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Electronic copy available at: http://ssrn.com/abstract=2194214
1
An Introduction to Oil Market Volatility Analysis
Walid Matar
1
, Saud M. AlFattah, Tarek Atallah, and Axel Pierru
King Abdullah Petroleum Studies and Research Center (KAPSARC)
ABSTRACT
Modeling 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 modeling 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,
WTI futures price data is used to illustrate these properties using nonparametric and conditional
modeling methods. The GARCHtype 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
Since 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. Longterm uncertainty in future oil prices can alter the incentives to develop new oil
fields in producing countries. This can also hinder the implementation of alternative energy
policies in consuming countries. In the shortterm, volatility can affect the demand for storage, as
greater volatility should lead to increased storage demand, spot prices, and the marginal
convenience yield
2
. Last but not least, volatility is a key variable in the pricing of derivatives
whose trading volume has significantly increased in the last decade. In all of these applications,
it is essential that some level of predictability can be captured when modeling oil price volatility.
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 properties and modeling
1
Email addresses: walid.matar@kapsarc.org, saud.fattah@kapsarc.org, tarek.atallah@kapsarc.org,
axel.pierru@kapsarc.org. 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.
Electronic copy available at: http://ssrn.com/abstract=2194214
2
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 the third section, the various
approaches to modeling volatility in the oil markets are detailed. The stylized properties of
volatility are explored in the fourth section, 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 comprehensive model, the fifth section
examines the external factors that may impact the volatility of the oil price.
2. CRUDE OIL PRICE RETURNS
2.1 Return and Volatility: Two Related Concepts
Volatility is typically quantified as the standard deviation
3
of 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 ∆t, which could range from seconds to
months, the standard definition of the price return is then derived by,
(1a)
Where is the price of crude oil at t. Hence,
(1b)
For illustrative purposes, Figures 1 and 2 provide the daily and monthly returns on WTI first
month futures price, respectively. The price data is observed from May 27
th
, 1987 to October
12
th
, 2011
4
. The daily returns have been adjusted for intermediate nontrading days – weekends
and holidays – following the procedure suggested by Pindyck (2004) and explained in Appendix
A. In calculating the returns at the monthly time scale, the futures price on the tenth day of each
month is considered to avoid proximity with contract expiration dates. For months whose tenth
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 20082009 global economic recession. In both
instances, the clustering of large changes in price was present for a significant period of time. An
example of price shocks in the daily returns data can be visualized on January 17
th
, 1991. Oil
prices dropped sharply that day as the mission to expel Iraqi troops from Kuwait was initiated.
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, http://www.eia.gov/.
Electronic copy available at: http://ssrn.com/abstract=2194214
3
2.2 Properties and Analysis of Returns
It is wellestablished in finance that returns do not follow a normal distribution, and one
stylized 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 skewness
5
of 0.99 and 0.20,
respectively, suggesting both curves are skewed to the left of the mean. Additionally, 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 analyzed is shown in Appendix B. The JarqueBera test rejects normality at
the 1% significance level for both distributions. For the purpose of illustration, Figure 3 fits both
distributions with continuous probability density functions.
Figure 1 – Adjusted Daily Returns of First Contract Futures (NYMEX)
5
The formulas used for skewness, kurtosis, and the JarqueBera test are described in Appendix A.
0.41
0.31
0.21
0.11
0.01
0.09
May 1987 Feb 1990 Nov 1992 Aug 1995 May 1998 Jan 2001 Oct 2003 Jul 2006 Apr 2009
4
Figure 2 – Monthly Returns of First Contract Futures (NYMEX)
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. Figure 4 displays the normal
QuantileQuantile plots for the daily and monthly returns. The presence of heavy tails in the
daily returns is prominent. While the data in the middle of the distribution lie closely along the
regression line, data at the left and right ends curve upward and downward, respectively. These
curvatures and their specific orientation indicate the presence of heavier tails than those of a
normal distribution. Since the kurtosis of the daily returns is far larger than that of the monthly
returns, heavy tails are more noticeable.
Figure 3 – Probability density functions of the Daily and Monthly Price Returns
0.5
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
0.5
May 1987 Feb 1990 Nov 1992 Aug 1995 May 1998 Jan 2001 Oct 2003 Jul 2006 Apr 2009
5
Figure 4 – QuantileQuantile Plots for Oil Price Returns
Returns do not share inherent predictive properties, as past returns do not provide
information on future returns. For both daily and monthly returns, this is illustrated in Figures 5
and 6 by applying the autocorrelation function, , defined below.
(2)
where is the time increment. The upper and lower boundaries represent the standard 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 zeroline suggest the presence is not substantive.
Figure 5 – Autocorrelation of the Daily Returns
0.1
0.08
0.06
0.04
0.02
0
0.02
0.04
0.06
0.08
0.1
0 10 20 30 40 50 60
Autocorrelation
Lags (Trading Days)
Returns
Upper and Lower Boundaries
6
Figure 6 – Autocorrelation of the Monthly Returns
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 behavior is best displayed when the absolute values of the returns are raised to the first
power [Cont (2001)].
(3)
If significant positive autocorrelation of absolute returns is observed for several lags, then the
clustering is present. Figures 7 and 8 present the autocorrelation of the absolute daily and
monthly returns. The autocorrelation for the daily returns is consistently above zero, showing the
clustering property. Although not as prominent, there is significant autocorrelation up to the
fourth lag for the monthly values.
It is often observed that negative movements in returns lead to greater volatility than positive
movements of the same magnitude. This phenomenon, called the leverage effect, is explored in a
later section.
0.25
0.2
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
0.25
0 3 6 9 12
Autocorrelation
Lags (Months)
Returns
Upper and Lower Boundaries
7
Figure 7 – Autocorrelation of the Absolute Adjusted Daily Returns
Figure 8 – Autocorrelation of the Absolute Monthly Returns
3. VOLATILITY MODELING AND MEASUREMENT
As stated previously, if the price return at time t follows a probability law with standard
deviation,
, then
is the volatility at time t. Empirical modeling of volatility can be performed
using nonparametric and parametric methods. Nonparametric methods directly compute
volatility without any functional specification, and they iteratively fit the data by factoring in
0.05
0
0.05
0.1
0.15
0.2
0.25
0 10 20 30 40 50 60
Autocorrelation
Lags (Trading Days)
Absolute Daily Returns
Upper and Lower Boundaries
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0 3 6 9 12
Autocorrelation
Lags (Months)
Absolute Monthly Returns
Upper and Lower Boundaries
8
lagged returns. An example of these methods used by Pindyck (2004) is determining the sample
standard deviation of returns over a moving window. This method provides 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 analyzing 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 generalized autoregressive conditional heteroskedasticity (GARCH) model is
used to provide estimates of volatility at different time scales. Contrary to nonparametric
methods, these conditional models fit data using maximum likelihood estimation and have the
capability of accounting for exogenous variables. Applied to volatility,
, 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, ε, have predictive influence on conditional variance. The notation of p and q refers to
how many lagged innovation and autoregressive terms are incorporated in the variance equation.
(4a)
(4b)
Where α
j
, β
j
, and γ
k
are the regression coefficients to be computed. is the mean of the
returns. α
0
is the unconditional volatility. L
k
denotes any external factors that have significant
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 analyzed for WTI firstcontract 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 Table 2B in Appendix B and the curve is
presented in Figure 9. For comparison, the result of a nonparametric method that directly
computes the standard deviation of a moving window is also shown with the GARCH model
results. Volatility spikes of over 20% are observed during the first Gulf War (19901991) and the
most recent global economic recession (20082009).
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
GARCHclass models available with the purpose of capturing observed characteristics of
volatility. Table 1 summarizes the features of different models.
Figure 9 –
Monthly Volatility of First Futures Crude Oil Contract Price
Table 1 – Different
Classes of GARCH
Model
(Standard) GARCH
The conditional volatility is a linear function of past volatility and
innovation. They are more effective in modeling short
Integrated GARCH
(IGARCH)
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 li
Fractionally Integrated
GARCH (FIGARCH)
A non
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
Exponential GARCH
(EGARCH)
A non
behavior in volatility by examining the ratio of the residual and the
coefficients to be positive, this model removes this
0
0.05
0.1
0.15
0.2
0.25
May 1987 Feb 1990
Nov 1992
9
Monthly Volatility of First Futures Crude Oil Contract Price
Classes of GARCH
Models and their Application to
Oil Market Volatility
Model Features
The conditional volatility is a linear function of past volatility and
innovation. They are more effective in modeling short
than longterm volatility.
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 li
maintains the lasting effect of shocks indefinitely.
A non

linear model that captures long memory shocks effectively.
Unlike IGARCH, it provides a slow decay of shocks over time.
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.
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
Nov 1992
Aug 1995 May 1998 Jan 2001 Oct 2003 Jul 2006
NonParametric Method
Conditional Method (GARCH)
Monthly Volatility of First Futures Crude Oil Contract Price
Oil Market Volatility
The conditional volatility is a linear function of past volatility and
innovation. They are more effective in modeling short
term volatility
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 li
near model
maintains the lasting effect of shocks indefinitely.
linear model that captures long memory shocks effectively.
Unlike IGARCH, it provides a slow decay of shocks over time.
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.
linear model that is effective in accounting for asymmetric
behavior in volatility by examining the ratio of the residual and the
1. While linear GARCH models often restrict
coefficients to be positive, this model removes this
restriction.
Apr 2009
10
Hyperbolic GARCH
(HYGARCH)
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 favorable
stationarity features of the standard GARCH model.
GARCHinMean
(GARCHM)
GARCHM 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 timevarying conditional
covariance of returns. These models are useful when simultaneously
computing the volatility of multiple assets.
Component GARCH
(CGARCH)
This model is a specific formulation of GARCH(2,2). It improves the
modeling of longterm effects by decomposing the model into long
run and shortrun components.
Neural Network
GARCH (NNGARCH)
A hybrid model that incorporates neural networks with GARCH
estimates the extreme values of volatility more effectively than
GARCH models alone.
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 misspecification.
The main differentiator in modeling and forecasting performance comes in the effectiveness
in accounting for longterm 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 external 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 GARCHclass model outperforms
the others in all situations. As the standard GARCH model falls short in capturing the effects of
longterm 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 GARCHclass models have been the most widelyused 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, stochastic 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. The studies dealing with modeling and
forecasting crude oil price volatility are summarized in Appendix C.
11
3.2 Alternative Definitions of Volatility
With the use of high frequency data feeds, realized volatility is the variance of the observed
returns over a fixed time interval. Computed at high sampling frequencies, realized volatility
could be used as a proxy for actual daily volatility. Typically used as the reference in forecasts,
the actual daily volatility at time t is then defined nonparametrically as the square of the return
at that time point.
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 t and the subsample mean, as described by the nonparametric 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 definition
deals with the option value of the asset, of which volatility is an important determinant.
Inherently, this is a forecast of volatility since it is computed from a forwardlooking derivative
price. IV is found as a better predictor of future volatility than historical values, but it is
generally outperformed in that regard by GARCHtype models for sufficiently long forecast
horizons [Agnolucci (2009); Christensen and Prabhala (1998)
*
; Szakmary et al. (2003)
*
]. 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.
Additionally, 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 sections.
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 movements
yield a larger rise in volatility. It can be illustrated by looking at the correlation of the square of
the return in time t with the value of the returns at t1; this is given by Equation 5. If the
correlation starts negative and decays to zero, then the leverage effect is present [Cont (2001)].
(5)
Narayan and Narayan (2007) analyzed oil price data during the period of 1991 to 2006 for
the volatility response to shocks using an EGARCH model to capture the asymmetric behavior.
*
These studies do not specifically deal with the oil price.
12
Their findings were mixed, as the computation results showed that for certain subsample
periods, the volatility was affected asymmetrically by shocks, whereas symmetric behavior was
observed for other periods. It is suggested, however, that for long 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 overarching behavioral 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 marketdependent. 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 leverage effect in the volatility in the
WTI market. The latter study does report such behavior for the Brent market.
Moreover, this absence of asymmetric behavior 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 specific 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 behavior may be attributed to the
differences in marketspecific 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 synchronized. 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 behavior.
To complement the previous discussion with practical analysis, the correlation defined by
Equation 5 is carried out for the WTI market returns data analyzed earlier to study the presence
of the leverage effect. The results of the correlation are displayed in Figures 10 and 11 for the
daily and monthly returns, respectively. For the daily values, there is asymmetry for the first lag,
and then it decays to zero at the 5% significance level; some longterm 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 nontrading 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 points.
13
Figure 10 – Daily Correlation of Lagged Returns with the Square of the Returns
Figure 11 – Monthly Correlation of Lagged Returns with the Square of the Returns
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 persistence
behavior is consistent with volatility, and there is an overwhelming consensus in the literature
0.25
0.2
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
0.25
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Correlation
Lags (Trading Days)
Upper and Lower Boundaries
Correlation
0.25
0.2
0.15
0.1
0.05
0
0.05
0.1
0.15
0.2
0.25
0 3 6 9 12
Correlation
Lags (Months)
Upper and Lower Boundaries
Correlation
14
that longterm 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 slowlydecaying 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 longterm
period, however, the behavior of clustering is clearly displayed. Going even a step further, Kang
et al. (2009) observed strong longterm persistence for WTI, Brent, and Dubai, which was later
confirmed by Wei et al. (2010) for the first two markets; Sidorenko (2002) observed the same
trends with Brent secondmonth 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 postprocessing of the results by Pindyck (2004), the
lasting effect of persistence of volatility was quantified by examining the halflife of historical
shocks. It was found that the impact of shocks is maintained for three to eleven 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
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 oilbased 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 suddenly change the variance
equation coefficients.
Other studies have contradicted this assertion and did report the existence of structural
breaks in the crude oil markets. Kang et al. (2011) employed univariate and bivariate 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 longterm 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
15
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 interval studied, the level of longterm persistence was also significantly
reduced. The halflife 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 nine years studied using the ICSS methodology, they reported a total of fifteen
sudden variance changes in first contract futures volatility due to external events; these events
ranged from OPEC 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 firstorder 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 formulation 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 likelihood of a structural break
at a point in time, t. Interestingly, a regimeswitching model that excludes the variance
component (becomes a function of returns only) outperformed one that did in the loglikelihood
statistic. A possible explanation given for this is the variance term may be an artifact 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 high persistence. Enforcing the concept of
persistence, it was found that regime switches are lowprobability 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 volatility.
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
16
relationship between two time series, and whether one series has a predictive relationship on
another. A time series X is said to Grangercause another if it is shown that historical values of X
provide 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 relationship
is forming between the oil market and other commodity markets. In the United States, for
example, 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 investor behavior in other
markets and cause volatility transfer.
To elaborate, Ji and Fan (2012) applied a bivariate EGARCH model to study the spillover
effects of oil volatility on the metal, agriculture, and aggregate nonenergy commodities markets.
Since 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 that the price spillover effects
between the WTI and the metal markets have been significant, 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 spillover in the opposite direction, especially when oil
prices are high [Ji and Fan (2012)].
In referencing structural breaks, a bivariate GARCH model was utilized 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; the WTI 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.
17
(1974) to explain the origins of oil price volatility. While the theory provides 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 significantly 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 mideighties, especially with the launch of the crude oil
futures trading on the NYMEX. The implementation of computerized trading systems on
commodity exchange markets has reduced the sensitivity of commercial dealers to shortterm
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 behavior 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 nearmonth and longterm futures prices) and the monthly levels of US
crude oil and OECD 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
transactions 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 supply and
demand will translate faster into price changes in the shortterm. Furthermore, Sidorenko et al.
(2002) previously found that both contemporaneous and lagged volumes significantly 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 parameters
explaining oil price volatility. Defined as the number of outstanding contracts existing 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 contractby
18
contract analysis technique to model the relationships between volatility, open interest, trading
volume, and datetomaturity as a linear regressive function at time t.
6
Their results reflect high significance of open interest and trading volume. Additionally, 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. Gollaway (1996) saw that the maturity effect can
be observed with many commodities’ futures prices, including crude oil, after taking into
account the cycle change of seasonal demand and supply. The findings of the model utilized by
Ripple and Moosa (2009) contradicted with the previous studies. Their contractbycontract
analysis demonstrated that there is weak correlation between maturity date and price volatility
with negative coefficient.
Figure 12 – Conditional Monthly Volatility of WTI First and Fourth Futures Crude Oil
Contracts Price
6
The volatility measure used by Ripple and Moosa (2009) is defined as
, following the
concept proposed by Parkinson (1980).
0
0.05
0.1
0.15
0.2
0.25
May 1987 Feb 1990 Nov 1992 Aug 1995 May 1998 Jan 2001 Oct 2003 Jul 2006 Apr 2009
First Futures Contract
Fourth Futures Contract
Volatility
To briefly explore this assertion,
historical volatility of the prices of fourth
during the period of May, 1987, to October, 2011
of the first
month contracts in Figure 12.
As Figure 12 and statistical indicators show, the difference in the volatility between the two
contracts is found to be minimal
Specifically, the mean absolute error (MAE) is used to compare the two series, and the
difference of the results amounts to 0.511%; the formula
Appendix A.
5.5 Exchange Rates
Multiple studies have
shown
effective exchange rate of the world’s main currencies
Yousefi and Wirjanto (2004) denote
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
invoic
ing currency of crude oil, the US dollar
economies that
have pegged their national
(2011) observed a historical
inverse relation
exchange rate.
A study performed by the Czech National Bank (CNB)
2005,
a 1% weakening of the effective exchange rate of the dollar has
accompanied by a rise in the Brent oil price of 2.1%.
correlation of about 0.6
has been exhibited
must be noted that both series are non
correlation between the two series may not last into the future.
Figure 13 –
Correlation between Brent crude oil and USD exchange rate [CNB]
19
To briefly explore this assertion,
a GARCH(1,2) model is employed
to determine the
historical volatility of the prices of fourth
month crude oil contracts traded
during the period of May, 1987, to October, 2011
. These findings are compared to the volatility
month contracts in Figure 12.
As Figure 12 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%; the formula
tion used
is given by Equation A
shown
a profound
link between crude oil price shocks and the real
effective exchange rate of the world’s main currencies
, w
ith a special emphasis on the U
Yousefi and Wirjanto (2004) denote
d
that a heavy fluctuation of the US dollar exchange rate
against other major currencies is likely to affect the international purchasing power from oil
rendering their reaction very unpredictable. In addition to being the
ing currency of crude oil, the US dollar
is also reference for
the many oil
have pegged their national
currency to the dollar for de
cades.
inverse relation
ship between the price of crud
e oil and the US
A study performed by the Czech National Bank (CNB)
additionally
estimated that since
a 1% weakening of the effective exchange rate of the dollar has
on average
accompanied by a rise in the Brent oil price of 2.1%.
Illustrated in Figure 13, a
has been exhibited
between Brent oil price and the
dollar
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.
Correlation between Brent crude oil and USD exchange rate [CNB]
to determine the
on the NYMEX
. These findings are compared to the volatility
As Figure 12 and statistical indicators show, the difference in the volatility between the two
, supporting the finding of Ripple and Moosa (2009)
.
Specifically, the mean absolute error (MAE) is used to compare the two series, and the
is given by Equation A
7 in
link between crude oil price shocks and the real
ith a special emphasis on the U
S dollar.
that a heavy fluctuation of the US dollar exchange rate
against other major currencies is likely to affect the international purchasing power from oil
rendering their reaction very unpredictable. In addition to being the
the many oil
exporting
cades.
Babusiaux et al.
e oil and the US
Dollar
estimated that since
on average
been
negative average
dollar
since 1983. It
stationary and are prone to spurious correlation. Any
Correlation between Brent crude oil and USD exchange rate [CNB]
20
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
(2009) suggested a shift in the reasons behind oil price shocks since the late nineties. His
interpretation suggests that the increase in oil price between 2003 and mid2008 was mainly
driven by global demand shocks rather than by the traditional disturbances arising from oil
supply shocks in the Middle East.
Natural disasters, characterized by an unpredictable damage scale, 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 offshore oil platforms in May 2006, WTI oil prices skyrocketed into 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. Pyndick (2004) investigated the possible effect of sweeping corporate ethical
misbehavior 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. Additionally, Barsky and Kilian (2002)
stated that institutional arrangements can lead to a stickiness of the nominal oil price resulting
from longterm 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 policymakers 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 longterm historical prices. These include the
stationarity of the price return, an increased inertial force to change in volatility regimes, regime
switches, and asymmetrical behavior in volatility.
An important aspect noticed in the reviewed studies was the prevalence of GARCH models.
None of them, however, have emerged 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 superiority of the
forecasting capabilities of these models. One promising alternative to study further is that of
21
artificial intelligence with a neural network, which has already been used to forecast the
volatility of financial markets. It is expected that this area of study will form the core of our
future research.
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25
APPENDIX A
This appendix provides further information on the computational approaches taken when analyzing
the oil prices and price return.
1.) Adjusted Daily Returns
Equation A1 adjusts for n1 intermediate nontrading days, following the procedure detailed by
Pindyck (2004).
(A1)
where
is the standard deviation of log price changes over an interval of one physical day, and
is
the standard deviation of log price changes over an interval of n physical 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.
(A2)
where,
N = The number of observed data in a sample.
Additionally, kurtosis of a distribution is given by Equation A3.
(A3)
The JarqueBera test for normality is defined below by Equation A4. is the number of estimated
coefficients used to create the series.
(A4)
3.) Standard Error for Autocorrelation Functions
At a five percent significance level, two standard errors are taken at either side of the horizontal axis.
The equation for the upper and lower boundaries in the autocorrelation computations is given by,
(A5)
4.) A Nonparametric Volatility Model (MovingWindow Approach)
To compute the price volatility by taking a nonparametric approach, the following discretized
equation may be used for the standard deviation of the returns.
denotes volatility, and N
s
is the sub
sample size within the time interval specified.
is the mean of the returns of the interval being
considered.
(A6)
5.) Mean Absolute Error (MAE)
To compare the conditional volatility results of WTI crude oil first and fourthmonth futures prices,
the following MAE formula is used.
(A7)
26
APPENDIX B
The descriptive statistics of the WTI firstmonth futures price returns are presented in the table below.
The price data is observed from May 27
th
, 1987 to October 12
th
, 2011.
Table 1B – Descriptive Statistical Analysis Results for Adjusted Daily and Monthly Returns
Parameter Adjusted Daily Returns Monthly Returns
Sample Size (N) 6,120 292
Mean (µ) 2.35(10
4
) 5.003(10
3
)
Sample Standard Deviation (σ
s
) 0.024 0.100
Skewness (S) 0.990 0.201
Kurtosis (K) 20.49 4.463
JarqueBera Test (JB) 78,997 28.02
Probability that Normality is
Exhibited 0*** 10
6
***
*** indicates that the null hypothesis is rejected at the 1% level.
Table 2B presents the results of the GARCH(1,2) estimation for the WTI first futures contract prices.
Table 2B – GARCH Regression Coefficients for Monthly First Futures Crude Oil Contract
Coefficient Value [Standard Error]
α
0
1.384(10
3
) [6.43(10
4
)]
α
1
0.136 [0.069]
β
1
1.199 [0.281]
β
2
0.471 [0.205]
27
APPENDIX C
Table 1C – Summary of Studies Modeling Crude Oil Price Volatility
Author(s) Asset(s)
Observation
Period and
Data
Frequency
Model(s)
Used
Forecast
Horizon Conclusion Comments
Agnolucci
(2009)
FirstMonth
Contract
Crude Oil
Futures on
WTI
December 31
st
,
1991 to May 2
nd
,
2005 [Daily]
GARCH and
CGARCH N/A
GARCHtype models are better predictors
of volatility than implied volatility. There
is no asymmetric behavior observed in the
volatility.
No mention of
forecast horizon
Arouri et al.
(2012)
WTI Crude
Oil Spot and
First and
Second
Contract
Futures
January 2
nd
,
1986 to March
15
th
, 2011
[Daily]
GARCH,
IGARCH
FIGARCH,
and GJR
1, 20, and
60 Days
No structural breaks are found in the crude
oil prices specifically. If such breaks exist,
however, a GARCH model that takes them
into account improves forecasting
accuracy.
Other oil
derivatives are
considered and
they do exhibit
breaks.
Brunetti
and Gilbert
(2000)
Second
Month Crude
Oil Futures
Contract of
Brent and
WTI
1983 to March
1999 (WTI) and
June 1988 to
March 1999
(Brent) [Daily]
Multivariate
FIGARCH
and Fractional
Cointegration
N/A WTI and Brent crude oil price volatilities
are cointegrated.
Monthly
volatility is
computed from
daily returns.
Chang
(2012)
WTI Crude
Oil Futures
January 1
st
, 1990
to July 28
th
,
2010 [Weekly]
Single
Regime and
Regime
Switching
EGARCH
using Markov
Switching
Process
1 Week
Incorporating regimeswitching into the
model increases its degrees of freedom,
which in turn improves forecasting
performance. It is found that as the basis
increases, the probability that a regime
state is maintained increases. A high
volatility state was more prevalent in the
time period of study.
Weekly prices
are taken as the
closing price at
the end every
Wednesday.
28
Cheong
(2009)
Spot WTI
and Brent Oil
Contracts
January 4
th
,
1993 to
December 31
st
,
2008 [Daily]
GARCH,
APRARCH,
FIGARCH,
and
FIAGARCH
5, 20, 60,
and 100
Days
Asymmetry is present in the Brent market
but not in WTI volatility. Persistence is
exhibited for both markets. The simple
GARCH model provides satisfactory short
term forecasts. The WTI forecasts
benefited from the addition of asymmetry
and longpersistence variables.
Ewing and
Malik
(2010)
WTI Crude
Oil Spot
Contracts
July 1
st
, 1993 to
June 30
th
, 2008
[Daily]
GARCH with
and without
structural
break
variables
N/A
The persistence parameter in GARCH was
significantly weakened after the
introduction of structural break variables,
and the duration of shock effects was
dramatically reduced. The model with
structural breaks improves the volatility
estimation.
Although
returns should
not be serially
correlated, the
authors include
the lagged
return in the
mean GARCH
equation.
Fengbin et
al. (2008)
WTI, Brent,
Tapis, Minas,
and Dubai
Crude Oil
Futures and
Spot
Contracts
January 2
nd
,
2003 to August
25
th
, 2006
[Daily]
Cross
correlation
Function and
Cointegration
ECM
N/A
The price spillover effects between the
WTI and the metal markets have been
significant, and that the variance spillover
has been significant for all three markets.
The impact of variance spillover from the
crude oil market on the three markets is far
greater when oil prices are high.
Fong and
See (2002)
WTI Second
Futures
Contract
January 2
nd
,
1992 to
December 31
st
,
1997 [Daily]
Markov
Switching
Process,
GARCH,
Regime
Switching
(RS) model,
RSARCH/
GARCH
1 Day
Two distinct volatility regimes are present.
RSARCH is most accurate for shortterm
forecasts. Neglecting multiple volatility
regimes can exaggerate the presence of
clustering. It is found that as the basis
increases, so does the probability that a
regime transition will take place.
Seasonal
(winter) and
contract
maturity
variables were
included as
external
regressors.
29
Hou and
Suardi
(2012)
WTI and
Brent Crude
Spot
Contracts
January 6
th
,
1992 to July
30
th
, 2010
[Daily]
Non
parametric
model,
GARCH,
EGARCH,
GJR,
IGARCH,
FIGARCH,
APARCH,
HYGARCH,
FIAPARCH
N/A
Nonparametric GARCH methods capture
high price movements more effectively
than parametric methods. The non
parametric methods show superior
prediction of volatility.
The study
claims that the
nonparametric
model used is
less sensitive to
model
misspecificati
on; for example,
falsely
neglecting
certain
regressors in
GARCH.
Ji and Fan
(2012)
WTI Crude
Oil, Metal,
Agriculture,
Aggregated
NonEnergy
Prices on
CRB Index
July 7
th
, 2006 to
June 30
th
, 2010
[Daily]
Bivariate
EGARCH N/A
The degree of volatility spillover from the
crude oil market to nonenergy commodity
markets is greater when oil prices are high.
The US Dollar influences crude oil price.
Kang et al.
(2009)
Crude Oil
Spot
Contracts on
WTI, Brent,
and Dubai
January 6
th
,
1992 to
December 29
th
,
2006 [Daily]
GARCH,
IGARCH,
CGARCH,
and
FIGARCH
1, 5, 20
Days
Longterm persistence must be factored
into forecasting volatility, and thus
CGARCH and FIGARCH, which are
effective in accounting for it, are superior
in performance.
30
Kang et al.
(2011)
WTI and
Brent Crude
Oil Spot
Contracts
January 5
th
,
1990 to March
27
th
, 2009
[Weekly]
GARCH and
Bivariate
GARCH
N/A
Five structural changes are observed for
both markets. Neglecting for structural
breaks in volatility overestimates the level
of persistence in the models. WTI has a
definite impact on Brent Crude, while the
bidirection flow of volatility is conditional
on the exclusion of structural breaks.
This study does
not take into
account long
memory in
GARCH, which
is a significant
limitation.
Weekly prices
are taken as the
closing price at
the end of the
trading week.
Narayan
and
Narayan
(2007)
Crude Oil
Contract
September 13
th
,
1991 to
September 15
th
,
2006 [Daily]
ARMA–
EGARCH N/A
The leverage effect and persistence are not
always present in shortterm analysis.
These properties appear consistently when
analyzing longterm data.
Oil market
information and
type of price
contract are not
specified.
Ou and
Wang
(2011)
WTI Spot
and China
Daqing Spot
Crude Oil
Contracts
N/A [Weekly] GARCH and
NNGARCH 1 Week
A hybrid model that incorporates neural
networks with GARCH estimates the
extreme values of volatility more
effectively than GARCH models alone.
Incorporating multiple hidden layers shows
improved performance over one hidden
layer.
Pindyck
(2004)
Crude Oil
and Natural
Gas Futures
and Spot
Contracts
May 2
nd
1990 to
February 26
th
,
2003 [Daily,
Weekly]
GARCH N/A
There is a strong positive dependence of
returns on volatility and interest rates. The
Enron scandal and the time trends have had
very little impact on volatility. Shocks
persist for up to 11 weeks in crude oil
market.
Makes no
mention of
market index.
The mean
equation
includes
volatility as a
regressor.
Regnier
(2007)
Producer
Price Index
(PPI) Prices
for Crude Oil
January 1945 to
August 2005
[Monthly]
The standard
deviation of
the returns is
directly
N/A
Crude oil prices have exhibited higher
degrees of volatility than 93% of a wide
range of commodities since the 1986 crash.
Policy measures to reduce volatility in the
Data is obtained
on a monthly
basis as an
average of
31
and many
other
commodities
(US
Department
of Labor)
computed over
5year
periods.
oil price should target consumption and its
deep integration in consumer activities.
prices of
different types
and producers
of crude oil.
Ripple and
Moosa
(2009)
WTI Crude
Oil Futures
Contracts 1,
2, 3, and 4
January 1995 to
December 2005
[Daily]
Autoregres
sive
Distributive
Lag (ARDL)
method; linear
contractby
contract
analysis
N/A
The influence of trading volume and open
interest dominate that of the maturity
effect. The regression shows that trading
volume is over twice as significant to
volatility as open interest. Unlike volume,
open interest shares an inverse relationship
with volatility.
ARDL
incorporates
lagged
variables,
whereas the
contractby
contract
regression
analysis does
not.
Sadorsky
(2006)
Crude Oil
Futures
Contract of
WTI; heating
oil, gasoline,
and natural
gas futures
February 5
th
,
1988 to January
31
st
, 2003
[Daily]
Random
Walk,
Historical
Mean, Moving
Average,
Exponential
Smoothing,
TGARCH,
GARCH,
GARCHM,
Bivariate
VAR,
Bivariate
GARCH
1 Day
The oneequation GARCH models
outperform the more complex bivariate
models. All models outperform the
Random Walk method.
A fiveyear
moving window
of daily returns
was used to
compute the
nextday
volatility.
Serletis
(1992)
Futures
Contracts of
Crude Oil,
Heating Oil,
and Unleaded
Gasoline
January 1987 to
July 1990
[Daily]
Ordinary
Least Squares N/A
While an inverse relationship is observed
between timetomaturity and volatility, the
relationship is weakened when introducing
trade volume as a regressor.
The extreme
daily prices are
used to generate
volatility
estimates.
32
Shiang
(2010)
Spot Crude
Oil and Gold
Prices
August 1995 to
July 2009
[Daily, Weekly]
Smooth
Transition
Exponential
Smoothing,
GARCH,
IGARCH,
PARCH,
EGARCH,
and TGARCH
N/A
Realized volatility was a better
representation of the actual variance than
the squared residuals. The higher frequency
forecasts with realized volatility use as the
reference had lower errors, indicating that
daily events contribute more useful
predictive information. The significance of
gold price returns was mixed as an
explanatory variable for crude oil volatility.
Gold price
return residuals
are used as
external
regressors in the
GARCH
models. The
closing prices
on Wednesday
were used for
the weekly
crude oil price.
Sidorenko
et al. (2002)
Second
Month Brent
Crude Oil
Futures
Contracts
August 1
st
, 1995
to July 31
st
,
2002 [Daily]
GARCH,
IGARCH, and
FIGARCH
N/A
Longterm persistence is strongly observed.
Due to the fact the sum of the GARCH
coefficients is close to unity, IGARCH and
FIGARCH models were used to better
model that persistence. Also, sameday and
pastday trading volumes play a significant
role in calculating volatility.
Vo (2009)
Spot WTI
Crude Oil
Contracts
January 3
rd
,
1986 to January
5
th
, 2008
[Weekly]
GARCH,
Stochastic
Volatiliy
(SV), Markov
Switching
(MS), and
MSSV
10 Weeks
There were regime switches present, and in
accounting for them, the halflife of shocks
was reduced by nearly 94%. The MSSV
performs well in capturing major events
affect the market.
Weekly price
data obtained as
the average of
daily prices.
The study finds
that returns are
autocorrelated.
Wang et al.
(2011)
WTI Spot
and Futures
Crude Oil
Contracts
January 2
nd
,
1990 to March
9
th
, 2010 [Daily]
Non
parametric
methods,
GARCH,
EGARCH,
APGARCH,
GJR,
FIGARCH
N/A
The degrees of longmemory in volatility
are timevarying, so a movingwindow
approach is suggested. GARCHclass
models can only capture longterm
persistence for time scales of longer than a
year.
The futures
contract details
are not
specified.
33
Wei et al.
(2010)
Crude Oil
Contracts for
WTI, Brent
January 6
th
,
1992 to
December 31
st
,
2009 [Daily]
GARCH,
IGARCH,
TGARCH,
EGARCH,
APARCH,
FIGARCH,
HYGARCH,
and
FIAPARCH
1, 5, and
20 Days
No one model outperforms another in all
situations. Asymmetry in the volatility is
clear in the Brent data, but is unclear in the
WTI analysis. High level of persistence is
present in both markets.
Wilson et
al. (1996)
Oil First
Futures
Contracts,
S&P 500
Returns, and
Returns of
Oil/Gas
Companies
January 1
st
, 1984
to December
31
st
, 1992
[Daily]
ARCH with
Structural
Breaks
N/A
Although ARCH effects should be
incorporated, ignoring sudden volatility
changes can overstate the level of
persistence. No spillover effects are present
between the oil market and the equity of
oilproducing companies.
The
methodology
used to
determine the
locations and
durations of
structural breaks
are detailed in
the reference.