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Modelling and forecasting crude oil price volatility is crucial in many financial and investment applications. The main purpose of this paper is to review and assess the current state of oil market volatility knowledge. It highlights the properties and characteristics of the oil price volatility that models seek to capture, and discuss the different modelling approaches to oil price volatility. Asymmetric response to price change, persistence and mean reversion, structural breaks, and possible market spillover of volatility are discussed.To complement the discussion, West Texas Intermediate futures price data are used to illustrate these properties using non-parametric and conditional modelling methods. The generalised autoregressive conditional heteroskedasticity-type models usually applied in the oil price volatility literature are also explored.We additionally examine the exogenous factors that may influence volatility in the oil markets.
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An introduction to oil market
volatility analysis1
Walid Matar,* Saud M. Al-Fattah,** Tarek Atallah*** and Axel Pierru****
*Sr. Research Analyst, Energy Research, King Abdullah Petroleum Studies and Research Center
(KAPSARC), Riyadh, Saudi Arabia
**Fellow, Energy Research, King Abdullah Petroleum Studies and Research Center (KAPSARC), PO Box
88550, Riyadh 11672, Saudi Arabia. Email:
***Sr. Research Analyst, Energy Research, King Abdullah Petroleum Studies and Research Center
(KAPSARC), Riyadh, Saudi Arabia
****Fellow, Energy Research, King Abdullah Petroleum Studies and Research Center (KAPSARC), Riyadh,
Saudi Arabia
Modelling and forecasting crude oil price volatility is crucial in many financial and investment appli-
cations. The main purpose of this paper is to review and assess the current state of oil market volatil-
ity knowledge. It highlights the properties and characteristics of the oil price volatility that models
seek to capture, and discuss the different modelling approaches to oil price volatility. Asymmetric
response to price change, persistence and mean reversion, structural breaks, and possible market
spillover of volatility are discussed.To complement the discussion, West Texas Intermediate futures
price data are used to illustrate these properties using non-parametric and conditional modelling
methods. The generalised autoregressive conditional heteroskedasticity-type models usually
applied in the oil price volatility literature are also explored. We additionally examine the exogenous
factors that may influence volatility in the oil markets.
1. Introduction
As crude oil plays a major role in global economic activity, understanding the volatility
of its price is of paramount importance. For risk managers, oil price volatility impacts
hedging and the assessment of projects whose cash flows are influenced by the expected
price of the commodity. Long-term uncertainty in future oil prices can alter the incen-
tives to develop new oil fields in producing countries. This can also hinder the imple-
mentation of alternative energy policies in consuming countries. In the short term,
volatility can affect the demand for storage, as greater volatility should lead to increased
storage demand, spot prices and the marginal convenience yield.2Last but not least,
volatility is a key variable in the pricing of derivatives whose trading volume has signifi-
cantly increased in the last decade. In all of these applications, it is essential that some
level of predictability can be captured when modelling oil price volatility.
© 2013 The Authors. OPEC Energy Review © 2013 Organization of the Petroleum Exporting Countries. Published by
John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.
Previous reviews of price volatility (e.g. Engle and Patton, 2001; Poon and Granger,
2003) have not specifically dealt with the crude oil price. Studying oil markets, Sadorsky
(2006) compared the performance of different classes of models and their attributes. We
extend on the literature by conducting a review of the general properties of price volatility
and how they apply to the oil markets, provide an updated look at the models applied to oil
prices, and explore exogenous factors that could be included in those models.The proper-
ties and modelling approaches are also demonstrated by the analysis of historical West
Texas Intermediate (WTI) prices.
In words, volatility refers to the degree to which prices fluctuate. It is not directly
observable and is estimated from the change in price; therefore, the return on price will be
discussed in the second section to lay the foundation for the subsequent sections. In
Section 3, the various approaches to modelling volatility in the oil markets are detailed.
The stylised properties of volatility are explored in Section 4, as it is important to consider
their presence when developing forecasts. We build on the model discussion by studying
how each approach attempts to account for these properties. In order to form a comprehen-
sive model, Section 5 examines the external factors that may impact the volatility of the oil
2. Crude oil price returns
2.1. Return and volatility: two related concepts
Volatility is typically quantified as the standard deviation3of price returns. This section is
therefore focused on the basic properties of returns, or relative price changes, and the
resulting insight regarding volatility. For the computation of volatility, the return on price
is commonly determined in continuous time. Given a time scale Dt, which could range
from seconds to months, the standard definition of the price return r(t,Dt) is then
derived by,
Pt e Pt t
rt t
Where P(t) is the price of crude oil at t. Hence,
rt t Pt
Pt t
For illustrative purposes, Figures 1 and 2provide the daily and monthly returns on
WTI first-month futures price, respectively. The price data is observed from 27 May 1987
to 12 October 2011.4The daily returns have been adjusted for intermediate non-trading
days—weekends and holidays—following the procedure suggested by Pindyck (2004)
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and explained in Appendix A. In calculating the returns at the monthly time scale, the
futures price on the 10th day of each month is considered to avoid proximity with contract
expiration dates. For months whose 10th day is not a trading day, the nearest previous or
succeeding trading days are incorporated instead.
As shown in Figure 1, two pronounced instances of price variability clustering are
observed in the early 1990s and more recently during the 2008–2009 global economic
Figure 1 Adjusted daily returns of first contract futures (NYMEX).
Figure 2 Monthly returns of first contract futures (NYMEX).
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recession. In both instances, the clustering of large changes in price was present for a sig-
nificant period of time. An example of price shocks in the daily returns data can be visual-
ised on 17 January 1991. Oil prices dropped sharply that day as the mission to expel Iraqi
troops from Kuwait was initiated.
2.2. Properties and analysis of returns
It is well established in finance that returns do not follow a normal distribution, and one
stylised statistical property is that as the time interval of data observations is increased, the
distribution of the returns increasingly appears normal in nature (Cont, 2001). Skewness is
a measure of the symmetry of the distribution. A normal distribution is symmetrical
around the mean, and thus would have a skewness of zero. For the daily and monthly oil
price returns presented in Figures 1 and 2, the distributions exhibit a skewness5of -0.99
and -0.20, respectively, suggesting both curves are skewed to the left of the mean.Addi-
tionally, kurtosis is a measure of the peakedness of the distribution curve, which decreases
as the curve becomes increasingly flat. A normal curve would have a kurtosis of 3, whereas
the distribution of daily (monthly) returns exhibits a kurtosis of 20.5 (4.5). The complete
set of descriptive statistics related to the data analysed is shown in Appendix B. The
Jarque–Bera test rejects normality at the 1 per cent significance level for both distribu-
tions. For the purpose of illustration, Figure 3 fits both distributions with continuous prob-
ability density functions. The presence of heavy tails at either side of the distribution curve
of the returns can be observed. This property is closely associated with a high kurtosis.
Returns do not share inherent predictive properties, as past returns do not provide
information on future returns. For the daily returns, this is illustrated in Figure 4 by apply-
ing the autocorrelation function, C(t), defined in the following.
Figure 3 Probability density functions of the daily and monthly price returns.
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C corr r t t r t t
,,,ΔΔ (2)
Where tis the time increment. The upper and lower boundaries represent the stand-
ard error, whose equation is defined by equation (A5) in Appendix A. In this range, the
autocorrelation values are not considered significantly different from zero. While some
significant autocorrelations are present in the daily returns, their small values and
the random nature of the oscillations around the zero-line suggest the presence is not
Moreover, another property observed to be consistent with returns is that of clustering
of returns. Simply put, large (small) price movements are more likely to be followed by
other large (small) price movements. In the autocorrelation family of functions given by
equation (3), this clustering behaviour is best displayed when the absolute values of the
returns are raised to the first power (Cont, 2001).
C corr r t t r t t
,,,ΔΔ (3)
If significant positive autocorrelation of absolute returns is observed for several lags,
then the clustering is present. Figure 5 presents the autocorrelation of the absolute daily
returns. The autocorrelation for the daily returns is consistently above zero, showing the
clustering property.Although not as prominent, we found significant autocorrelation up to
the fourth lag for the monthly values. It is often observed that negative movements in
Figure 4 Autocorrelation of the daily returns.
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returns lead to greater volatility than positive movements of the same magnitude. This phe-
nomenon, called the leverage effect, is explored in a later section.
3. Volatility modelling and measurement
As stated previously, if the price return at time tfollows a probability law with standard
deviation, st, then stis the volatility at time t. Empirical modelling of volatility can be per-
formed using non-parametric and parametric methods. Non-parametric methods directly
compute volatility without any functional specification, and they iteratively fit the data by
factoring in lagged returns. An example of these methods used by Pindyck (2004) is deter-
mining the sample standard deviation of returns over a moving window. This method pro-
vides a basic estimation of the volatility, and its associated governing equation is listed in
Appendix A. Sadorsky (2006) also cited the historical mean model, which estimates
present volatility as the average of previous volatility values, and the moving average
model. He found that they often outperformed parametric approaches.
3.1. Conditional oil price volatility models
More commonly used in analysing oil and energy markets, parametric methods specify
non-trivial functions of historical values and observable variables. To examine the most
popular of such methods, the generalised autoregressive conditional heteroskedasticity
(GARCH) model is used to provide estimates of volatility at different time scales.
Figure 5 Autocorrelation of the absolute adjusted daily returns.
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Contrary to non-parametric methods, these conditional models fit data using maximum
likelihood estimation and have the capability of accounting for exogenous variables.
Applied to volatility, st, the family of GARCH(p,q) models can be generally described by
the return mean and variance equations given by equations (4a) and (4b), respectively.
In this approach, the lagged variance and the residual, e, have predictive influence on
conditional variance. The notation of pand qrefers to how many lagged innovation and
autoregressive terms are incorporated in the variance equation.
σα αε βσ γ
=+ + +
Where aj,bjand gkare the regression coefficients to be computed, mis the mean of the
returns, a0is the unconditional volatility, Lkdenotes any external factors that have signifi-
cant impact on the volatility. Factors influencing oil price volatility will be discussed in
forthcoming sections.
A GARCH(1,2) model is applied to provide our own estimate of the volatility of the
adjusted daily returns previously analysed for WTI first contract futures crude oil prices.
For the sake of illustration, this straightforward implementation does not consider any
external variables.The results of the GARCH(1,2) estimation are displayed in Tab l e 2B in
Appendix B and the plot is presented in Figure 6. For comparison, the result of a non-
parametric method that directly computes the standard deviation of a moving window is
Figure 6 Monthly volatility of first futures crude oil contract price.
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also shown with the GARCH model results. Volatility spikes of over 20 per cent are
observed during the first Gulf War (1990–1991) and the most recent global economic
recession (2008–2009).
The standard GARCH model, which has been the most prevalent, has evolved through
the years to account for more information in estimating volatility. There is now a plethora
of GARCH-class models available with the purpose of capturing observed characteristics
of volatility. Ta b l e 1 summarises the features of different models.
There has been no extensive application of neural network models in the area of
crude oil volatility. Ou and Wang (2011) claimed that a hybrid model that incorporates
neural networks with GARCH estimates the extreme values of oil price volatility more
effectively than standard GARCH models alone and that they are less sensitive to
The main differentiator in modelling and forecasting performance comes in the effec-
tiveness in accounting for long-term memory of market events. Despite the multitude of
studies available, there is inconsistency in which model is preferred. These contradictions
can arise from varying specifications of the models, observed data samples, and the exter-
nal factors considered. While Kang et al. (2009) found superiority in CGARCH and
FIGARCH models due to their capability of capturing persistence, Wei et al. (2010) found
that no one GARCH-class model outperforms the others in all situations. As the standard
GARCH model falls short in capturing the effects of long-term shocks, they found that
HYGARCH captures them more effectively. Hou and Suardi (2012) have noted that
HYGARCH collapses to a FIGARCH specification in some instances.
While GARCH-class models have been the most widely used conditional models,
Sadorsky (2006) also experimented with least squares and vector autoregression (VAR)
methods. He reported that despite the complexity of bivariate GARCH and VAR models,
they are seemingly outperformed by the standard GARCH. As another alternative, sto-
chastic volatility (SV) models have also been applied to oil price (Vo, 2009). SV models
are built on the belief that volatility is not necessarily influenced by the lagged innovations
that drive returns. With that said, however, the mean equation in the SV framework is
dependent on the variance. The application of these models to oil price volatility has not
been widespread.
3.2. Alternative definitions of volatility
With the use of high frequency data feeds, realised volatility is the variance of the observed
returns over a fixed time interval. Computed at high sampling frequencies, realised vola-
tility could be used as a proxy for actual daily volatility. Typically used as the reference in
forecasts, the actual daily volatility at time tis then defined non-parametrically as the
square of the return at that time point.
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Tab l e 1 Different classes of GARCH models and their application to oil market volatility
Model Model features
(Standard) GARCH The conditional volatility is a linear function of past volatility and
innovation.They are more effective in modeling short-term
volatility than long-term volatility.
Integrated GARCH
The sum of the variance equation coefficients of GARCH(1,1)
model is often close to unity, which is an indication of long
memory in the volatility. IGARCH is better equipped to account
for this long memory due to the integration over lag variables.
This linear model maintains the lasting effect of shocks
Fractionally Integrated
A non-linear model that captures long memory shocks effectively.
Unlike IGARCH, it provides a slow decay of shocks over time.
Threshold GARCH
(TGARCH); Golsten,
Jagannathan, and
Runkle (GJR)
TGARCH and GJR add another residual term to the standard
GARCH to account for asymmetrical behavior in volatility; this
term is only present if the residual is negative.
Exponential GARCH
A non-linear model that is effective in accounting for asymmetric
behavior in volatility by examining the ratio of the residual and
the volatility at t-1. While linear GARCH models often restrict
coefficients to be positive, this model removes this restriction.
Hyperbolic GARCH
This model is a mixture of standard GARCH, IGARCH and
FIGARCH models. This model provides the same slow decay of
shocks that is present in FIGARCH, while maintaining the
favourable stationarity features of the standard GARCH model.
GARCH-M allows for the mean of the returns to be a function of
the conditional volatility. This accounts for risk aversion as the
computed returns increase during periods of high volatility.
Multivariate GARCH This class of GARCH models incorporates time-varying
conditional covariance of returns.These models are useful when
simultaneously computing the volatility of multiple assets.
Component GARCH
This model is a specific formulation of GARCH(2,2). It improves
the modeling of long-term effects by decomposing the model
into long-run and short-run components.
Neural Network-GARCH
A hybrid model that incorporates neural networks with GARCH
estimates the extreme values of volatility more effectively than
GARCH models alone.
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Despite the fact they are not used in a mainstream fashion, there have been instances
where other definitions of volatility have been applied. Parkinson (1980) postulated the
use of local extreme return values in a moving window to estimate volatility, rather than
using the difference of the return at time tand the subsample mean, as described by the
non-parametric standard deviation defined earlier. Parkinson argued that this method is
superior because it achieves the same amount of variance with a much smaller sample size.
Looking into the future, another type of volatility is implied volatility (IV). This defi-
nition deals with the option value of the asset, of which volatility is an important determi-
nant. Inherently, this is a forecast of volatility since it is computed from a forward-looking
derivative price. IV is found as a better predictor of future volatility than historical values,
but it is generally outperformed in that regard by GARCH-type models for sufficiently
long forecast horizons [Agnolucci (2009); Christensen and Prabhala (1998) and
Szakmary et al. (2003), although these studies do not specifically deal with the oil price].
A model that combines both GARCH and IV may be an option to pursue.
4. Properties of volatility
Volatility displays different properties that include the leverage effect, persistence, mean
reversion and possible sudden alternations between high and low volatility regimes. Addi-
tionally, due to increased market interaction and diversification of investment portfolios,
volatility is often transmitted between markets.These properties are sometimes exhibited
more prominently in one market than another. They are discussed in depth in the following
4.1. The leverage effect
Volatility is often associated with asymmetric reactions to sudden positive and negative
movements in price.This phenomenon, called the leverage effect, suggests negative move-
ments yield a larger rise in volatility. It can be illustrated by looking at the correlation of the
square of the return in time twith the value of the returns at t-1; this is given by equa-
tion (5). If the correlation starts negative and decays to zero, then the leverage effect is
present (Cont, 2001).
C corr r t t r t t
Narayan and Narayan (2007) analysed oil price data during the period of 1991 to 2006
for the volatility response to shocks using an EGARCH model to capture the asymmetric
behaviour. Their findings were mixed, as the computation results showed that for certain
subsample periods, the volatility was affected asymmetrically by shocks, whereas sym-
metric behaviour was observed for other periods. It is suggested, however, that for long
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sample periods, the presence of asymmetry is significant. Particularly, negative shocks
may increase volatility more than positive shocks of the same magnitude. So while oil
prices may have over-arching behavioural trends, those trends may not be consistent in
shorter time periods.
Cheong (2009) studied the spot prices of both the WTI and Brent crude oil markets
from 1993 to 2008, and the leverage effect results were found to be market dependent.
While there was no asymmetry displayed in the volatility results of the WTI prices, it was
present in the Brent market during the sample period. In support of this assertion,
Agnolucci (2009), Chang (2012) and Wei et al. (2010) also found no evidence of this lev-
erage effect in the volatility in the WTI market. The latter study does report such behaviour
for the Brent market.
Moreover, this absence of asymmetric behaviour was also reported by Pindyck (2004).
The GARCH estimation showed a strong direct relationship between returns and volatility.
While the study does not specify the crude oil market, much of the other data used is spe-
cific to the United States; this leads to the belief that WTI prices are used.
Historically, both WTI crude oil and Brent crude have tended to follow similar trends
in price movements. The reported inconsistencies in price volatility behaviour may be
attributed to the differences in market-specific delivery, trading hours and oil grades. The
WTI price is the price of the oil traded in the central region of the United States, while the
Brent price is set for oil delivered from the North Sea; thus, the impact of transportation
cost differences is in play. While both markets have trading after hours, the regular trading
times are not synchronised. The effect of relevant news stories and other external factors
may therefore be imbalanced. Additionally, WTI crude oil is lighter than Brent Crude,
which could have an impact on customer behaviour.
To complement the previous discussion with practical analysis, the correlation defined
by equation (5) is carried out for the WTI market returns data analysed earlier to study the
presence of the leverage effect.The results of the correlation are displayed in Figure 7 for
the daily returns. We find asymmetry for the first lag, and then it decays to zero at the 5 per
cent significance level; some long-term lags also show a negative correlation. In words, the
negative return is succeeded by higher volatility. This contradicts what previous research
has found, but it could be attributed to the especially lengthy period under study or the fact
we adjusted for non-trading days. For the monthly data, the correlation is weak, suggesting
the absence of the leverage effect. One possible reason for this discrepancy is that the
effect of asymmetric shocks dissipates in the longer period between the monthly data
4.2. Persistence and mean reversion
As shown previously, clustering of returns is a property of the price variability that can be
best displayed by examining the autocorrelation of the absolute returns. This persistent
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behaviour is consistent with volatility, and there is an overwhelming consensus in the lit-
erature that long-term persistence of volatility is present in the oil markets. Most GARCH
models have the limitation where the persistence decays quickly, where it is in fact a slowly
decaying process (Brunetti and Gilbert, 2000). Narayan and Narayan (2007) found that the
presence of persistence is inconsistent when viewing oil prices within a short time
window. Over a long-term period, however, the behaviour of clustering is clearly dis-
played. Going even a step further, Kang et al. (2009) observed strong long-term persist-
ence for WTI, Brent and Dubai, which was later confirmed by Wei et al. (2010) for the first
two markets; Sidorenko et al. (2002) observed the same trends with Brent second-month
futures contract volatility. Although the results were not strongly indicative of clustering,
Sadorsky (2006) observed some degree of persistence in the crude oil futures volatility. As
part of post-processing of the results by Pindyck (2004), the lasting effect of persistence of
volatility was quantified by examining the half-life of historical shocks. It was found that
the impact of shocks is maintained for 3–11 weeks depending on whether daily or weekly
returns were used. In any case, Engle and Patton (2001) recommended that a good asset
price volatility model should account for persistence for up to a year after a shock.
In addition, even during moments of high clustering, there is always a normal level to
which volatility eventually returns. This characteristic, called mean reversion, should be
exhibited during the development of forecasts (Engle and Patton, 2001).
4.3. Structural breaks and regime switches
As shown with the property of persistence, the change in asset prices is often impacted by
sudden external events. Extreme movements in price can generate structural instability, or
Figure 7 Daily correlation of lagged returns with the square of the returns.
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switches between high and low volatility regimes, in the market. Neglecting the impact of
breaks could result in the exaggerated display of persistence in the models, which would
mean that the notion of volatility predictability is weakened. To factor in these possible
regime switches, several approaches have been incorporated in the literature.
While Arouri et al. (2012) found no structural breaks in the WTI crude oil market, they
were observed for other oil-based commodities.The methodology used to determine when
a sudden change in variance takes place, if any, is the iterated cumulative sum of squares
(ICSS) statistic test. As thoroughly detailed by the authors, the test finds an estimate for the
break dates. A model modified to account for these switches would have the ability to sud-
denly change the variance equation coefficients.
Other studies have contradicted this assertion and did report the existence of struc-
tural breaks in the crude oil markets. Kang et al. (2011) employed univariate and bivari-
ate GARCH models with and without structural breaks considered. The ICSS method
was used to identify the structural change points. Five structural changes were observed,
corresponding to major global events. Accounting for these breaks significantly reduced
the level of long-term persistence in the models. Furthermore, Ewing and Malik (2010)
previously used the same method to determine the presence of regime switches in WTI
price volatility. The GARCH variance equation was amended to include a dummy term
for each break observed, similar to the external factors terms in equation (4b). When
accounting for the multiple breaks that were detected by the ICSS algorithm in the inter-
val studied, the level of long-term persistence was also significantly reduced. The half-
life of the shock effects was dramatically cut from about 41 days without structural
breaks to just 3 days.
Wilson et al. (1996) also highlighted the importance of considering sudden changes in
variance. In the 9 years studied using the ICSS methodology, they reported a total of 15
sudden variance changes in first contract futures volatility due to external events; these
events ranged from Organization of the Petroleum Exporting Countries policy changes,
war, to extreme weather.
Taking a different approach, Fong and See (2002) also observed two distinct high and
low volatility regimes when using a first-order Markov switching model.The model allows
for sudden changes in the coefficients in the mean and variance equations, depending on
the volatility state. To determine the regime specification, a transition probability formu-
lation is used that is driven by the basis at the previous time step; the basis can be defined as
the logarithmic difference of spot and futures prices. This method determines the likeli-
hood of a structural break at a point in time t. Interestingly, a regime-switching model that
excludes the variance component (becomes a function of returns only) outperformed one
that did in the log-likelihood statistic. A possible explanation given for this is the variance
term may be an artefact of the results. Ultimately, it was found that neglecting these breaks
in data can give the false perception of high predictability of volatility due to inaccurately
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high persistence. Enforcing the concept of persistence, it was found that regime switches
are low-probability events.
Furthermore, Vo (2009) took the same method as Fong and See (2002) to detect the
presence of regime switches, but an SV model was used instead for the estimation of vola-
tility. Examining another study, Chang (2012) modified the GARCH mean and variance
equations by including two different basis terms for the high and low volatility regimes.
Transition probabilities are used in a Markov switching model to detect structural breaks.
The findings regarding structural breaks in both studies are consistent with the general
views discussed previously.
4.4. Volatility spillover between markets
The spillover of information between markets is an essential area to explore given the
increasing interaction of global markets. On a broader economic level, the volatility of oil
prices has a significant impact on economic activity, and oil price changes are important
explanatory variables in movements in stock returns. It is found that price turbulence is
often transmitted from larger to small markets (Milunovich and Thorp, 2006). Pindyck
(2004) reported that as to be expected, crude oil volatility transfers to the natural gas
market, but not vice versa. The explanation is oil prices are determined on a more global
level than those of natural gas.
Moreover, Lu et al. (2008) studied this phenomenon and the Granger causality
between global crude oil markets. Granger causality was developed by Granger (1969) to
study the relationship between two time series, and whether one series has a predictive
relationship on another.A time series Xis said to Granger-cause another if it is shown that
historical values of Xprovide information about the future values of the other series. Both
the WTI and Brent markets exhibit spillover effects on each other, with the former being
slightly more dominant. There is also bidirectional information transfer between the WTI,
Brent, Dubai and Tapis oil markets.
With the increased consumption of biofuels and fuel blends in general, a closer rela-
tionship is forming between the oil market and other commodity markets. In the United
States, e.g., the major source of ethanol is corn; in Brazil, it is sugarcane. Tang and Xiong
(2010) found significant correlation between crude oil price and other commodity prices
since 2004. They also found the role of financial investors was more pronounced as they
aimed to diversify their portfolios. Great volatility in one market can often influence inves-
tor behaviour in other markets and cause volatility transfer.
To elaborate, Ji and Fan (2012) applied a bivariate EGARCH model to study the spillo-
ver effects of oil volatility on the metal, agriculture and aggregate non-energy commodi-
ties markets. Because most commodities are valued in US dollars, the currency’s index
was included as an external factor.The metal market was specified because increases in oil
prices usually lead to a rise in metal prices due to inflation. Interestingly, the study found
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that the price spillover effects between the WTI and the metal markets have been signifi-
cant and that the volatility spillover has been significant for all three markets. Volatility
spillover from the crude oil market to the three markets has been far greater than the spillo-
ver in the opposite direction, especially when oil prices are high (Ji and Fan, 2012).
In referencing structural breaks, a bivariate GARCH model was utilised by Kang et al.
(2011) to assess the effect of accounting for regime switches on volatility transmission
between the Brent and WTI markets.When neglecting the impact of structural changes in
the bivariate model, their study found that a bidirectional volatility transfer was present
between the two markets. When different volatility regimes were considered, however, the
shocks in the Brent market did not significantly impact the WTI market; theWTI effect on
Brent remained. When considering multiple assets or markets, taking a multivariate
approach is appropriate.
5. Factors influencing oil price volatility
A multitude of factors have been identified in the literature to influence the volatility of the
crude oil price. These factors range from the elasticity of supply and demand and inventory
levels to the trading volume and the open interest of options. Geopolitical events also play
a key role in influencing price movements.
5.1. Elasticity of supply and demand
The elasticity of oil supply and demand is one of the most prominent factors affecting the
price volatility. A lower elasticity in oil supply or demand generates higher price change
when a shock takes place. Yang et al. (2002) referred to the switching elasticity theory of
Greenhut et al. (1974) to explain the origins of oil price volatility. While the theory pro-
vides an estimate for the expected price elasticity of demand of a stable market, the authors
showed that external intervention has resulted in actual elasticity figures that are signifi-
cantly lower; thus, there is an inherent instability in the market structure.
Both Hamilton (2009b) and Baumeister and Peersman (2009) have observed a decline
of oil supply and demand elasticity since the mid-80s, especially with the launch of the
crude oil futures trading on the NYMEX. The implementation of computerised trading
systems on commodity exchange markets has reduced the sensitivity of commercial
dealers to short-term price fluctuations as fewer physical purchases are made and the
response to price development is limited by future oil contracts.
5.2. Inventory levels and storage
The behaviour of price movements may also be influenced by volume of stocks. Geman
and Ohana (2009) performed correlation tests between the volatility of WTI price spreads
(i.e. the difference between the near-month and long-term futures prices) and the monthly
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levels of US crude oil and Organisation for Economic Co-operation and Development
petroleum products inventories. In both cases, a negative correlation was reported during
the period of study. One plausible explanation for this is that a drop in inventory volumes
makes it more difficult for market players to quickly react to price changes. In a related
study, Pirrong (2010) reported significant positive correlation between US inventory
stocks and oil price spreads between 2000 and 2008.
5.3. Volume of transactions
There is a general finding in the literature of a positive correlation between volume of trans-
actions and volatility of oil price. Baumeister and Peersman (2009) suggested that if a
greater volume of oil transactions is made on the spot market, the variations of oil supplyand
demand will translate faster into price changes in the short term. Furthermore, Sidorenko
et al. (2002) previously found that both contemporaneous and lagged volumessignificantly
contribute to explain crude oil price variability. This results from the fact that hedgers
choose their volume of trading depending on their expectations of future price movements.
5.4. Open interest and maturity effect
Ripple and Moosa (2009) incorporated open interest as an external variable to the param-
eters explaining oil price volatility. Defined as the number of outstanding contracts exist-
ing at the end of the day in a futures market, open interests are considered as an offset to the
positive influence of trading volume on volatility. A large number of open interests in the
market will be translated into an increased market depth leading to greater contracts
liquidity and thus reducing volatility. Similar to Serletis (1992) and Herbert (1995),
Ripple and Moosa (2009) used a contract-by-contract analysis technique to model the
relationships between volatility, open interest, trading volume, and date-to-maturity as
a linear regressive function at time t.6
Their results reflect high significance of open interest and trading volume. Addition-
ally, the analysis showed that the two variables have different magnitude coefficients with
the negative influence of open interest on price volatility to be around half the respective
positive influence of trading volume. Hence, despite open interest being a variable of
statistical importance, its attenuating influence on volatility is only expected to reduce a
fraction of the one induced by the effect of trading volume, especially for the June and
December contracts which are typically the most heavily traded ones.
Furthermore, Samuelson (1965) suggested the volatility of any asset price decreases
when the maturity date of a contract is farther ahead in the future. The reason proposed for
this is that as the maturity date of a contract is approached, the prices become increasingly
sensitive to news and other external factors (Ripple and Moosa, 2009). Opinions diverge
about the role of maturity date on the volatility of future price. Galloway and Kolb (1996)
saw that the maturity effect can be observed with many commodities’ futures prices,
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including crude oil, after taking into account the cycle change of seasonal demand and
supply. The findings of the model utilised by Ripple and Moosa (2009) contradicted with
the previous studies. Their contract-by-contract analysis demonstrated that there is weak
correlation between maturity date and price volatility with negative coefficient.
To briefly explore this assertion, a GARCH(1,2) model is employed to determine the
historical volatility of the prices of 4-month crude oil contracts traded on the NYMEX
during the period of May 1987 to October 2011. These findings are compared to the vola-
tility of the first-month contracts in Figure 8.
As Figure 8 and statistical indicators show, the difference in the volatility between the
two contracts is found to be minimal, supporting the finding of Ripple and Moosa (2009).
Specifically, the mean absolute error (MAE) is used to compare the two series, and the
difference of the results amounts to 0.511 per cent; the formulation used is given by
equation (A7) in Appendix A.
5.5. Exchange rates
Multiple studies have shown a profound link between crude oil price shocks and the real effec-
tive exchange rate of the world’s main currencies, with a special emphasis on the US dollar.
Yousefi and Wirjanto (2004) denoted that a heavy fluctuation of the US dollar exchange
rate against other major currencies is likely to affect the international purchasing power from
oil revenues of most producers, rendering their reaction very unpredictable. In addition
to being the invoicing currency of crude oil, the US dollar is also reference for the many
oil-exporting economies that have pegged their national currency to the dollar for decades.
A study performed by the Czech National Bank (2011) estimated that since 2005,
a 1 per cent weakening of the effective exchange rate of the dollar has, on average, been
Figure 8 Conditional monthly volatility of WTI first and fourth futures crude oil contracts price.
Introduction to oil market volatility analysis 263
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accompanied by a rise in the Brent oil price of 2.1 per cent. The study also found a negative
average correlation of about -0.6 has been exhibited between Brent oil price and the dollar
since 1983. It must be noted that both series are non-stationary and are prone to spurious
correlation. Any correlation between the two series may not last into the future.
5.6. Economic, geopolitical and other shocks
Geopolitical and economic instabilities play an important role in shaping fluctuations of
crude oil prices due to supply and demand fears. Over recent decades, multiple political
instabilities have led to considerable increases in oil prices that were succeeded by fast
price adjustments once the crises were abated. Such examples of price shocks include the
invasion of Kuwait in 1990, the Iraq war in 2003 and the Libyan revolution in 2011.
However, Hamilton (2009a) suggested a shift in the reasons behind oil price shocks since
the late 90s. His interpretation suggests that the increase in oil price between 2003 and
mid-2008 was mainly driven by global demand shocks rather than by the traditional distur-
bances arising from oil supply shocks in the Middle East.
Natural disasters tend to generate asymmetric and disproportional responses from
traders resulting in record high oil price volatility. Ramsay (2009) explained that when
Hurricane Katrina destroyed more than one hundred off-shore oil platforms in May 2006,
WTI oil prices exhibited steep and sustained increases, outpacing the repercussions of
many political shocks.
Researchers have also tried to find if there were any other factors that can influence oil
price volatility. Pindyck (2004) investigated the possible effect of sweeping corporate
ethical misbehaviour leading to significant fluctuation in volatility. When reviewing the
example of the Enron scandal in 2001, he found that there was no significant statistical
increase in volatility during the considered period. Baumeister and Peersman (2009)
stated that increased macroeconomic stability can possibly translate to smaller disruptions
in the demand for oil and can be a factor in the reduction of oil price variability. Addition-
ally, Barsky and Kilian (2002) stated that institutional arrangements can lead to a sticki-
ness of the nominal oil price resulting from long-term crude oil contractual agreements.
6. Conclusion
This paper illustrated the sizeable amount of research that has been done on the subject
of crude oil price volatility, especially in recent years when policy-makers from both oil
consuming and producing countries have paid a large attention to crude oil price
changes. Certain properties of volatility have been consistently observed in long-term
historical prices. These include the lack of correlation in the change in price, an
increased inertial force to change in volatility regimes, regime switches and asymmetri-
cal behavior in volatility.
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An important aspect noticed in the reviewed studies was the prevalence of GARCH
models, none of them however emerging as a paramount reference for the forecasting of
crude oil price volatility. Comparative studies, which have examined the effect of differing
factors that influence oil price volatility, generally result in a lack of consensus on the supe-
riority of the forecasting capabilities of these models. It seems clear that there is an inher-
ent need to study alternative approaches. One promising alternative to study further is that
of artificial intelligence, which has already been used to forecast the volatility of equity
markets; however, this approach has not been thoroughly explored for oil price volatility. It
is expected that this area of research will form the core of our future research agenda.
1. The authors are grateful for the helpful comments provided by James L. Smith.
2. The marginal convenience yield is the economic benefit from having physical possession of
the commodity.
3. In some instances, e.g. Sadorsky (2006), volatility is defined as the variance of price returns.
4. Price data were obtained from the Energy Information Administration.
5. The formulas used for skewness, kurtosis and the Jarque–Bera test are described in
Appendix A.
6. The volatility measure used by Ripple and Moosa (2009) is defined as
ln ln( )high price low price
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Appendix A
This appendix provides further information on the computational approaches taken when
analysing the oil prices and price return.
1. Adjusted daily returns
Equation (A1) adjusts for n-1 intermediate non-trading days, following the procedure
detailed by Pindyck (2004).
rtn s
Pt n
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Where s1is the standard deviation of log price changes over an interval of one physical
day, and snis the standard deviation of log price changes over an interval of nphysical days.
When computing the returns from spot price, an additional adjustment is necessary to
account for the convenience yield (Pindyck, 2004).
2. Normality properties
To test for normality, the following distribution properties are examined. The skewness
property of a data set is computed by using equation (A2).
where Nis the number of observed data in a sample.
Additionally, kurtosis of a distribution is given by equation (A3).
The Jarque–Bera test for normality is defined in the following by equation (A4). kis the
number of estimated coefficients used to create the series.
3. Standard error for autocorrelation functions
At a 5 per cent significance level, two standard errors are taken at either side of the hori-
zontal axis. The equation for the upper and lower boundaries in the autocorrelation com-
putations is given by,
4. A non-parametric volatility model (moving-window approach)
To compute the price volatility by taking a non-parametric approach, the following discre-
tised equation may be used for the standard deviation of the returns. stdenotes volatility
and Nsis the subsample size within the time interval specified. r
ts,is the mean of the returns
of the interval being considered.
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5. MAE
To compare the conditional volatility results of WTI crude oil first- and fourth-month
futures prices, the following MAE formula is used.
i fourth i first
,, (A7)
Appendix B
The descriptive statistics of the WTI first-month futures price returns are presented
in the following table. The price data is observed from 27 May 1987 to 12 October
Table 2B presents the results of the GARCH(1,2) estimation for the WTI first futures
contract prices.
Tab l e 1 B Descriptive statistical analysis results for adjusted daily and monthly returns
Parameter Adjusted daily returns Monthly returns
Sample size (N) 6120 292
Mean (m) 2.35 (10-4) 5.003 (10-3)
Sample standard deviation (ss) 0.024 0.100
Skewness (S)-0.990 -0.201
Kurtosis (K) 20.49 4.46
Jarque–Bera test (JB) 78,997 28.02
Probability that normality is exhibited 0*** 0***
*** Indicates that the null hypothesis is rejected at the 1 per cent level.
Tab l e 2 B GARCH regression coefficients for monthly first futures crude oil contract
Coefficient Value [standard error]
a01.384 (10-3) [6.43(10-4)]
a10.136 [0.069]
b11.199 [0.281]
b2-0.471 [0.205]
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The volatility is one of the essential characteristics of financial time series, which is vital for the knowledge acquisition from financial data. However, since the high noise and nonsteady features, the volatility identification of financial time series is still a challenging problem. In this paper, from a perspective of granule complex network, a novel approach is proposed to study this problem. First, numeric time series is structured into fuzzy information granules (FIGs), where the segments of time series in each granule would own similar volatility features. Second, by using the transfer relations among granules, granule complex network is to be constructed, which intuitively describes the transfer processes among the different volatility patterns. Third, a novel community detection algorithm is applied to divide the granule complex networks, where granules with frequent mutual transfers would belong to the same granule community. Finally, Markov chain model is carried out to analyze the higher level of transfer processes among different granule communities, which would further describe the larger-scale transitions of volatility in overall financial time series. An empirical study of the proposed system is applied in the Shanghai stock index market, where volatility patterns of financial data can be effectively acquired and the corresponding transfer processes can be analyzed by means of the granule communities.
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This paper aims to investigate the bidirectional relationship between oil market and the Saudi stock market (Tadawul), in addition to studying whether the positive and negative shocks in one market have asymmetric effects on the other market or not. Data are collected Weekly from the 15th of May 2007 for the main sample and from the 9Th of September 2014 for the subsample to the 2nd of October 2018 for both samples. The Asymmetric BEKK-GARCH (1,1) Model is employed to achieve the study objectives. The crude oil implied volatility index (OVX) derived from oil option prices is used to measure oil prices. The structural breaks tests were applied and the researcher didn't detect any structural breaks in both series of oil and stock returns. In addition, oil and stock market returns should be used instead of their prices based on unit root and Stationarity tests. The findings show a unidirectional relationship from the Saudi stock market to the oil market. Besides, there is no significant difference between the effects of positive and negative shocks on the conditional volatility of returns in each market. There is an evidence for the weak-form efficiency in the Saudi stock market, but this evidence is not detected in the oil market. The findings of this paper is useful for investors, financial experts, and policy makers. In addition, several avenues for future researches are proposed.
The beginning of the new century was marked with another petroleum boom and bust cycle. Oil prices were hovering around $18-20/bbl through most of the 1990s after which crude prices collapsed to $10/bbl in 1998 and 1999. Soon thereafter oil prices began a steady and, at times, sharp rise on the way to $147/bbl in July 2008. This climb was followed by an abrupt decline after the onset of the global “Lehman” economic crises in September 2008 driving down the crude oil price to as low as $32/bbl in December 2008. After a relatively swift recovery, another oil shock “market share” took place in 2014-2016; average oil prices plunged from $108/bbl in the second quarter of 2014 to $30/bbl in the first quarter of 2016. Brent kicked off 2018 with average oil prices of $69/bbl in January toggling around the $85/bbl during October 2018; since then, however, oil prices were dwindling from $80/bbl to $51/bbl by 2018 year end. The year of 2019 started with a fluctuating Brent oil prices around the 55-65$/bbl range. The rapid increase in the oil price and its sudden and dramatic decline raises a fundamental question about the oil industry: Why is it so difficult to accurately predict the price of oil? Supply-demand balance, economic growth, oil inventories, and spare capacity are market fundamentals that drive oil prices and market dynamics. Market financialization, resources availability, technology advancements, and geopolitical events are also important drivers of oil price movements. Collaborative efforts should be geared towards: an acceptable and reasonable level of oil prices for the benefits of oil producers and consumers alike; meeting the future oil demand and availing adequate spare capacity to the market; and incentivizing upstream capital investment. Reasonable predictions of oil prices require a reliable and consistent data, rigorous advanced analytical methods, intelligent forecasting tools, and a better understanding of the influential factors impacting the oil prices and oil market conditions.
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We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
Previous researches on oil price volatility have been done with parametric models of GARCH types. In this work, we model volatility of crude oil price based on GARCH(p,q) by using Neural Network which is one of powerful classes of nonparametric models. The empirical analysis based on crude oil prices in US and China show that the proposed models significantly generate improved forecasting accuracy than the parametric model of normal GARCH(p,q). Among nine different combinations of hybrid models (for p = 1,2,3 and q = 1,2,3), it is found that NN-GARCH(1,1) and NN-GARCH(2,2) perform better than the others in US market whereas, NN-GARCH(1,1) and NN-GARCH(3,1) outperform in Chinese case.
A volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications. In this paper we outline some stylized facts about volatility that should be incorporated in a model: pronounced persistence and mean-reversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables influencing volatility. We use data on the Dow Jones Industrial Index to illustrate these stylized facts, and the ability of GARCH-type models to capture these features. We conclude with some challenges for future research in this area.
The influence of price volatility in the crude oil market is expanding to non-energy commodity markets. With the substitution of fossil fuels by biofuel and hedge strategies against inflation induced by high oil prices, the link between crude oil market and agriculture markets and metal markets has increased. This study measures the influence of the crude oil market on non-energy commodity markets before and after the 2008 financial crisis. By introducing the US dollar index as exogenous shocks, we investigate price and volatility spillover between commodity markets by constructing a bivariate EGARCH model with time-varying correlation construction. The results reveal that the crude oil market has significant volatility spillover effects on non-energy commodity markets, which demonstrates its core position among commodity markets. The overall level of correlation strengthened after the crisis, which indicates that the consistency of market price trends was enhanced affected by economic recession. In addition, the influence of the US dollar index on commodity markets has weakened since the crisis.
This study employs a flexible regime-switching EGARCH model with Student-t distributed error terms to investigate whether volatility regimes and basis affect the behavior of crude oil futures returns, including the conditional mean, variance, skewness, kurtosis as well as the extent of heavy-tailedness. The study also examines whether volatility regimes and asymmetric basis effects can improve the forecasting accuracy. The main merit of the empirical model is that the basis effect is allowed to be asymmetric and to vary across volatility regimes. Empirical results suggest that the conditional mean and variance respond to the basis asymmetrically and nonlinearly, and that the responses of transition probabilities to the basis are symmetric. Furthermore, the conditional higher moments are sensitive to the absolute value of basis, and the heavy tailed characteristic can be greatly alleviated by taking into account the asymmetric basis effects and regime switches. Finally, the regime switches and asymmetric basis effects play decisive roles in forecasting return, volatility and tail distribution.
This study examines the influence of structural changes in volatility on the transmission of information in two crude oil prices. In an effort to assess the impact of these structural changes, we first identify the time points at which structural changes in volatility occurred using the ICSS algorithm, and then incorporate this information into our volatility modeling. From the estimation results using a bi-variate GARCH framework with and without structural change dummies, we find that the degree of persistence of volatility can be reduced via the incorporation of these structural changes in the volatility model. In this direction, we conclude that ignoring structural changes may distort the direction of information inflow and volatility transmission between crude oil markets.
Using Hong's method based on Cross Covariance Function (CCF) and Error Correction Model (ECM), this article studies Granger causality and information spillovers among major global crude oil markets including London, New York, Dubai as well as Tapis and Minas in Southeast Asia. The results show that London and New York futures markets play dominant roles in information spillover, and WTI crude oil futures has a slight edge over Brent crude oil futures in information transmission by using methodology introduced by Hong. In addition, empirical results show Hong's method is more effective than ECM in testing Granger causality and information spillovers.
The use of parametric GARCH models to characterise crude oil price volatility is widely observed in the empirical literature. In this paper, we consider an alternative approach involving nonparametric method to model and forecast oil price return volatility. Focusing on two crude oil markets, Brent and West Texas Intermediate (WTI), we show that the out-of-sample volatility forecast of the nonparametric GARCH model yields superior performance relative to an extensive class of parametric GARCH models. These results are supported by the use of robust loss functions and the Hansen's (2005) superior predictive ability test. The improvement in forecasting accuracy of oil price return volatility based on the nonparametric GARCH model suggests that this method offers an attractive and viable alternative to the commonly used parametric GARCH models.Highlights► We employ a nonparametric method to model and forecast oil price return volatility. ► The out-of-sample volatility forecast of the nonparametric GARCH model is superior to parametric GARCH models. ► The results are further supported by Hansen's (2005) superior predictive ability test. ► Improvement in forecasting accuracy of oil price return volatility suggests usefulness of the nonparametric approach.