0001
115.68
< 0.0001
AR1 ARCH0 ARCH1 GARCH1
20.41
< 0.0001
Normality Test
115.59
< 0.0001
R Sq. log L
0.69 −5351
0.69 −5350
The estimates for ARCH1 and GARCH1 terms are 0.083 and 0.787, indicating stationarity. The estimate for is 1.310, indicating a peaked distribution relative to normal. This is also shown by the normality tests (H0: = 2; Chi-square statistics 115.59 and 115.68), which reject (with p-value < 0.0001) the null hypothesis of normality. The GJR-GARCH type of variance specification with the GED is applied to test possible asymmetric consequences of positive and negative innovations (see [25]). The estimate for is insignificant with pvalue of 0.314, which means that there is no reason to reject the basic GARCH-GED model. Thus, we report the remaining results based on that model. Next, we allow the weights of the uncertainty components to depend on the demand for crude oil related information and factors characterizing the market wide uncertainty. In model (5), 0 is a constant term and corresponds in Model (2). Other explanatory variables include a dummy variable for search term related to crude oil indicating the highest quartile of the searches (see [10], and dummy variables OVXh and OVXl, indicating the highest and the lowest quartiles of the OVX. VIXh and VIXl, as well as WTIh and WTIl, are dummy variables with similar definitions.
Table 3 Dependence of the component weights ( ) and (1 − ) on web search term “WTI” and market conditions. Basic model
Const. 0
“WTI” OVXh OVXl VIXh VIXl WTIh WTIl AR1 ARCH0 ARCH1 GARCH1 R Sq. log L
Model with OVX
Model with VIX
Model with WTI
Full model
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
−0.105 0.518 0.086
−0.97 44.31 3.78
0.334 < 0.001 0.000
−0.093 0.555 0.127 −0.096 −0.048
−0.82 33.20 5.71 −4.35 −1.93
0.410 < 0.001 < 0.001 < 0.001 0.054
−0.132 0.535 0.098
−1.24 46.90 6.15
0.216 < 0.001 < 0.001
−0.108 0.543 0.071
−0.95 33.48 3.18
0.340 < 0.001 0.002
−0.080 0.051
−4.83 2.22
< 0.001 0.027
−0.066 −0.016
−2.56 −0.61
0.011 0.540
−0.145 0.573 0.062 −0.008 −0.061 −0.084 0.054 −0.044 0.008
−1.34 31.85 2.93 −0.32 −2.21 −3.20 2.14 −1.97 0.31
0.181 < 0.001 0.004 0.749 0.027 0.001 0.033 0.049 0.753
0.092 5.438 0.093 0.756 1.315
3.63 2.66 3.59 10.30 20.08
0.000 0.008 0.000 < 0.001 < 0.001
0.089 4.492 0.084 0.793 1.323
3.63 2.57 3.48 12.42 20.20
0.000 0.010 0.001 < 0.001 < 0.001
0.089 5.364 0.089 0.758 1.333
3.36 2.37 3.44 9.23 19.79
0.001 0.018 0.001 < 0.001 < 0.001
0.089 4.478 0.084 0.794 1.311
4.14 2.61 3.54 12.60 20.35 0.69 −5342
< 0.001 0.009 0.000 < 0.001 < 0.001
0.085 1.253 0.039 0.926 1.326
3.35 3.04 2.89 42.69 20.25
0.001 0.002 0.004 < 0.001 < 0.001
0.69 −5337
0.69 −5327
145
0.69 −5338
0.70 −5321
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Table 4 Dependence of the component weights ( ) and (1 − ) on web search term “BRENT” and market conditions. Basic model
Const. 0
“BRENT” OVXh OVXl VIXh VIXl WTIh WTIl AR1 ARCH0 ARCH1 GARCH1 R Sq. log L
Model with OVX
Model with VIX
Model with WTI
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
−0.101 0.523 0.072
−0.91 39.99 3.37
0.364 < 0.001 0.001
−0.085 0.554 0.104 −0.083 −0.045
−0.74 31.73 3.94 −3.23 −1.93
0.460 < 0.001 < 0.001 0.001 0.054
−0.116 0.541 0.084
−1.04 32.3 3.89
0.300 < 0.001 0.000
−0.102 0.551 0.045
−0.96 41.65 1.87
0.336 < 0.001 0.061
−0.079 0.046
−3.64 1.64
0.000 0.102
−0.072 −0.002
−3.58 −0.08
0.000 0.934
−0.132 0.582 0.041 −0.002 −0.065 −0.091 0.052 −0.050 0.010
−1.17 30.54 1.49 −0.07 −2.34 −3.50 2.12 −2.19 0.38
0.242 < 0.001 0.135 0.941 0.020 0.001 0.034 0.029 0.707
0.093 5.333 0.088 0.762 1.323
3.5 2.61 3.6 10.38 20.13
0.001 0.009 0.000 < 0.001 < 0.001
0.089 4.470 0.079 0.796 1.331
3.6 2.58 3.49 12.55 20.46
0.000 0.010 0.001 < 0.001 < 0.001
0.090 5.573 0.088 0.754 1.335
3.49 2.29 3.41 8.74 19.71
0.001 0.022 0.001 < 0.001 < 0.001
0.092 4.641 0.085 0.789 1.312
3.81 2.56 3.50 12.03 20.40
0.000 0.010 0.001 < 0.001 < 0.001
0.087 4.384 0.078 0.801 1.317
0.69 −5344
3.36 2.30 3.24 11.49 20.19
0.001 0.021 0.001 < 0.001 < 0.001
0.69 −5338
0.69 −5331
hedging is to make a given position as immune as possible to small changes in the price of the underlying asset. Since the deltas themselves can be affected by changes in the implied volatilities, their behavior can be better understood by analyzing the effects of the uncertainty com¯ t2 on deltas. This is illustrated in Fig. 4, in which ponents OVXt2 and VIX an increase in either component increases the call delta. It suggest that the effect of one component is almost linear, thus the total effect of the components is determined to be almost a flat surface. Figs. 5 and 6 present the corresponding effects for put option values and their deltas, respectively. Analyzing out-of-the-money put options is central, since they are the ones that are commonly used for crash insurance purposes. Fig. 5 illustrates that the joint effect of the components can be substantial also for a put option. As is the case for the call deltas, according to Fig. 6, the put deltas behave in almost a linear fashion as well. Put together, empirical results are in line with our postulation. Thus, we can conclude that the energy sector companies’ uncertainty, measured from the market participants expectations manifested in option prices, consists of two components, the oil uncertainty component OUC
0.69 −5340
5. Conclusions The importance of energy sector for the world economy is evident, not only from the direct dependence of GDP growth on oil price, but also from the fact that many of the biggest corporations in the world operate in the energy sector. Thus, it is vital for researchers, both in the fields of energy and economics, as well as for practitioners (such as energy companies, hedgers and energy traders) and policy makers, to understand the sources and dynamics of uncertainty arising from energy sector and energy companies. Following this, we study the sources and dynamics of energy
0.09 0.08
0.06 0.05 0.04 0.03 0.02
40 % 15 % -10 %
0.01
48%
Change in stock market variance 146
-60 % 57%
39%
21%
30%
3%
12%
-35 % -6%
-15%
0
Change in crude oil variance
0.07
-60% -51% -42% -33% -24%
0.09-0.1 0.08-0.09 0.07-0.08 0.06-0.07 0.05-0.06 0.04-0.05 0.03-0.04 0.02-0.03 0.01-0.02 0-0.01
0.70 −5324
and the stock market uncertainty component SUC. Of these, the first is more important with 55% weight, provided that the percentage chances of both uncertainty components are assumed equal. Moreover, we can conclude that high general interest in crude oil increases the relative weight for the OUC. Finally, we document how these weights depend on the general crude oil and stock market conditions, especially in regard of high or low levels of volatility measures.
0.1
Call value
Full model
Fig. 3. A simulated illustration of the impact of the changes in implied crude oil and stock market volatilities (ceteris paribus) on a call option value. This figure illustrates a hypothetical impact of changes in the implied crude oil and stock market volatilities on out-of-the money (15%) call option values (ceteris paribus) assuming that the percentage change in energy sector volatility is determined by ¯ t2 . The opVXXLEt2 = 0.55 OVXt2 + 0.45 VIX tion values are calculated using the BlackScholes-Merton option pricing model assuming that the initial VXXLE volatility level is 23.53% (corresponding the mean value in the sample) and with one month time-to-maturity and with 1.0% continuously compounded interest rate. The horizontal axis represent percentage ¯ 2 . The vertical axis changes in OVX 2 and VIX gives the corresponding call values.
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0.14-0.16 0.12-0.14
0.16 0.14 0.12
0.1-0.12
0.1
0.08-0.1
0.08
0.06-0.08 0.04-0.06 0.02-0.04 0-0.02
0.06 0.04 40 % 15 % -10 %
0.02
-60 % 60%
44%
52%
28%
-35 % 36%
-60% -52% -44% -36% -28% -20% -12% -4% 4% 12% 20%
0
Change in crude oil variance
Delta
Fig. 4. A simulated illustration of the impact of the changes in implied crude oil and stock market volatilities (ceteris paribus) on a call delta. This figure illustrates a hypothetical impact of changes in the implied crude oil and stock market volatilities on out-of-the money (15%) call delta (ceteris paribus) assuming that the percentage change in energy sector volatility is determined ¯ t2 . The by VXXLEt2 = 0.55 OVXt2 + 0.45 VIX deltas are calculated using the Black-ScholesMerton option pricing model assuming that the initial VXXLE volatility level is 23.53% (corresponding the mean value in the sample) and with one month time-to-maturity and with 1.0% continuously compounded interest rate. The horizontal axis represent percentage changes in ¯ 2 . The vertical axis gives the corOVX 2 and VIX responding delta values.
Change in stock market variance companies’ market uncertainty, measured by energy market participants’ view of the future uncertainty. Our novel purpose is to extend the existing literature by investigating the energy sector companies’ market uncertainty by dividing it into separate components, the crude oil uncertainty component (OUC) and the market wide uncertainty of the stock market component (SUC). Furthermore, we suggest how the weights for these components can be estimated by using implied volatilities. Finally, we show how public interest in oil market affects the weights of the components, along with general crude oil and stock market conditions. Our empirical results, utilizing several implied volatility series, such as the one on energy sector companies (VXXLE), reveal that, weight of for the percentage change in the OUC is higher than that of SUC in explaining the energy sector uncertainty (55% vs. 45%), the estimates
Put value
being statistically highly significant. Together, these components can explain 69% of the variability in the energy sector uncertainty. Furthermore, we show how the public attention, measured by internet searches with crude oil related search terms, affect the weights in crude oil market so that high demand for information increases the relative weight of the OUC and decreases that of the SUC. These weights are also affected by general crude oil and stock market conditions, such as high crude oil price, or low and high levels of the implied volatilies of crude oil or stock markets. Finally, we present illustrative simulations, suggesting (ceteris paribus) that even moderate percentage changes in the values of the uncertainty components can lead to a substantial effect on option values. In derivatives markets, the economic effect can be significant, depending on the other characteristics of the contracts. The paper contributes to the existing literature both theoretically
0.09 0.08
0.07-0.08 0.06-0.07
0.07 0.06
0.05-0.06
0.05
0.04-0.05
0.04
0.03-0.04
0.03
0.02-0.03 0.01-0.02 0-0.01
0.02
60 % 40 % 20 % 0% -20 % -40 % -60 %
0.01 0 -60%
-40%
-20%
0%
20%
40%
60%
Change is stock market variance 147
Change in crude oil variance
0.08-0.09
Fig. 5. A simulated illustration of the impact of the changes in implied crude oil and stock market volatilities (ceteris paribus) on put option value. This figure illustrates a hypothetical impact of changes in the implied crude oil and stock market volatilities on out-of-the money (15%) put option values (ceteris paribus) assuming that the percentage change in energy sector volatility is determined by ¯ t2 . The opVXXLEt2 = 0.55 OVXt2 + 0.45 VIX tion values are calculated using the BlackScholes-Merton option pricing model assuming that the initial VXXLE volatility level is 23.53% (corresponding the mean value in the sample) and with one month time-to-maturity and with 1.0% continuously compounded interest rate. The horizontal axis represent percentage ¯ 2 . The vertical axis changes in OVX 2 and VIX gives the corresponding put values.
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0
-0.02
-0.04
-0.02-0 -0.06
-0.06--0.04 -0.08--0.06
-0.08
-0.1--0.08 -0.12--0.1
-0.1
-0.12 -60 %
-40 %
-20 %
0%
20 %
40 %
Change in crude oil variance
-0.04--0.02
-60% -40% -20% 0% 20% 40% 60% 60 %
Fig. 6. A simulated illustration of the impact of the changes in implied crude oil and stock market volatilities (ceteris paribus) on put delta. This figure illustrates a hypothetical impact of changes in the implied crude oil and stock market volatilities on out-of-the money (15%) put delta (ceteris paribus) assuming that the percentage change in energy sector volatility is determined ¯ t2 . The by VXXLEt2 = 0.55 OVXt2 + 0.45 VIX deltas are calculated using the Black-ScholesMerton option pricing model assuming that the initial VXXLE volatility level is 23.53% (corresponding the mean value in the sample) and with one month time-to-maturity and with 1.0% continuously compounded interest rate. The horizontal axis represent percentage changes in ¯ 2 . The vertical axis gives the corOVX 2 and VIX responding delta values.
Change in stock market value and empirically, by presenting a novel idea of dividing the energy sector uncertainty into components, by proposing a research design to compute the weights for those components based on implied volatilities, and by providing empirical evidence to support these ideas and showing how different variables, such as public interest, level of oil price, or level of implied volatilities in oil and stock markets affect the proposed weights. Thus, our paper provides important implications for policy makers, in order to manage economic risks; for energy companies, to identify and hedge for financial risks; and for practitioners, to model volatility, option pricing and to cross-hedge volatility risks of energy sector companies.
empirical analysis of implied volatility index. Energy 2013;55:860–8. [9] Dutta A. Oil and energy sector stock markets: an analysis of implied volatility indexes. J Multinational Financ Manage 2018;44:61–8. [10] Nikkinen J, Rothovius T. The EIA WPSR release, OVX and crude oil internet interest. Energy 2019;166:131–41. [11] Maghyereh A, Awartani B, Bouri E. The directional volatility connectedness between crude oil and equity markets: new evidence from implied volatility indexes. Energy Econ 2016;57:78–93. [12] Campos I, Cortazar G, Reyes T. Modeling and predicting oil VIX: Internet search volume versus traditional mariables. Energy Econ 2017;66:194–204. [13] Luo X, Qin S. Oil price uncertainty and Chinese stock returns: new evidence from the oil volatility index. Financ Res Lett 2017;20:29–34. [14] Dutta A, Nikkinen J, Rothovius T. Impact of oil price uncertainty on Middle East and African stock markets. Energy 2017;123:189–97. [15] Hasanhodzic J, Lo A. Can hedge-fund returns be replicated? The linear case. J Investment Manage 2007;5:5–45. [16] Guo J, Ji Q. How does market concern derived from the internet affect oil prices? Appl Energy 2013;12:1536–43. [17] Qadan M, Nama H. Investor sentiment and the price of oil. Energy Econ 2017;69:42–58. [18] Tjaaland S, Westgaard S, Osmundsen P, Frydenberg S. Oil and gas risk factor sensitivies for US energy companies. J Energy Develop 2016;41:135–73. [19] Nikkinen J, Sahlström P. International transmission of uncertainty implicit in stock index option prices. Global Financ J 2004;15:1–15. [20] Engle R. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 1982;50:987–1007. [21] Bollerslev T. Generalized autoregressive conditional heteroscedasticity. J Economet 1986;31:307–27. [22] Nelson D. Conditional heteroscedasticity in asset returns: a new approach. Econometrica 1991;59:347–70. [23] Fan Y, Zhang Y-J, Tsai H-T, Wei Y-M. Estimating ‘Value at Risk’ of crude oil price and its spillover effect using the GED-GARCH approach. Energy Econ 2008;30:3156–71. [24] Hamilton J. Time series analysis. Princeton University Press; 1994. [25] Glosten L, Jagannathan R, Runkle D. On the relation between the expected value and the volatility of the nominal excess return on stocks. J Financ 1993;48:1779–801. [26] Christoffersen P, Jacobs K, Chang B. Forecasting with option-implied information. Handbook Econ Forecast 2012;2:581–656. [27] Ji Q, Guo J. Oil price volatility and oil-related events: an internet concern study perspective. Appl Energy 2015;137:256–64. [28] Yao T, Zhang Y-J, Ma C-Q. How does investor attention affect international crude oil prices? Appl Energy 2017;205:336–44. [29] Klemola A, Nikkinen J, Peltomäki J. Changes in investors’ market attention and near-term stock market returns. J Behav Financ 2016;17:18–30. [30] Wang X, Ye Q, Zhao F, Kou Y. Investor sentiment and the Chinese index futures market: Evidence from the internet search. J Futures Markets 2018;38:468–77. [31] Agbeyegbe T. An inverted U-shaped crude oil price return-implied volatility relationship. Rev Financ Econ 2015;27:28–45.
Acknowledgements Jussi Nikkinen expresses his gratitude for support from the OP Financial Group Research Foundation. We would also like to thank the editor-in-chief, professor Jinyue Yan, associate editor, professor YiMing Wei, and two anonymous referees for their valuable comments, which helped to improve the paper substantially. Any remaining errors are in our responsibility. References [1] Eyden R, Difeto M, Gupta R, Wohar M. Oil price volatility and economic growth: evidence from advance economies using more than a century’s data. Appl Energy 2019;233:612–21. [2] Chen H, Liao H, Tang B-J, Wei Y-M. Impacts of OPEC’s political risk on the international crude oil prices: an empirical analysis based on the SVAR models. Energy Econ 2016;57:42–9. [3] Tulloch D, Diaz-Rainey I, Premachandra I. The impact of regulatory change on EU energy utility returns: the three liberalization packages. Appl Econ 2018;50:957–72. [4] Spada M, Paraschiv F, Burgherr P. A comparison of risk measures for accidents in the energy sector and their implications on decision-making strategies. Energy 2018;154:277–88. [5] Restrepo N, Uribe J, Manotas D. Financial risk network architecture of energy firms. Appl Energy 2018;215:630–42. [6] Cong R-G, Wei Y-M, Jiao J-L, Fan Y. Relationships between oil price shocks and stock market: an empirical analysis from China. Energy Policy 2008;36:3544–53. [7] Lopez R. The behaviour of energy-related volatility indices around scheduled news announcements: implications for variance swap investments. Energy Econ 2018;72:356–64. [8] Liu M, Ji Q, Fan Y. How does oil market uncertainty interact with other markets? An
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Energy sector uncertainty decomposition: New approach based on implied volatilities Jussi Nikkinen1, Timo Rothovius
T
⁎
School of Accounting and Finance, University of Vaasa, Finland
HIGHLIGHTS
sector companies’ market uncertainty consists of two main components. • Energy oil uncertainty component (OUC) and stock market uncertainty component (SUC). • Crude crude oil uncertainty component is more important, and it is enhanced with Internet interest in crude oil. • The • The level of oil price and implied volatilities of oil or stock markets affect the weights. ARTICLE INFO
ABSTRACT
Keywords: Crude oil Energy company Uncertainty Volatility Risk
The source(s) of uncertainty for energy sector companies is of interest for managers and investors, both trying to manage the uncertainty. In this paper, we suggest decomposing this uncertainty into crude oil and stock market uncertainty components. Using time-series data on implied volatility indexes, we estimate the weights of the components (55% and 45%, respectively) by applying a maximum likelihood method. We find that the model accounts for 69% of the variability in the changes of energy sector uncertainty. Furthermore, we report that during high public interest in crude oil, measured by internet interest using crude oil related search terms, the weight of the crude oil (stock market) component increases (decreases), but when the price of oil or implied volatilities of crude oil or stock markets are high, it decreases (increases). Thus, we contribute by showing how energy sector companies’ market uncertainty can be divided into separate components; by suggesting how the weights of the components can be estimated using implied volatilities; and by providing empirical evidence on the effects of public interest and general crude oil and stock market conditions on the obtained weights.
1. Introduction Many of the World’s largest companies lie in the energy sector, such as China Petroleum & Chemical Corporation, Royal Dutch Shell, China National Petroleum Corporation, BP Plc and Exxon Mobil, of which even the smallest is included in the top 20 of the Fortune 500 companies. Given their importance, as well as the importance of oil price uncertainty in general for the economy, as explained for example in Eyden et al. [1], understanding the sources and dynamics of uncertainty associated with these companies is important for the companies themselves, but also for investors in managing the uncertainty and hedging against risks in the sector. For decades, the risks in the energy sector have been in the interest of research, because of their fundamental value for markets, societies and environment. For example, Chen et al. [2] report that political risk
of OPEC countries affects crude oil prices and their fluctuations. Tulloch et al. [3] claim that legislative changes aimed at liberalization, increase systematic risk exposure of the sector and reduce it as a defensive investment asset. Spada et al. [4] in turn discuss the usefulness of different risk measures in the evaluation of accident risks in the energy sector, whereas Restrepo et al. [5], explore the volatility spillovers and directional connectedness of oil firms and finds shock transmitters and receivers among them. Some previous research finds only weak evidence of relationship between oil price shocks and stock markets, for example Cong et al. [6] in Chinese stock market. Lopez [7] investigates the effect of scheduled news announcements on two implied volatility indexes, including the energy sector, concluding that news resolve market’s uncertainty. In contrast to previous research, we look at the risks of energy sector companies from another angle: What are the sources and dynamics of
Corresponding author at: University of Vaasa, Dept. of Accounting and Finance, P.O. Box 700, FIN-65101 Vaasa, Finland. E-mail addresses: [email protected] (J. Nikkinen), [email protected] (T. Rothovius). 1 University of Vaasa, Dept. of Accounting and Finance, P.O. Box 700, FIN-65101 Vaasa, Finland. ⁎
https://doi.org/10.1016/j.apenergy.2019.04.095 Received 22 December 2018; Received in revised form 10 April 2019; Accepted 16 April 2019 Available online 24 April 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.
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their market uncertainty. For this purpose, we employ implied volatility indexes, deduced from option markets. They measure energy and stock market’s view of the future volatility (uncertainty) during the maturity of the options. In this respect, our study is related to several recent papers using implied volatility indexes, among others Liu et al. [8], Dutta [9], and Nikkinen and Rothovius [10].2 In order to extend the existing literature, we investigate energy sector companies’ market uncertainty by postulating that it consists of two main components: the crude oil uncertainty component, OUC, and the market wide uncertainty, or the stock market component, SUC. Thus, the purpose of our paper is first, to show how the uncertainty of energy sector companies can be decomposed, second, to empirically measure their weights, and third, to investigate how these weights are affected by public interest in the sector. The basis for the decomposition is solid. Given that the stock market performance of energy sector companies is influenced by crude oil prices, the energy sector uncertainty must have a crude oil dependent component. Similarly, the performance of the energy companies is affected by the performance of business enterprises in general, so the energy sector uncertainty should depend on a stock market component. Thus, in order to understand the energy sector uncertainty fundamentally, it is important to realize this decomposition and overall dynamics of the phenomenon. The magnitudes of the OUC’s and SUC’s weights is an empirical question, which we address from a novel perspective as well, thus providing also methodological contribution to the existing energy literature.3 To estimate the weights, we propose utilizing timeseries data on changes in the corresponding implied variances. Furthermore, on top of decomposing energy sector uncertainty and calculating the weights, we extend the existing literature by studying the effect of public attention towards crude oil market. Previous studies on the subject, for example Guo and Ji [16], or recently Qadan and Nama [17] and Nikkinen and Rothovius [10], using measures inferred from internet searches, suggest that high search volumes manifest high interest in oil market at the time and highlight market participants’ need for new, meaningful information. This, along with variables describing general market conditions, such as oil price or volatility levels, will enable us to study dynamic changes in the weights of the uncertainty components. Our approach is completely novel, but related to the existing literature in the following way. Many of the previous studies, such as Tjaaland et al. [18], study the risk factors driving oil company stocks, and others, like Liu et al. [8] utilize the implied volatility series like crude oil (OVX), stock market (VIX), gold (GVZ), and euro vs. dollar exchange rate (EVZ) to examine the association of uncertainty across these markets. Dutta et al. [14] in turn use the OVX to investigate its’ impact on stock market volatilities in the Middle East and Africa. Dutta [9] investigates the lead lag relationships of the OVX and VIX pair-wise against energy sector uncertainty using Toda-Yamamoto test, and finds on a weekly basis that only the OVX causes energy sector uncertainty. Unlike Dutta [9], our perspective is to decompose the energy sector uncertainty directly into two uncertainty components. This enables us to assess the weights of the crude oil and general stock market uncertainty simultaneously, and on top of that, to show how the market conditions affect these weights. Furthermore, the results of Dutta [9] are contradictory to, for example, Liu et al. [8]. According to Dutta [9], the reason for this may be due to either using different causality tests, or the fact that the results are sample period sensitive. The conflicting evidence suggests that it might be advantageous to study the contemporaneous relationships instead, which we are able to do. Most recently, Nikkinen and Rothovius [10] model the behavior of the OVX
and VIX indexes at the Energy Information Administration (EIA) Weekly Petroleum Status Report (WPSR) release at the times of high and low internet attention in crude oil. Overall, these recent studies, along with many others, point out the relevance of examining various research questions on energy market related uncertainty. In order to measure the uncertainty of the energy sector companies, and the uncertainties of the crude oil and stock markets, we utilize the Chicago Board Option Exchange (CBOE) implied volatility indexes VXXLE, OVX and VIX. The VXXLE implied volatility index is based on the market prices of options on Energy Select Sertor Index (XLE) Exchange Traded Fund (ETF), which contains large energy sector companies, such as Exxon Mobil Corporation, Chevron Corporation, Schlumberger NV and Conoco Phillips. Thus, the VXXLE implied volatility index represents the future stock price uncertainty of the companies in the energy sector. The OVX is the crude oil ETF Volatility Index (also called the Oil VIX), which measures the market's expectation of future volatility of crude oil prices. The first official index of implied volatilities, the VIX, is a 30-day expected volatility of the U.S. stock market, derived from options on one of the most used stock market indexes, the S&P 500. All the other indexes are calculated in the similar manner as the VIX. While various implied volatility indexes and their relationships have attracted researchers’ attention for years,4 studies utilizing the VXXLE index are scarce, with only few above-cited exceptions, Dutta [9] and Lopez [7]. This provides also practical motivation to investigate the VXXLE index and provide further analysis based on it. The main implications of the paper are as follows. Because of the better understanding of energy sector uncertainty, its components and relevant sources, policy makers can benefit in managing economic risks, energy company managers can identify and hedge financial risks, and investors can model volatility in energy sector and thus, benefit in option pricing and cross-hedging volatility risks of energy sector companies. The same applies also for managers and investors in other sectors, especially in banking, where the financial risks are an important source of total risk. The reminder of the paper is organized as follows. Section 2 presents the model for energy sector uncertainty. Section 3 presents the data used, after what the results of the empirical analyses are provided in Section 4. Finally, Section 5 concludes the paper. 2. Model for energy sector uncertainty We postulate that energy sector uncertainty consists of two components, first, the crude oil uncertainty component (OUC) and second, the stock market uncertainty component (SUC). Both components are assumed to be linearly related to the energy sector uncertainty in the following way: 2 Energy, t
=
2 Crude _oil, t
+ (1
)
2 Stock _market , t
(1)
where represents the energy sector uncertainty expected by the 2 2 market participants at time t, and Crude _oil, t and Stock _market , t are the uncorrelated OUC and SUC, respectively, expected at time t. The terms and (1 ) are the weights of the OUC and SUC, respectively. In order to model the impact of the changes in the OUC and SUC on the energy sector uncertainty, the weights of the components needs to be estimated. Given that the implied volatility indexes VXXLE, OVX and VIX describe the expected uncertainty of the energy sector, crude oil and stock market, constant weights and (1 ) are estimated by applying the following empirical equation: 2 Energy, t
VXXLEt2 = where OVXt2
2
Other related studies are, among others, Maghyereh et al. [11], Campos et al. [12], Luo and Qin [13] and Dutta et al. [14]. 3 A similar type of approach is used by Hasanhodzic and Lo [15] to obtain linear clones to replicate risk exposures of hedge funds.
4
142
+
OVXt2 + (1
¯ t2 + ) VIX
t
(2)
VXXLEt2 log(VXXLEt2) log(VXXLEt2 1) , and ¯ t2 is obtained as a residual from log(OVXt2) log(OVXt2 1). VIX
See, e.g. [19] for early evidence.
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a regression in which VIXt2 is explained by OVXt2 , implying that ¯ t2 are uncorrelated. This removes the effect of the OVXt2 and VIX crude oil uncertainty from the stock market uncertainty, since they are documented to be correlated (see, e.g., [8]). Similar restriction of the sum of the regression coefficients to unity is used by Hasanhodzic and Lo [15], for example, in constraining the beta coefficients of risk factors to obtain linear clones when replicating risk exposures of hedge funds. In our case, the weights and (1 ) multiplied by the respective percentage changes in OUC and SUC, determine the percentage change in the energy sector’s uncertainty. It is assumed that, i, t = i, t i i, t 1, where i is an autoregressive parameter and i, t is an error term modeled using the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle [20] and Bollerslev [21]. According to the model, the conditional variance, hi, t , is expressed as a function of past errors and the lagged conditional variances hi, t = i + i i2, t 1 + i hi, t 1, where i, t is then given by i, t = hi, t z i, t . The term z i, t is i.i.d. (independent and identically distributed) and modelled with the generalized error distribution (GED) as suggested by Nelson [22] and later used also in energy related research, for example by Fan, Zhang, Tsai and Wei [23] to estimate Value at Risk of crude oil price and its spillover effects. This specification is flexible, enabling wide range of shapes for the error distribution. The GED, normalized to have zero mean and unit variance, is defined by
ve
f ( t )=
2
The data consist of time series of the West Texas Intermediate (WTI) and Brent crude oil prices, and implied volatility indexes,6 the VXXLE, OVX and VIX, all from 16/3/2011 to 30/6/2017, yielding 1644 daily observations per each series. These data are sourced from the Thomson Reuters DataStream. Monthly Google Search Volume Indexes (SVI) for search terms “WTI” and “Brent” are used to measure the internet interest in crude oil market.7 The SVIs are obtained from the Google Trends, readily available on the Google web page.8 Fig. 1 illustrates the development of the crude oil price during the sample period. Price was at a relatively high level following the financial crisis, until the end of year 2013, when the oil market experienced a clear change in price regime. After that, the market can be characterized as a low price era. Fig. 2 presents the development of the Chicago Board Options Exchange (CBOE) implied volatility indexes used in the study. These are the VXXLE, OVX and VIX indexes, which represent energy sector, crude oil and stock market uncertainty, respectively. Of these indexes, the CBOE Volatility Index (VIX) was introduced already in 1993, and is based on the prices of the S&P 500 stock index options. It may be the most cited measure of risk in the equity markets, sort of “fear gauge”, around the world. The other two volatility indexes, the Oil Volatility Index (OVX) and Energy Sector ETF Volatility Index (VXXLE), were introduced in 2008 and 2013, respectively.9 The OVX and VXXLE measure the price uncertainty of their underlying markets in the similar manner to the VIX. The crude oil implied volatility index, OVX, also called the Oil VIX, is based on the price of options on the United States Oil Fund (USO), which is an Exchange Traded Fund (ETF) that follows the WTI light, sweet crude oil futures contracts. The USO itself has been under examination as well, for example by Agbeyegbe [31]. The VXXLE is calculated similarly, using the option prices on the energy sector ETF (XLE ETF). A visual inspection of Figs. 1 and 2 suggests that, the VXXLE, OVX and VIX indexes are correlated more with each other when the price of crude oil is relatively high, and the inter-dependence has been lower during low oil price era, starting from 2014. Overall, these indexes seem to develop in a similar manner, at least to some extent. Interestingly, the behavior of the VXXLE seems to reflect the behavior of the OVX and VIX indexes, but when the crude oil prices are low, the OVX is at a relatively higher level than the VIX, compared to high crude oil price era. All in all, the volatilities of energy sector companies, crude oil and stock markets have varied considerably during the past years. Table 1 presents the descriptive statistics of the three uncertainty measures used in the paper. Panel A reports the implied volatility indexes VXXLE, OVX, and VIX. Of these, the OVX has both the highest values and highest standard deviation. Interestingly though, the same variable is also closest to the normal distribution, meaning that the implied oil volatility does not have as many extreme values as the other series, and at the same time it is not as concentrated around the mean value. Panel B provides the corresponding logarithmic changes of implied VXXLEt2 log(VXXLEt2) log(VXXLEt2 1) , variances, defined as
(3)
(1/v )
where (·) is the gamma function and
=
3. Data used in the study
1 | / |v 2 t
2(v + 1)/ v
2/ v
changes in the uncertainty components OUC and SUC (ceteris paribus) on call and put option values, as well as the corresponding delta values.
(1/ v ) (3/ v )
is given by
1/2
(4)
and v is a parameter that determines the fatness of the tails [24,p. 668]. Furthermore, the GJR-GARCH type of variance specification with the GED is applied to test possible asymmetric consequences of positive and negative innovations.5 In the second step of our analyses, we relax the assumption of the constant weights and (1 ), by allowing to be some function t = f (·) . Specifically, we test the hypotheses that t is linearly related to certain Google search terms regarding crude oil market, reflecting the crude oil related internet interest (see, e.g. [10]), as well as a set of variables, which are the crude oil price and volatility levels, and the stock market volatility level, that characterize general market conditions. Hence, the dependence of the weights on the general market conditions takes the following form: t
=
0
+
(SVI VARIABLES)t (5)
+ (MARKET CONDITION VARIABLESti )
where SVI variables are based on the Google Search Volume Index and the market condition variables are as explained above. The variables and their empirical counterparts are defined in details in the following data section. The parameter values are obtained via maximum likelihood estimation. We present also practical implications of the estimation results for the market participants illustrated via simulations, based on the BlackScholes-Merton option pricing model. According to the model, the theoretical value for a European call option is given by ct = St N (d ) Xe r (T t ) N [d t )], where N (·) is a cumulative t (T normal distribution function and d = [ln
( ) + (r + St X
2 t
2
) (T
6 A comprehensive explanation of various implied volatility indexes can be found in Christoffersen et al. [26]. 7 Several studies use the Google Search Volume Index (SVI) as a measure of demand for information. It is used, for example, by Guo and Ji [16], Ji and Guo [27], Yao et al. [28] and Campos et al. [12], or most recently, Nikkinen and Rothovius [10], focusing on in crude oil markets and, Klemola et al. [29], focusing the stock markets and Wang et al. [30] focusing on the futures markets.. 8 http://www.google.com/trends. 9 The VXXLE data are available from 16/3/2011.
t )]/[ t
(T t )], and the call delta is equal to N (d ) . The corresponding values for European put options are obtained via the put-call parity condition. The following hypothetical examples illustrate the effects of percentage 5 Glosten et al. [25] suggest a GJR-GARCH model that can incorporate the asymmetric consequences of positive and negative innovations.
143
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120
WTI crude oil price in $
100 80 60 40 20 0 2011
2012
2012
2013
2014
2015
2016
2017
2015
2016
2017
Year Fig. 1. WTI crude oil price.
90 80 70
Index value
60 50 40 30 20 10 0 2011
2012
2012
2013
2014
Year VXXLE
OVX
VIX
Fig. 2. Implied volatility indexes.
that the changes in implied oil variance are further away from the mean, and has more extreme (positive) changes. However, these differences are quite small. In the empirical analyses VXXLEt2 , OVXt2 , ¯ t2 are used. The VIX ¯ t2 is obtained as a residual from a reand VIX gression in which VIXt2 is explained by OVXt2 .
Table 1 Descriptive statistics of uncertainty measures. Panel A. CBOE implied volatility indexes (%)
Mean Median Std Dev Skewness Kurtosis Minimum Maximum
VXXLE
OVX
VIX
23.53 21.64 7.37 1.40 1.93 13.53 57.47
34.00 32.77 11.61 0.63 0.18 14.50 78.97
16.53 14.97 5.63 2.11 5.32 9.36 48.00
4. Empirical analysis Table 2 reports the empirical results on the weights of percentage changes in the crude oil uncertainty component OUC and the stock market uncertainty component SUC. The weight for the OUC is denoted ). by and the weight for the SUC can be simply calculated by (1 The estimates are provided for both GARCH(1,1)-GED and GJR-GARCH (1,1)-GED specifications. Both models are estimated with an autoregressive term. The results for the GARCH-GED show that the weights for the OUC and SUC are 0.55 and 0.45, respectively. This finding suggests that, regarding the energy sector uncertainty, the percentage change of the OUC has a slightly higher weight than that of the SUC. Thus, assuming equal-sized percentage changes in the uncertainty components, oil related uncertainty is more important for energy sector companies than stock market related uncertainty. However, the total effect on energy sector uncertainty is determined by both of these weights and the sizes of the percentage changes in the OUC and SUC. The R2 of the model is 0.69, indicating that these two components alone are able to explain quite a large proportion, more than two thirds, of the variability in the energy sector uncertainty.
Panel B. Logarithmic changes of implied variances (%)
Mean Median Std Dev Skewness Kurtosis Minimum Maximum
VXXLE
OVX
VIX
−0.07 −0.40 10.84 0.52 2.49 −42.77 58.54
−0.04 −0.39 9.62 0.86 12.09 −87.98 84.99
0.00 0.09 13.27 0.39 4.00 −76.10 74.40
OVXt2 log(OVXt2) log(OVXt2 1) , VIXt2 log(VIXt2) and log(VIXt2 1) . Contrary to Panel A, the change in implied oil variance is further away from the normality than that of the other series, meaning 144
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The results are shown in Table 3 for the search term “WTI”. The weight for the OUC range from 0.518 to 0.573 throughout the estimations. As expected, when the internet interest towards crude oil is high, the weight for the OUC is higher and that for the SUC lower. The statistically highly significant coefficient estimates for the dummy variable “WTI” vary between 0.062 and 0.127. However, extreme market conditions, characterized by the remaining explanatory variables, lowers the weight of the OUC, and the negative relationship is statistically highly significant. This means that during periods of high oil and stock market volatilities and high crude oil prices, the oil related uncertainty becomes less important. The R2s are quite stable and high, ranging from 0.69 to 0.70. Table 4 reports corresponding results for the search term “BRENT” instead of the “WTI”. The results for 0 are very close to the ones reported in Table 3. Depending on the specification, the coefficient estimate lies between 0.523 and 0.582. In all cases, the p-values are highly significant with values less than 0.001. Regarding the other variables, the results are well in line with the findings reported in Table 3, showing how the weight of the crude oil component is lowered by high volatilities and high oil price. To further elaborate our results, we implement an example on how the results can be used for the real applications by an experiment. Based on our estimations in Table 2, we assume that the change in energy ¯ t2 . sector volatility is determined by VXXLEt2 = 0.55 OVXt2 + 0.45 VIX We further assume that the options are 15% out-of-the money (i.e. the difference between the underlying asset price and the exercise price is 15%) and with one month time-to-maturity. The initial VXXLE volatility level is 23.53%, the mean of the sample. The continuously compounded risk-free interest rate is assumed to be one percent. Fig. 3 illustrates the effects of various combinations of percentage ¯ t2 (ceteris paribus) changes in the uncertainty components OVXt2 and VIX on a call option value. In the figure, the horizontal axis represents ¯ 2 , while the vertical axis provides percentage changes in OVX 2 and VIX the call values. As can be seen from the figure, an increase in either uncertainty component increases (ceteris paribus) the call value. However, for small percentage changes, the impact is relatively small in absolute terms, but even moderate changes can be substantial in relative terms. An increase in option value is further magnified if both uncertainty components increase at the same time, and for large changes in the components, the joint effect can be substantial. On the other hand, opposite changes in the components may also offset each others’ effect so that the total effect remains negligible. The effects of similar changes on call delta are important, since it is the key statistic in the delta-hedging scheme. The purpose of the delta
Table 2 Components of energy sector uncertainty. The reported results are estimated ¯ t2 + t , where OVXt2 + (1 ) VIX using the following model: VXXLEt2 = + VXXLEt2 log(VXXLEt2) log(VXXLEt2 1) , and OVXt2 log(OVXt2) log(OVXt2 1) . ¯ t2 is obtained as a residual from a regression in which VIXt2 is explained VIX by OVXt2 . i, t = i, t i i, t 1, where i is an autoregressive parameter and i, t is the error term which is modeled using a (GJR)-GARCH(1,1)-GED model. GARCH-GED
GJR-GARCH-GED
Variable
Estimate
t-value
Pr > |t|
Estimate
t-value
Pr > |t|
Intercept
−0.106 0.550 0.089 4.808 0.083 0.787
−1.07 63.70 3.82 2.74 3.52 12.63
0.2837 < 0.0001 0.0001 0.0062 0.0004 < 0.0001
1.310
−0.121 0.551 0.088 5.254 0.108 0.771 −0.041 1.311
−1.14 59.61 3.89 2.86 3.01 12.07 −1.01 20.46
0.2557 < 0.0001 0.0001 0.0044 0.0026 < 0.0001 0.3138 < 0.0001
115.68
< 0.0001
AR1 ARCH0 ARCH1 GARCH1
20.41
< 0.0001
Normality Test
115.59
< 0.0001
R Sq. log L
0.69 −5351
0.69 −5350
The estimates for ARCH1 and GARCH1 terms are 0.083 and 0.787, indicating stationarity. The estimate for is 1.310, indicating a peaked distribution relative to normal. This is also shown by the normality tests (H0: = 2; Chi-square statistics 115.59 and 115.68), which reject (with p-value < 0.0001) the null hypothesis of normality. The GJR-GARCH type of variance specification with the GED is applied to test possible asymmetric consequences of positive and negative innovations (see [25]). The estimate for is insignificant with pvalue of 0.314, which means that there is no reason to reject the basic GARCH-GED model. Thus, we report the remaining results based on that model. Next, we allow the weights of the uncertainty components to depend on the demand for crude oil related information and factors characterizing the market wide uncertainty. In model (5), 0 is a constant term and corresponds in Model (2). Other explanatory variables include a dummy variable for search term related to crude oil indicating the highest quartile of the searches (see [10], and dummy variables OVXh and OVXl, indicating the highest and the lowest quartiles of the OVX. VIXh and VIXl, as well as WTIh and WTIl, are dummy variables with similar definitions.
Table 3 Dependence of the component weights ( ) and (1 − ) on web search term “WTI” and market conditions. Basic model
Const. 0
“WTI” OVXh OVXl VIXh VIXl WTIh WTIl AR1 ARCH0 ARCH1 GARCH1 R Sq. log L
Model with OVX
Model with VIX
Model with WTI
Full model
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
−0.105 0.518 0.086
−0.97 44.31 3.78
0.334 < 0.001 0.000
−0.093 0.555 0.127 −0.096 −0.048
−0.82 33.20 5.71 −4.35 −1.93
0.410 < 0.001 < 0.001 < 0.001 0.054
−0.132 0.535 0.098
−1.24 46.90 6.15
0.216 < 0.001 < 0.001
−0.108 0.543 0.071
−0.95 33.48 3.18
0.340 < 0.001 0.002
−0.080 0.051
−4.83 2.22
< 0.001 0.027
−0.066 −0.016
−2.56 −0.61
0.011 0.540
−0.145 0.573 0.062 −0.008 −0.061 −0.084 0.054 −0.044 0.008
−1.34 31.85 2.93 −0.32 −2.21 −3.20 2.14 −1.97 0.31
0.181 < 0.001 0.004 0.749 0.027 0.001 0.033 0.049 0.753
0.092 5.438 0.093 0.756 1.315
3.63 2.66 3.59 10.30 20.08
0.000 0.008 0.000 < 0.001 < 0.001
0.089 4.492 0.084 0.793 1.323
3.63 2.57 3.48 12.42 20.20
0.000 0.010 0.001 < 0.001 < 0.001
0.089 5.364 0.089 0.758 1.333
3.36 2.37 3.44 9.23 19.79
0.001 0.018 0.001 < 0.001 < 0.001
0.089 4.478 0.084 0.794 1.311
4.14 2.61 3.54 12.60 20.35 0.69 −5342
< 0.001 0.009 0.000 < 0.001 < 0.001
0.085 1.253 0.039 0.926 1.326
3.35 3.04 2.89 42.69 20.25
0.001 0.002 0.004 < 0.001 < 0.001
0.69 −5337
0.69 −5327
145
0.69 −5338
0.70 −5321
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Table 4 Dependence of the component weights ( ) and (1 − ) on web search term “BRENT” and market conditions. Basic model
Const. 0
“BRENT” OVXh OVXl VIXh VIXl WTIh WTIl AR1 ARCH0 ARCH1 GARCH1 R Sq. log L
Model with OVX
Model with VIX
Model with WTI
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
Est.
t-val.
p-val.
−0.101 0.523 0.072
−0.91 39.99 3.37
0.364 < 0.001 0.001
−0.085 0.554 0.104 −0.083 −0.045
−0.74 31.73 3.94 −3.23 −1.93
0.460 < 0.001 < 0.001 0.001 0.054
−0.116 0.541 0.084
−1.04 32.3 3.89
0.300 < 0.001 0.000
−0.102 0.551 0.045
−0.96 41.65 1.87
0.336 < 0.001 0.061
−0.079 0.046
−3.64 1.64
0.000 0.102
−0.072 −0.002
−3.58 −0.08
0.000 0.934
−0.132 0.582 0.041 −0.002 −0.065 −0.091 0.052 −0.050 0.010
−1.17 30.54 1.49 −0.07 −2.34 −3.50 2.12 −2.19 0.38
0.242 < 0.001 0.135 0.941 0.020 0.001 0.034 0.029 0.707
0.093 5.333 0.088 0.762 1.323
3.5 2.61 3.6 10.38 20.13
0.001 0.009 0.000 < 0.001 < 0.001
0.089 4.470 0.079 0.796 1.331
3.6 2.58 3.49 12.55 20.46
0.000 0.010 0.001 < 0.001 < 0.001
0.090 5.573 0.088 0.754 1.335
3.49 2.29 3.41 8.74 19.71
0.001 0.022 0.001 < 0.001 < 0.001
0.092 4.641 0.085 0.789 1.312
3.81 2.56 3.50 12.03 20.40
0.000 0.010 0.001 < 0.001 < 0.001
0.087 4.384 0.078 0.801 1.317
0.69 −5344
3.36 2.30 3.24 11.49 20.19
0.001 0.021 0.001 < 0.001 < 0.001
0.69 −5338
0.69 −5331
hedging is to make a given position as immune as possible to small changes in the price of the underlying asset. Since the deltas themselves can be affected by changes in the implied volatilities, their behavior can be better understood by analyzing the effects of the uncertainty com¯ t2 on deltas. This is illustrated in Fig. 4, in which ponents OVXt2 and VIX an increase in either component increases the call delta. It suggest that the effect of one component is almost linear, thus the total effect of the components is determined to be almost a flat surface. Figs. 5 and 6 present the corresponding effects for put option values and their deltas, respectively. Analyzing out-of-the-money put options is central, since they are the ones that are commonly used for crash insurance purposes. Fig. 5 illustrates that the joint effect of the components can be substantial also for a put option. As is the case for the call deltas, according to Fig. 6, the put deltas behave in almost a linear fashion as well. Put together, empirical results are in line with our postulation. Thus, we can conclude that the energy sector companies’ uncertainty, measured from the market participants expectations manifested in option prices, consists of two components, the oil uncertainty component OUC
0.69 −5340
5. Conclusions The importance of energy sector for the world economy is evident, not only from the direct dependence of GDP growth on oil price, but also from the fact that many of the biggest corporations in the world operate in the energy sector. Thus, it is vital for researchers, both in the fields of energy and economics, as well as for practitioners (such as energy companies, hedgers and energy traders) and policy makers, to understand the sources and dynamics of uncertainty arising from energy sector and energy companies. Following this, we study the sources and dynamics of energy
0.09 0.08
0.06 0.05 0.04 0.03 0.02
40 % 15 % -10 %
0.01
48%
Change in stock market variance 146
-60 % 57%
39%
21%
30%
3%
12%
-35 % -6%
-15%
0
Change in crude oil variance
0.07
-60% -51% -42% -33% -24%
0.09-0.1 0.08-0.09 0.07-0.08 0.06-0.07 0.05-0.06 0.04-0.05 0.03-0.04 0.02-0.03 0.01-0.02 0-0.01
0.70 −5324
and the stock market uncertainty component SUC. Of these, the first is more important with 55% weight, provided that the percentage chances of both uncertainty components are assumed equal. Moreover, we can conclude that high general interest in crude oil increases the relative weight for the OUC. Finally, we document how these weights depend on the general crude oil and stock market conditions, especially in regard of high or low levels of volatility measures.
0.1
Call value
Full model
Fig. 3. A simulated illustration of the impact of the changes in implied crude oil and stock market volatilities (ceteris paribus) on a call option value. This figure illustrates a hypothetical impact of changes in the implied crude oil and stock market volatilities on out-of-the money (15%) call option values (ceteris paribus) assuming that the percentage change in energy sector volatility is determined by ¯ t2 . The opVXXLEt2 = 0.55 OVXt2 + 0.45 VIX tion values are calculated using the BlackScholes-Merton option pricing model assuming that the initial VXXLE volatility level is 23.53% (corresponding the mean value in the sample) and with one month time-to-maturity and with 1.0% continuously compounded interest rate. The horizontal axis represent percentage ¯ 2 . The vertical axis changes in OVX 2 and VIX gives the corresponding call values.
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J. Nikkinen and T. Rothovius
0.14-0.16 0.12-0.14
0.16 0.14 0.12
0.1-0.12
0.1
0.08-0.1
0.08
0.06-0.08 0.04-0.06 0.02-0.04 0-0.02
0.06 0.04 40 % 15 % -10 %
0.02
-60 % 60%
44%
52%
28%
-35 % 36%
-60% -52% -44% -36% -28% -20% -12% -4% 4% 12% 20%
0
Change in crude oil variance
Delta
Fig. 4. A simulated illustration of the impact of the changes in implied crude oil and stock market volatilities (ceteris paribus) on a call delta. This figure illustrates a hypothetical impact of changes in the implied crude oil and stock market volatilities on out-of-the money (15%) call delta (ceteris paribus) assuming that the percentage change in energy sector volatility is determined ¯ t2 . The by VXXLEt2 = 0.55 OVXt2 + 0.45 VIX deltas are calculated using the Black-ScholesMerton option pricing model assuming that the initial VXXLE volatility level is 23.53% (corresponding the mean value in the sample) and with one month time-to-maturity and with 1.0% continuously compounded interest rate. The horizontal axis represent percentage changes in ¯ 2 . The vertical axis gives the corOVX 2 and VIX responding delta values.
Change in stock market variance companies’ market uncertainty, measured by energy market participants’ view of the future uncertainty. Our novel purpose is to extend the existing literature by investigating the energy sector companies’ market uncertainty by dividing it into separate components, the crude oil uncertainty component (OUC) and the market wide uncertainty of the stock market component (SUC). Furthermore, we suggest how the weights for these components can be estimated by using implied volatilities. Finally, we show how public interest in oil market affects the weights of the components, along with general crude oil and stock market conditions. Our empirical results, utilizing several implied volatility series, such as the one on energy sector companies (VXXLE), reveal that, weight of for the percentage change in the OUC is higher than that of SUC in explaining the energy sector uncertainty (55% vs. 45%), the estimates
Put value
being statistically highly significant. Together, these components can explain 69% of the variability in the energy sector uncertainty. Furthermore, we show how the public attention, measured by internet searches with crude oil related search terms, affect the weights in crude oil market so that high demand for information increases the relative weight of the OUC and decreases that of the SUC. These weights are also affected by general crude oil and stock market conditions, such as high crude oil price, or low and high levels of the implied volatilies of crude oil or stock markets. Finally, we present illustrative simulations, suggesting (ceteris paribus) that even moderate percentage changes in the values of the uncertainty components can lead to a substantial effect on option values. In derivatives markets, the economic effect can be significant, depending on the other characteristics of the contracts. The paper contributes to the existing literature both theoretically
0.09 0.08
0.07-0.08 0.06-0.07
0.07 0.06
0.05-0.06
0.05
0.04-0.05
0.04
0.03-0.04
0.03
0.02-0.03 0.01-0.02 0-0.01
0.02
60 % 40 % 20 % 0% -20 % -40 % -60 %
0.01 0 -60%
-40%
-20%
0%
20%
40%
60%
Change is stock market variance 147
Change in crude oil variance
0.08-0.09
Fig. 5. A simulated illustration of the impact of the changes in implied crude oil and stock market volatilities (ceteris paribus) on put option value. This figure illustrates a hypothetical impact of changes in the implied crude oil and stock market volatilities on out-of-the money (15%) put option values (ceteris paribus) assuming that the percentage change in energy sector volatility is determined by ¯ t2 . The opVXXLEt2 = 0.55 OVXt2 + 0.45 VIX tion values are calculated using the BlackScholes-Merton option pricing model assuming that the initial VXXLE volatility level is 23.53% (corresponding the mean value in the sample) and with one month time-to-maturity and with 1.0% continuously compounded interest rate. The horizontal axis represent percentage ¯ 2 . The vertical axis changes in OVX 2 and VIX gives the corresponding put values.
Applied Energy 248 (2019) 141–148
J. Nikkinen and T. Rothovius
0
-0.02
-0.04
-0.02-0 -0.06
-0.06--0.04 -0.08--0.06
-0.08
-0.1--0.08 -0.12--0.1
-0.1
-0.12 -60 %
-40 %
-20 %
0%
20 %
40 %
Change in crude oil variance
-0.04--0.02
-60% -40% -20% 0% 20% 40% 60% 60 %
Fig. 6. A simulated illustration of the impact of the changes in implied crude oil and stock market volatilities (ceteris paribus) on put delta. This figure illustrates a hypothetical impact of changes in the implied crude oil and stock market volatilities on out-of-the money (15%) put delta (ceteris paribus) assuming that the percentage change in energy sector volatility is determined ¯ t2 . The by VXXLEt2 = 0.55 OVXt2 + 0.45 VIX deltas are calculated using the Black-ScholesMerton option pricing model assuming that the initial VXXLE volatility level is 23.53% (corresponding the mean value in the sample) and with one month time-to-maturity and with 1.0% continuously compounded interest rate. The horizontal axis represent percentage changes in ¯ 2 . The vertical axis gives the corOVX 2 and VIX responding delta values.
Change in stock market value and empirically, by presenting a novel idea of dividing the energy sector uncertainty into components, by proposing a research design to compute the weights for those components based on implied volatilities, and by providing empirical evidence to support these ideas and showing how different variables, such as public interest, level of oil price, or level of implied volatilities in oil and stock markets affect the proposed weights. Thus, our paper provides important implications for policy makers, in order to manage economic risks; for energy companies, to identify and hedge for financial risks; and for practitioners, to model volatility, option pricing and to cross-hedge volatility risks of energy sector companies.
empirical analysis of implied volatility index. Energy 2013;55:860–8. [9] Dutta A. Oil and energy sector stock markets: an analysis of implied volatility indexes. J Multinational Financ Manage 2018;44:61–8. [10] Nikkinen J, Rothovius T. The EIA WPSR release, OVX and crude oil internet interest. Energy 2019;166:131–41. [11] Maghyereh A, Awartani B, Bouri E. The directional volatility connectedness between crude oil and equity markets: new evidence from implied volatility indexes. Energy Econ 2016;57:78–93. [12] Campos I, Cortazar G, Reyes T. Modeling and predicting oil VIX: Internet search volume versus traditional mariables. Energy Econ 2017;66:194–204. [13] Luo X, Qin S. Oil price uncertainty and Chinese stock returns: new evidence from the oil volatility index. Financ Res Lett 2017;20:29–34. [14] Dutta A, Nikkinen J, Rothovius T. Impact of oil price uncertainty on Middle East and African stock markets. Energy 2017;123:189–97. [15] Hasanhodzic J, Lo A. Can hedge-fund returns be replicated? The linear case. J Investment Manage 2007;5:5–45. [16] Guo J, Ji Q. How does market concern derived from the internet affect oil prices? Appl Energy 2013;12:1536–43. [17] Qadan M, Nama H. Investor sentiment and the price of oil. Energy Econ 2017;69:42–58. [18] Tjaaland S, Westgaard S, Osmundsen P, Frydenberg S. Oil and gas risk factor sensitivies for US energy companies. J Energy Develop 2016;41:135–73. [19] Nikkinen J, Sahlström P. International transmission of uncertainty implicit in stock index option prices. Global Financ J 2004;15:1–15. [20] Engle R. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 1982;50:987–1007. [21] Bollerslev T. Generalized autoregressive conditional heteroscedasticity. J Economet 1986;31:307–27. [22] Nelson D. Conditional heteroscedasticity in asset returns: a new approach. Econometrica 1991;59:347–70. [23] Fan Y, Zhang Y-J, Tsai H-T, Wei Y-M. Estimating ‘Value at Risk’ of crude oil price and its spillover effect using the GED-GARCH approach. Energy Econ 2008;30:3156–71. [24] Hamilton J. Time series analysis. Princeton University Press; 1994. [25] Glosten L, Jagannathan R, Runkle D. On the relation between the expected value and the volatility of the nominal excess return on stocks. J Financ 1993;48:1779–801. [26] Christoffersen P, Jacobs K, Chang B. Forecasting with option-implied information. Handbook Econ Forecast 2012;2:581–656. [27] Ji Q, Guo J. Oil price volatility and oil-related events: an internet concern study perspective. Appl Energy 2015;137:256–64. [28] Yao T, Zhang Y-J, Ma C-Q. How does investor attention affect international crude oil prices? Appl Energy 2017;205:336–44. [29] Klemola A, Nikkinen J, Peltomäki J. Changes in investors’ market attention and near-term stock market returns. J Behav Financ 2016;17:18–30. [30] Wang X, Ye Q, Zhao F, Kou Y. Investor sentiment and the Chinese index futures market: Evidence from the internet search. J Futures Markets 2018;38:468–77. [31] Agbeyegbe T. An inverted U-shaped crude oil price return-implied volatility relationship. Rev Financ Econ 2015;27:28–45.
Acknowledgements Jussi Nikkinen expresses his gratitude for support from the OP Financial Group Research Foundation. We would also like to thank the editor-in-chief, professor Jinyue Yan, associate editor, professor YiMing Wei, and two anonymous referees for their valuable comments, which helped to improve the paper substantially. Any remaining errors are in our responsibility. References [1] Eyden R, Difeto M, Gupta R, Wohar M. Oil price volatility and economic growth: evidence from advance economies using more than a century’s data. Appl Energy 2019;233:612–21. [2] Chen H, Liao H, Tang B-J, Wei Y-M. Impacts of OPEC’s political risk on the international crude oil prices: an empirical analysis based on the SVAR models. Energy Econ 2016;57:42–9. [3] Tulloch D, Diaz-Rainey I, Premachandra I. The impact of regulatory change on EU energy utility returns: the three liberalization packages. Appl Econ 2018;50:957–72. [4] Spada M, Paraschiv F, Burgherr P. A comparison of risk measures for accidents in the energy sector and their implications on decision-making strategies. Energy 2018;154:277–88. [5] Restrepo N, Uribe J, Manotas D. Financial risk network architecture of energy firms. Appl Energy 2018;215:630–42. [6] Cong R-G, Wei Y-M, Jiao J-L, Fan Y. Relationships between oil price shocks and stock market: an empirical analysis from China. Energy Policy 2008;36:3544–53. [7] Lopez R. The behaviour of energy-related volatility indices around scheduled news announcements: implications for variance swap investments. Energy Econ 2018;72:356–64. [8] Liu M, Ji Q, Fan Y. How does oil market uncertainty interact with other markets? An
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