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www.elkjournals.com
………………………………………………………………………………………………
SYMMETRIC AND ASYMMETRIC VOLATILITY MODELLING FOR CRUDE OIL
PRICES IN INDIA
Mr. Prasad V. Daddikar, Dr. Mahesh Rajgopal, Assistant Professor, BET’s Associate Professor, DOS in Business
Global Business School, Belagavi Administration, University of Mysore
Mobile: 9916771502, Mobile: 9886639536,
Email: [email protected] Email: [email protected]
ABSTRACT
The crude oil price volatility represents a substantial source of risk to both macro and micro economic entities
as crude oil has been a major factor affecting their performance. Therefore, crude oil price volatility analysis
and its influence on the real economy is vital in the contemporary globalized scenario to safeguard the bottom
lines of economic entities. This paper empirically analyses the crude oil price return volatility patterns using
both the symmetric & asymmetric GARCH family models. The time series data comprises of daily spot and near
month expiry futures contract price of crude oil sourced from MCX for past ten years. i.e. January 2006 to
December 2015. Based on AIC & SIC principles; the study reveals that GARCH (1,1) and EGARCH(1,1)
models with student’s t distribution were found to better analyze the symmetric and asymmetric volatility
estimates of near month expiry futures contract crude oil price returns respectively. The risk premium
parameter related to GARCH-M (1,1) disclosed positive and insignificant value; signifying absence of
risk/return trade-off. The leverage effect in EGARCH (1,1) is negatively significant indicating diverse impact of
past periods good and bad news on the volatility. Asymmetric effect in TGARCH (1,1) is positively significant
displaying greater influence of bad news on volatility. Finally, diagnostic tests reported insignificant results for
all the GARCH family models and therefore support the model fit prerequisites related to crude oil price
volatility estimation.
Keywords : Commodity, volatility, crude oil, stationarity, autocorrelation, heteroscedasticity, ARCH, GARCH,
EGARCH, TGARCH etc. JEL Classification Code: C22, C32, C53, C58
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INTRODUCTION
The world in past two decades has
observed and documented the extreme
volatility in crude oil prices and the
variations are typically larger than earlier
recorded historical crude oil price
fluctuations (James L. Williams). The
crude oil price instability represents a
significant source of risk to both macro
and micro economic entities as crude oil is
a major factor affecting their performance.
Hence, the influence of crude oil price
volatility on the real economy is vital in
the contemporary globalized scenario
(Aparna A.). Rapid socio-economic
expansion in emerging Asian, African and
Latin American countries had impacted the
crude oil demand-supply equation, greater
demand for oil derivative contracts,
hedging practices by market participants,
uncertain political conditions in crude oil
producing countries have boosted the
crude oil prices to historic levels. The
same factors, when combined with the
realities of a global economic recession
and an adverse credit environment, had the
opposite effect, causing the crude oil price
to crash down with alarming speed leading
to commodity super cycle bust. This
cyclical phenomenon related to crude oil
prices was witnessed by the modern
economies post global financial crisis of
2008 (Sebastian Dullien & et all).
India is not self-sufficient &
technologically advanced in extraction &
production of crude oil; though our
country has been endowed with huge oil
reserves which we are not able to
capitalize on the on account of political
policy regime, lack of technological
advancement etc. Indian crude oil or
petroleum sector is highly regulated and
free market forces do not have any
relevance in the present context. The
International Energy Agency, World Bank
and other genuine sources say, we are
among top five crude oil consuming &
importing countries in the world. The
imported crude oil had fulfilled 70% of our
total crude oil requirement and domestic
sources provided the remaining 30% of
our consumption (Petroleum Annual
Report 2015). As we are heavily
dependent on crude oil import, it becomes
very essential to understand the crude oil
price volatility observed in the
international markets so that appropriate
decisions would be taken by the policy
makers or government.
This paper analyses crude oil price
volatility related to both the spot price and
near term expiry future prices of crude oil
on MCX. The daily logarithmic returns
were calculated & used as an input to
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measure the crude oil price volatility using
econometrics models. Both, symmetric &
asymmetric volatility models were used to
ascertain the impact of positive and
negative news/shocks on the crude oil
price volatility.
This empirical research paper consists of
following sections. Section I provides a
brief review of relevant literature. Section
II specifies objectives of the paper. Section
III discusses the overview of Indian
petroleum industry. Section IV describes
the concepts of crude oil price volatility.
Section V represents the methodology and
data description. Section VI contains the
empirical hypothesis testing & results, VII
offer findings & section VIII concludes the
paper.
I LITERATURE REVIEW
Numerous studies on the subject of crude
oil price volatility measurement and
forecasting have been made. The majority
of the research work has been done
internationally. Some of these important
empirical studies have been reviewed
critically to develop objectives in the
context of India, and further to analyze it
and draw some important conclusions.
Namit Sharma (1998), in his study
compares different methods of forecasting
price volatility in the crude oil futures
market using daily data for the period
November 1986 through March 1997. The
study also checked and confirmed that the
conditional Generalized Error Distribution
(GED) better describes fat-tailed returns in
the crude oil market as compared to the
conditional normal distribution.
Robert S. Pindyck (2001) examines the
role of volatility in short-run commodity
market dynamics, as well as the
determinants of volatility itself and
developed a model describing the joint
dynamics of inventories, spot and futures
prices, and volatility, and estimate it using
daily and weekly data for the petroleum
complex: crude oil, heating oil, and
gasoline.
Robert S. Pindyck (2004), in this paper
examines the behavior of natural gas and
crude oil price volatility in the United
States since 1990 and says there exists
some evidence that crude oil volatility and
returns have predictive power for natural
gas volatility and returns, but not the other
way around.
Syed Aun Hassan (2011), in this paper
focuses on how shocks to volatility of
crude oil prices may affect future oil
prices. The results show high persistence
and asymmetric behavior in oil price
volatility, and reveal that negative and
positive news have a different impact on
oil price volatility.
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Afees A. Salisu & Ismail O. Fasanya
(2012) found that oil price was most
volatile during the global financial crises
compared to other sub samples. Based on
the appropriate model selection criteria,
the asymmetric GARCH models appear
superior to the symmetric ones in dealing
with oil price volatility.
Olga Efimova (2013) in his master’s
thesis investigates the empirical properties
of oil, natural gas and electricity price
volatilities using a range of univariate and
multivariate GARCH models on daily data
from U.S. wholesale markets for the
period from 2000 to 2012.
Farhad Taghizadeh-Hesary, Ehsan
Rasolinezhad, and Yoshikazu
Kobayashi (2015) tried to shed light on
the impact of crude oil price volatility on
each sector in Japan, the world’s third-
largest crude oil consumer. Their findings
indicate that some economic sectors, such
as the residential sector, did not have
ignificant sensitivity to the sharp oil price
fluctuations.
Sang Hoon Kang & Seong-Min Yoon in
their paper investigate volatility models
and their forecasting abilities for three
types of petroleum futures contracts traded
on the New York Mercantile Exchange
(West Texas Intermediate crude oil,
heating oil #2, and unleaded gasoline) and
suggest some stylized facts about the
volatility of these futures markets,
particularly in regard to volatility
persistence (or long-memory properties).
Duong T Le (2015), in his paper examines
the causes and behavior of price volatility
in the US crude oil market. He showed that
the crude oil market is characterized by
volatility persistence, a negative shock has
more impact on future volatility.
S. Aun Hassan & Hailu Regassa, in their
paper attempts to focus on fluctuations in
gas prices across different regions of the
US and the effects of exogenous shocks on
their volatility by using time series data.
II OBJECTIVES
To offer an overview of Indian
petroleum industry/crude oil - gas
sector
To explore the significant concepts of
crude price volatility
To assess price volatility of crude oil
using appropriate GARCH family
models
To ascertain the existence of leverage
effect in crude oil price returns
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To identify the best model for crude oil
price volatility based on diagnostic
tests
III OVERVIEW OF INDIAN PETROLEUM INDUSTRY
Upstream
segment -
exploration & production
State-owned ONGC dominate the upstream segment, It is the largest upstream
company in the Exploration and Production (E&P) segment, accounting for
approximately 59.43 per cent of the country’s total oil output (FY15)
Midstream
segment –
storage & transportation
IOCL operates a 11,214 km network of crude, gas and product pipelines, with a
capacity of 1.6 mbpd of oil and 10 mmscmd of gas
This is around 30 per cent of the nation’s total pipeline network
Downstream
segment –
refining, processing &
marketing
IOCL is the largest company, control 10 out of 22 Indian refineries, with a
combined capacity of 1.31 mbpd
Reliance launched India’s first privately owned refinery in 1999 and gained
considerable market share (30 per cent)
Source: TechSci Research & India Brand Equity Foundation
PORTER’S FIVE FORCES MODEL
Competitive Rivalry
Competitive rivalry is low as just one-two players operate in Upstream, Midstream and Downstream segments
Although a few private operators have entered the industry in the last couple of years, they do not pose any
major threat as of now
Threat of New Entrants
Threat of new entrants continues to be low, due to
the capital intensive nature of the industry and
economies of scale
Substitute Products
Threat is low, as other sources of energy like solar,
wind, coal and hydroelectric power are less developed.
Pressure from alternative sources might rise in future
Bargaining Power of Suppliers
Bargaining power is medium as despite few players
operating, government at times delays subsidy
payment to oil companies, thereby increasing losses
Bargaining Power of Customers
Customers have low/nonexistent bargaining power
Customers are price-taker not a price maker
Source: TechSci Research & India Brand Equity Foundation
Future opportunities Upstream segment Midstream segment Downstream segment
Locating new fields for
exploration: 78 per cent of the
country’s sedimentary area is yet to
be explored
Development of unconventional
resources: CBM fields in the deep
sea
Opportunities for secondary
/tertiary oil producing techniques
Higher demand for skilled labor
and oilfield services and equipment
Expansion in the transmission
network of gas pipelines
LNG imports have increased
significantly; this provides an
opportunity to boost production
capacity
In light of mounting LNG
production, huge opportunity lies
for LNG terminal operation,
engineering, procurement and
construction services
India is already a refining hub with
21 refineries and expansions
planned for tapping foreign
investment in export oriented
infrastructure, including product
pipelines and export terminals
Development of City Gas
Distribution (CGD) networks,
which are similar to Delhi and
Mumbai’s CGDs
Expansion of the country’s
petroleum product distribution
network
Source: TechSci Research & India Brand Equity Foundation
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IV CONCEPTS OF CRUDE OIL
PRICE VOLATILITY
The term volatility has been given
different definitions by different scholars
across disciplines. Price volatility refers to
the degree to which prices rise or fall over
a period of time. In an efficient market,
prices reflect recognized existing and
anticipated future circumstances of supply
and demand and factors that could affect
them. Changes in market prices tend to
reflect changes in what markets
collectively knows or anticipate. When
market prices tend to change a lot over
relatively a short time, the market is said to
have high volatility. When relatively stable
prices prevail, the market is assumed to
have low volatility. In relation to crude oil
price, volatility is the variation in the
worth of a variable, especially price
(Routledge, 2002) as cited in (Busayo,
2013). Volatility is the measure of the
tendency of oil price to rise or fall sharply
within a period of time, such as a day, a
month or a year (Ogiri et al. 2013). Lee
(1998) as cited in Oriakhi and Osazee
(2013) defines volatility as the standard
deviation in a given period. It concluded
by saying that it is volatility/change in
crude oil prices rather than oil price level
that has a significant influence on
economic growth. In a nutshell, volatility
is a measurement of the fluctuations (i.e.
rise and fall) of the price of commodity for
example crude oil price over a period of
time.
It has been maintained that presently the
price of crude oil does not seem to be
amplified by traditional demand and
supply relationships, but by dynamics of
interlinked financial markets and changing
Geopolitical landscape. Several factors
have been identified as causes of oil price
volatility; these factors range from demand
and supply of crude oil, OPEC decisions,
economic downturn, oil derivative
contracts, exchange rates, gold prices etc.
The political and in some cases military
upheavals in Nigeria, Venezuela, Libya,
Egypt, Syria, and other MENA countries,
the boycott of Iranian crude oil in response
to its nuclear weapons program, and the
risk of terrorist attacks all have conspired
to make oil markets more volatile. Thus
far, these events have not seriously
disrupted oil supplies, but it is conceivable
that they could. Merino and Ortiz (2005)
adopt the traditional approach to assessing
the tightness of the oil market, they states
that the evolution of oil inventories should
reflect the interaction between supply and
demand forces, which should contribute in
explaining oil price changes. The
unexpected economic developments could,
in standard, shake crude oil markets and
increases volatility. The fear of global
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shortage of crude oil may also account for
changes in oil price. As noted by
Appenzeller (2004), there have been
diverse arguments about how much more
of crude oil reserve the world has before
the wells dry up. Although, history has it
that oil price shocks were mainly caused
by physical disruptions of supply, the price
run-up of 2007- 2008 was caused by
strong demand confronting world
production (Hamilton, 2009; Cale, 2004).
Oil price fluctuations heavily affect
consumers, producers and the overall
incentive to invest.
V METHODOLOGY
The use of high frequency time series data
was done in this paper for modeling crude
oil price volatility. After referring to the
past literature, it was observed that the use
of symmetric and asymmetric models were
most widely used methods for
demonstrating crude oil price volatility.
The high frequency time series data
exhibit time-varying volatility for crude oil
price returns, i.e. volatility clustering, and
suggests that residual or error term is
conditionally heteroscedastic and it can be
represented by ARCH & GARCH models.
As this paper utilizes time series data
having a high frequency interval, it is
necessary to examine both the symmetric
(linear) and asymmetric (non-linear)
nature of crude oil price returns volatility.
The study employed GARCH(1,1) &
GARCH-M(1,1) linear models to test the
persistence of shocks to volatility and
EGARCH(1,1) & TARCH(1,1) non-linear
models were used to assess the diverse
effects of good/ bad news on the crude oil
price volatility.
Data Description
The data consists of daily closing prices of
Crude Oil which is traded on Multi
Commodity Index (MCX), India. The
authors have used both the spot prices and
near month expiry futures contract prices
of crude oil with a total of 2960 usable
observations based upon a time interval
ranging from January 1, 2006 to December
31 2015. The nature and properties of data
distribution are represented in the
descriptive statistic summary along with
the normality test for observed daily prices
& calculated daily log returns of crude oil
prices related to spot and near month
expiry futures contract in the following
section.
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VI EMPIRICAL ANALYSIS
Table No. 1 Descriptive Statistics & Normality Test
Particulars Spot price returns Futures price returns
Mean -0.002901 -0.002585
Std. Dev. 2.118504 1.794380
Maximum 17.48352 17.38519
Minimum -14.19558 -9.127090
Skewness 0.200628 0.630854
Kurtosis 9.180412 10.87178
Jarque-Bera 4730.881 7838.685
Probability 0.000000 0.000000
Observations 2960 2960
Source: Compiled, edited data from MCX & computed using EViews 7
The descriptive statistical analysis was
carried on the daily returns series of both
spot & futures price of crude oil. The mean
value for both return series are negative,
demonstrating the fact that crude oil prices
have decreased during the reference period
of the this study. It has been observed that
the spot price return series had shown
lower price decline than the futures price
return series but the greater standard
deviation in spot price return series
indicating larger variability patterns during
the period. It is also evident that the crude
oil prices are reducing post global
economic crisis, the recent commodity
super-cycle bust and the geo-political
instability in the MENA region. The
maximum & minimum values have
demonstrated wider spread for the spot
price return series as compared to the
futures price return series and this result
supports the presence of volatility patterns
is the return series. The recorded skewness
values are positive in both the return
series, signifying the tail on the right side
is longer or fatter than the left side and
thus it validates the nonconformity of
normal distribution. The kurtosis had
revealed an excessive positive values for
spot & futures price return series
representing leptokurtic nature of heavy-
fatter tailed distribution and it denotes
non-normality of data. The Jarque-Bera
test is significant at 1% level and therefore
authors reject the null hypothesis, i.e.
returns series are normally distributed and
accept the alternative hypothesis, i.e.
returns series are not normally distributed.
The descriptive statistical outcome is
similar to past studies performed on crude
oil price volatility and facilitates the
authors to apply ARCH/GARCH models
in order to assess the volatility patterns on
the documented time-series data.
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Stationarity Test [Unit Root Test] Figure No. 1 Figure No. 2
From the graphical analysis it has been
observed that both returns series have
shown time-varying fluctuations during
Jan, 2006 – Dec, 2015. It can be witnessed
that spot & futures crude oil price returns
have changed over time due to influence of
long memory and illustrated volatility
clustering for financial returns series. This
indicates that low volatility patterns have a
tendency to follow small volatility patterns
for an extended time period and the high
volatility tend to be followed by large
volatility for a prolonged time period.
Therefore, it justifies the volatility is
clustering and the return series vary
around the constant mean but the variance
is changing with time.
Table No. 2 Unit root test results Particular Spot price return series Futures price return series
ADF test PP test ADF test PP test
t-statistics -59.10764 -59.08978 -53.23714 -53.23953
Prob.* (p-value) 0.0000 0.0000 0.0000 0.0000
Critical value
1% -3.961143 -3.961143 -3.961143 -3.961143
5% -3.411325 -3.411325 -3.411325 -3.411325
Test equation coefficient
SPLR(-1) & FPLR(-1) -1.083240 -1.083240 -0.980401 -0.980401
@TREND(1) -6.22E-05 -6.22E-05 -5.42E-05 -5.42E-05
*Mackinnon (1996) one-sided p-values. Source: Compiled, edited data from MCX & computed using EViews 7
The above table display the results of unit
root test using the ADF & PP tests at
levels for crude oil price returns series.
Since the data has been non-normal, it is
necessary to check the stationarity of
returns series using ADF & PP tests. The
authors have observed that both the tests
have shown significant result as p-values
are < 0.01 and rejection of null hypothesis,
i.e. crude oil price returns are non-
stationary & times series data have a unit
root has been justified. Therefore it is
concluded that, both the returns series are
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SPLR
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FPLR
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stationary at levels, representing the mean
reverting feature. The test equation proved
to be viable & model fit assumption is
validated as the coefficients have shown
negative values which is a desirable
condition for unit root tests.
Pre-Assessment Investigation
Table No. 3 Table No. 4 ARCH-LM Heteroskedasticity Test for
Crude oil Spot price return series
ARCH-LM Heteroskedasticity Test for
Crude oil Futures price return series
F-statistic 30.162 Prob. F(1,2957) 0.0000 F-statistic 39.36389 Prob. F(1,2957) 0.0000
Obs*R-squared 29.877 Prob. Chi-Square(1) 0.0000 Obs*R-squared 38.87304 Prob. Chi-Square(1) 0.0000
Source: Compiled, edited data from MCX & computed using EViews 7
Figure No. 3 Figure No. 4
Source: Compiled, edited data from MCX & computed using EViews 7
The pre-assessment investigation was
carried out in three steps as suggested by
Engle (1982) & other research
scholars/authors. The first step uses the
descriptive statistical analysis, second step
is in the form of a graphical analysis and
the third step utilizes ARCH LM test.
Table no. 1 provides details pertaining to
crude oil price returns series using various
descriptive statistical techniques and
normality test. Figure no. 3 & 4 represents
volatility clustering in fitted residual and
actual, confirming graphical identification
of heteroscedasticity effects. As a final
step, the ARCH-LM test was employed in
order to quantitatively justify the existence
of autoregressive conditional
heteroscedasticity in the returns series and
it is presented in the table no. 3 & 4. And it
is concluded that the ARCH-LM test is
highly significant, since the p-value is less
than one percent significance level (0.000
< 0.01). Therefore, the null hypothesis, i.e.
‘there is no ARCH effect’ is rejected and
the alternative hypothesis, i.e. ‘there is an
ARCH effect’ is accepted at 1% level of
significance, which confirms the existence
of autoregressive conditional
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heteroscedasticity effects in the residuals
of crude oil price returns series. Thus, the
pre-assessment investigation results permit
for the volatility analysis using appropriate
ARCH/GARCH family models.
Empirical Analysis and Interpretation
This section of the paper deals with the
volatility analysis of crude oil price returns
series using symmetric and asymmetric
GARCH family models along with
diagnostic test results in order to determine
whether there exist any remaining
autoregressive conditional
heteroscedasticity effect in the residuals of
the assessed GARCH family models.
Since the normality and heteroscedasticity
tests were highly significant as it was
learnt in the above sections, hence it is
concluded that residuals are not
conditionally normally distributed. In such
circumstances, selection of error
distribution option requires a special
consideration for computation of
parameter estimates related to select
symmetric and asymmetric volatility
GARCH family models. The authors have
used two error distribution options based
on the past literature references to arrive at
the best fit model for crude oil daily price
returns volatility analysis. First being
Normal (Gaussian) error distribution in
which it is necessary to mention the
heteroscedasticity consistent covariance
option to compute the quasi-maximum
likelihood (QML) covariances and
standard errors as described by Bollerslev
& Wooldridge (1992) with Marquardt
optimization algorithm for iterative
process. The second error distribution
option being used for parameter estimates
is Student’s t with Berndt-Hall-Hall-
Hausman (BHHH) optimization algorithm
for iterative process. The leptokurtic
heavy-fatter tailed crude oil price returns
series distribution supports the selection of
Student’s t option.
Table No. 5 Results of Symmetric GARCH models for crude oil spot price returns Error distribution Normal (Gaussian) Student’s t
Volatility Model GARCH(1,1) GARCH-M(1,1) GARCH(1,1) GARCH-M(1,1)
Coefficients of Mean Equation
μ (Constant) 0.034481
(0.2599)
-0.035091
(0.7518)
0.034438
(0.2210)
-0.015271
(0.8760)
λ (Risk premium) -- 0.042984
(0.5156)
-- 0.030009
(0.6030)
Coefficients of Variance Equation
ω (Constant) 0.029658
(0.0018)
0.029656
(0.0018)
0.025979
(0.0093)
0.025859
(0.0095)
α (ARCH effect) 0.048094
(0.0000)
0.048100
(0.0000)
0.047598
(0.0000)
0.047593
(0.0000)
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β (GARCH effect) 0.945587
(0.0000)
0.945574
(0.0000)
0.948046
(0.0000)
0.948090
(0.0000)
α + β 0.993681 0.993674 0.995644 0.995683
Log likelihood -6015.294 -6015.065 -5916.804 -5916.672
AIC 4.067091 4.067611 4.001219 4.001806
SIC 4.075189 4.077735 4.011342 4.013954
ARCH-LM Test Result
Test statistics 0.208177 0.191336 0.274015 0.261224
Prob. Chi-Square
(1)
0.6482 0.6618 0.6007 0.6093
Correlogram Squared Residuals Test Result (36 Lags)
Q-Stat Insignificant Insignificant Insignificant Insignificant
Prob. Insignificant Insignificant Insignificant Insignificant
Source: Compiled, edited data from MCX & computed using EViews 7
The results of symmetric GARCH family
models for crude oil spot price returns are
reported in the table no. 5. The mean
equation has been expressed as a function
of exogenous variable with an error term
and the constant term (μ) was found to be
insignificant in both the distributions at all
standard levels of significance. It was
observed that GARCH-M (1,1), model has
produced negative value for constant term
and this reveals the influence of standard
deviation in the equation. The risk
premium (λ) parameter in mean equation
for both the distributions has disclosed
positive insignificant value and hence it
suggests that there is no significant
influence of volatility or expected risk on
the expected returns. Thus, it is inferred
that there is nonexistence of risk/return
trade-off for the crude oil spot price
returns time series data used in this paper.
The parameter estimates of the GARCH
(1,1) in variance equation for both the
distributions are found to be significant at
1% level. ARCH effect coefficients
(0.048094 & 0.047598) are highly
significant with positive value and it
illustrates that information related to past
volatility has an influence of current
volatility. GARCH effect coefficients
(0.945587 & 0.948046) are also
significantly positive, which implies that
previous period’s forecast variance has an
impact on current volatility. Since the
GARCH effect is much larger than ARCH
effect it look likes the market has a
memory longer than one period and
volatility is more sensitive to its lagged
values than it is to new surprises in the
market. The significant ARCH & GARCH
values also suggest the influence of
internal dynamics on the crude oil price
volatility. The sum of α and β is 0.993681
& 0.995644 respectively for both the
distributions and this is approximately
equal to one. This specifies the shocks to
volatility are highly persistent and the
impacts of these shocks would endure in
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future periods too for a longer duration.
Thus, the analysis shows that memory of
shocks or surprises are recollected in
relation to daily spot price of crude oil
price returns volatility. The diagnostic
tests were conducted in order to verify the
correct model specification. The ARCH-
LM test was used to analyze the remainder
of additional ARCH effect if any and the
test statistic reported insignificant outcome
at all standard levels of significance. Since
the p-value > 0.05, the null hypothesis, i.e.
‘there is no ARCH effect’ is accepted.
Further, the correlogram squared residuals
test was found insignificant at all standard
levels and it supports the acceptance of
null hypothesis, i.e. ‘there is no serial
correlation in the residual’. Therefore,
authors conclude that model specification
was accurate on the basis of insignificant
diagnostic tests results.
The coefficients of the GARCH-M (1,1) in
variance equation for both the distributions
are significant at 1% level. ARCH effects
(0.048100 & 0.047593) are extremely
significant with positive value and it
explains the impact of past volatility
information on current volatility. GARCH
effect coefficients (0.945574 & 0.948090)
are positive and signifies that past period’s
predicted variance has an impression on
current period’s volatility. The crude oil
price volatility has been triggered by its
own internal dynamics as ARCH &
GARCH coefficients in variance equation
have reported significant values for both
the distributions. The total of α and β for
both the distributions is close to one and
this states the shocks to volatility are
highly persistent and it would sustain in
future periods too for an extended time
duration. The diagnostic tests were
employed to validate the right model
specification. The ARCH-LM test was
executed to check for remaining ARCH
effect if any and it found that the test
statistic was insignificant at all standard
levels of significance. The p-value > 0.05
and supports the acceptance of null
hypothesis, i.e. ‘there is no ARCH effect’.
The correlogram squared residuals test was
performed & observed that test output has
been insignificant at all standard levels and
it suggests to acceptance of null
hypothesis, i.e. ‘there is no serial
correlation in the residual’. Therefore, it is
conclude that model specification was
exact on the basis of insignificant
diagnostic tests results.
The above empirical results and discussion
shows that crude oil prices in India were
exposed to substantial volatility during the
reference period of the study. For the
above used symmetric GARCH models,
the best model selection was done using
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the AIC & SIC principles. The norm says,
a model with lower AIC & SIC value is
best with respect to error distribution and
optimization algorithm for iterative
process. Referring to table no. 5, it is
concluded that GARCH (1,1) with
student’s t distribution is the best model in
symmetric class to estimate the daily crude
oil spot price volatility for the sample data
used in this paper.
Table No. 6 Results of Asymmetric GARCH models for crude oil spot price returns
Error
distribution
Normal (Gaussian) Student’s t
Model TGARCH(1,1) EGARCH(1,1) TGARCH(1,1) EGARCH(1,1)
Coefficients of Mean Equation
μ (Constant) 0.011571
(0.7071)
0.028915
(0.3686)
0.021294
(0.4509)
0.025269
(0.3658)
Coefficients of Variance Equation
ω (Constant) 0.031984
(0.0014)
-0.060700
(0.0000)
0.023339
(0.0085)
-0.055637
(0.0000)
α (ARCH effect) 0.022706
(0.0172)
0.099344
(0.0000)
0.020226
(0.0049)
0.087149
(0.0000)
β (GARCH effect) 0.946427
(0.0000)
0.990279
(0.0000)
0.954433
(0.0000)
0.994195
(0.0000)
γ (Leverage
effect)
0.046865
(0.0004)
-0.045818
(0.0001)
0.041516
(0.0002)
-0.039291
(0.0000)
α + γ 0.069571 0.053526 0.061742 0.047858
Log likelihood -6002.639 -6001.233 -5909.232 -5907.282
AIC 4.059216 4.058265 3.996778 3.995461
SIC 4.069339 4.068389 4.008926 4.007608
ARCH-LM Test Result
Test Statistics 0.7533 2.106371 1.289728 3.361246
Prob. Chi-
Square(1)
0.3854 0.1467 0.2561 0.0667
Correlogram Squared Residuals Test Result (36 Lags)
Q-Stat Insignificant Insignificant Insignificant Insignificant
Prob. Insignificant Insignificant Insignificant Insignificant Source: Compiled, edited data from MCX & computed using EViews 7
The above table summarizes the results of
asymmetric GARCH family models for
crude oil spot price returns. In the mean
equation constant term (μ) was found to be
insignificant with respect to both the error
distributions at all levels. The asymmetric
GARCH family models are used in
volatility estimation to analyze the
influence of good & bad news on asset
returns as well as leverage effect if any
using the TGARCH and EGARCH
models.
The coefficients of TGARCH (1,1) in
variance equation for both the error
distributions are reported to be significant
at 1% & 5% level. ARCH effects are
significant at 5% level with positive value.
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It proves that good news associated with
the past volatility has an impact on current
volatility. GARCH coefficients have
shown significantly positive values, which
indicates that previous period’s forecast
variance has an influence on present
volatility. Leverage effect (γ) is positive,
greater than zero & significant at 1% level.
Hence it is inferred that, bad news have a
bigger impact on volatility and bad news
may increase the future volatility. The sum
of α and γ is 0.069571 & 0.061742 for
both the distributions and this exhibits the
approximate impact of bad news on
volatility. The sum of α and β is near to
unity, which specifies high persistency of
volatility with longer durability. The
diagnostic tests were conducted in order to
justify the model fit specification. The
ARCH-LM test has been used to explore
the remainder of ARCH effect and the test
statistic described insignificant result at all
levels of significance. Since the p-value >
0.05, the null hypothesis, i.e. ‘there is no
ARCH effect’ is accepted. Additionally,
the correlogram squared residual test was
insignificant and it supports the acceptance
of null hypothesis, i.e. ‘there is no serial
correlation in the residual’. Thus, authors
state that model specification was accurate
on the basis of insignificant diagnostic
tests results.
The parameter estimate coefficients of
EGARCH (1,1) in variance equation for
both the error distributions are observed to
be highly significant at 1% level. This
model is utilized to scrutinize the presence
of leverage effect in return series of daily
crude oil spot prices. The sum of α and β is
more than one, which states greater
persistent volatility having longer
extension. Leverage effect (γ) is negative
& significant at 1% level suggesting
existence of leverage effect in return series
and reporting diverse impact of previous
periods good & bad news on the volatility.
Thus, it is inferred that, past period’s bad
news effect is much greater than the
influence of good news of the same
quantum. The diagnostic tests were
conducted to validate the model fit
requirement. The ARCH-LM test was used
to ascertain the remainder of ARCH effect
and the test statistic provided insignificant
result at all significance levels. Since the
p-value > 0.05, the null hypothesis, i.e.
‘there is no ARCH effect’ is accepted.
Moreover, the correlogram squared
residual test was observed to be
insignificant and it facilitates the
acceptance of null hypothesis, i.e. ‘there is
no serial correlation in the residual’.
Therefore, on the basis of insignificant
diagnostic tests results it is validated that
model specification was correct.
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Based on the observed results it has been
realized that crude oil prices in India are
subjected to significant volatility. In order
to arrive at the best model of asymmetric
GARCH family, the AIC & SIC standards
are used. The AIC & SIC principle
stipulates, best model must have lower
AIC & SIC value with respect to error
distribution and optimization algorithm for
iterative process. From table no. 6, it is
discovered that EGARCH (1,1) with
student’s t distribution is the best model in
asymmetric class to estimate the daily
crude oil spot price volatility for the
sample data used in this paper.
Table No. 7 Results of Symmetric GARCH models for crude oil futures price returns
Error distribution Normal (Gaussian) Student’s t
Volatility Model GARCH(1,1) GARCH-
M(1,1)
GARCH(1,1) GARCH-
M(1,1)
Coefficients of Mean Equation
μ (Constant) 0.039788
(0.1676)
-0.028276
(0.8044)
0.015873
(0.5055)
0.079370
(0.3514)
λ (Risk premium) -- 0.047675
(0.5390)
-- -0.043161
(0.4410)
Coefficients of Variance Equation
ω (Constant) 0.021311
(0.0252)
0.021234
(0.0238)
0.014368
(0.0346)
0.014791
(0.0320)
α (ARCH effect) 0.042310
(0.0000)
0.042337
(0.0000)
0.045234
(0.0000)
0.045439
(0.0000)
β (GARCH effect) 0.951708
(0.0000)
0.951698
(0.0000)
0.954198
(0.0000)
0.953897
(0.0000)
α + β 0.994018 0.994035 0.999432 0.999336
Log likelihood -5616.773 -5616.524 -5474.292 -5473.988
AIC 3.797820 3.798327 3.702224 3.702695
SIC 3.805918 3.808450 3.712348 3.714842
ARCH-LM Test Result
Test statistics 0.416338 0.386294 0.325984 0.352632
Prob. Chi-Square
(1)
0.5188 0.5343 0.5680 0.5526
Correlogram Squared Residuals Test Result (36 Lags)
Q-Stat Insignificant Insignificant Insignificant Insignificant
Prob. Insignificant Insignificant Insignificant Insignificant Source: Compiled, edited data from MCX & computed using EViews 7
The above table reports the results of
symmetric GARCH family models for
crude oil futures price returns. The risk
premium (λ) coefficient in mean equation
for both the distributions has revealed
positive insignificant value even at 10%
level and it is recommended that there is
no significant influence of volatility or
expected risk on the expected returns.
Therefore there is no risk/return trade-off
for the crude oil futures price returns time
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series and this result is similar to crude oil
spot price returns data used in this paper.
GARCH (1,1) parameters in variance
equation for both the distributions are
found to be significant at 1% level. ARCH
& GARCH effect coefficients are highly
significant with positive values and they
explains that previous period’s volatility
information had an impact of current
volatility. Since the GARCH effect is
closer to one and it appears the market has
a memory longer and volatility is more
sensitive to its lagged values than it is to
fresh shocks in the market. The significant
ARCH & GARCH values too support the
influence of internal dynamics on the
crude oil futures price volatility. The total
of α and β is almost equal to one & this
specifies persistent shocks with a longer
duration. Diagnostic tests were conducted
in order to substantiate the precise model
specification. The ARCH-LM test was
used to analyze the remaining ARCH
effect if any and the test statistic reported
insignificant result. Since the p-value >
0.05, the null hypothesis, i.e. ‘there is no
ARCH effect’ is accepted. The
correlogram squared residuals test was
found insignificant and it supports the
acceptance of null hypothesis, i.e. ‘there is
no serial correlation in the residual’.
The parameter coefficients of the
GARCH-M (1,1) in variance equation for
both the distributions are significant at 1%
level. ARCH effect is significant and it
describes the impression of previous
period volatility information on current
period volatility. GARCH effect is positive
and implies that past period’s anticipated
variance has an influence on current
period’s volatility. The ARCH & GARCH
coefficients complements the effects of
internal dynamics on crude oil price
volatility for both the distributions. The
total of α and β for both the distributions is
close to one and this states the shocks to
volatility are highly persistent and it would
sustain in future periods too for an
extended time duration. The diagnostic
tests were employed to validate the right
model specification. The ARCH-LM test
was executed to check for remaining
ARCH effect if any and it found that the
test statistic was insignificant at all
standard levels of significance. The p-
value > 0.05 and supports the acceptance
of null hypothesis, i.e. ‘there is no ARCH
effect’. The correlogram squared residuals
test was performed & observed that test
output has been insignificant at all
standard levels and it suggests to
acceptance of null hypothesis, i.e. ‘there is
no serial correlation in the residual’.
Therefore, it is conclude that model
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specification was exact on the basis of
insignificant diagnostic tests results.
For the symmetric GARCH family
models, the best model selection was done
using the AIC & SIC standards. The
standard claims that the model with lower
AIC & SIC value is best fit model with
respect to error distribution and
optimization algorithm for iterative
process. From table no. 7, it is concluded
that GARCH (1,1) with student’s t
distribution is the best model in symmetric
class to estimate the daily crude oil futures
price volatility for the sample data used in
this paper.
Table No. 8 Results of Asymmetric GARCH models for crude oil futures price returns
Error
distribution
Normal (Gaussian) Student’s t
Model TGARCH(1,1) EGARCH(1,1) TGARCH(1,1) EGARCH(1,1)
Coefficients of Mean Equation
μ (Constant) 0.015097
(0.5856)
-7.37E-05
(0.9978)
0.012276
(0.6091)
0.007771
(0.7429)
Coefficients of Variance Equation
ω (Constant) 0.021262
(0.0239)
-0.056816
(0.0000)
0.012666
(0.0452)
-0.061710
(0.0000)
α (ARCH effect) 0.014269
(0.1038)
0.090850
(0.0000)
0.018881
(0.0076)
0.094979
(0.0000)
β (GARCH effect) 0.953276
(0.0000)
0.990769
(0.0000)
0.957160
(0.0000)
0.994426
(0.0000)
γ (Leverage
effect)
0.054395
(0.0001)
-0.041280
(0.0009)
0.048702
(0.0000)
-0.036689
(0.0000)
α + γ 0.068664 0.04937 0.067583 0.05829
Log likelihood -5593.539 -5585.823 -5464.438 -5462.677
AIC 3.782796 3.777583 3.696242 3.695052
SIC 3.792920 3.787706 3.708390 3.707200
ARCH-LM Test Result
Test Statistics 0.414320 0.662718 0.332765 0.603408
Prob. Chi-
Square(1)
0.5198 0.4156 0.5640 0.4373
Correlogram Squared Residuals Test Result (36 Lags)
Q-Stat Insignificant Insignificant Insignificant Insignificant
Prob. Insignificant Insignificant Insignificant Insignificant Source: Compiled, edited data from MCX & computed using EViews 7
The table no. 8 reports the results of
asymmetric GARCH family models for
crude oil futures price returns. In the mean
equation constant term (μ) was found to be
insignificant with respect to both the error
distributions at all levels.
TGARCH (1,1) coefficients in variance
equation for student’s t error distribution is
reported to be significant at 1% level.
ARCH effect is significant at 1% level
with positive value. It substantiates that
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good news linked with the past volatility
has an impact on current volatility.
GARCH coefficients have shown
significantly positive values for both
distribution, which indicates that previous
period’s forecast variance has an influence
on present volatility. Leverage effect (γ) is
positive, more than zero & significant at
1% level. So, it is inferred that, bad news
have a superior impact on volatility and
bad news may enhance the future
volatility. The sum of α and γ for both the
distributions exhibits the approximate
impact of bad news on volatility. The sum
total of α and β is close to one, which
identifies persistency of volatility for
longer time duration. The diagnostic tests
were conducted to defend the model fit
specification. The ARCH-LM test was
utilized to look for the remainder of
ARCH effect and the test statistic showed
insignificant result. Since the p-value >
0.05, the null hypothesis, i.e. ‘there is no
ARCH effect’ is accepted. The
correlogram squared residual test was also
insignificant and it supports the acceptance
of null hypothesis, i.e. ‘there is no serial
correlation in the residual’.
The parameters of EGARCH (1,1) in
variance equation for both the error
distributions are observed to be highly
significant at 1% level. This model tests
the existence of leverage effect in return
series of daily crude oil futures prices. The
sum of α and β is greater than unity, which
specifies bigger persistent volatility with
enduring feature. Leverage effect (γ) is
negative & significant at 1% level
supporting the presence of leverage effect
in return series and reporting varied effects
of previous periods good & bad news on
the volatility. Hence, past period’s bad
news impact is larger than the effect of
good news of the same degree. The
diagnostic tests were conducted to validate
the model fit prerequisite. The ARCH-LM
test was used to ascertain the ARCH effect
and the test statistic provided insignificant
result. Since the p-value > 0.05, the null
hypothesis, i.e. ‘there is no ARCH effect’
is accepted. Likewise, the correlogram
squared residual test was observed to be
insignificant and it facilitates the
acceptance of null hypothesis, i.e. ‘there is
no serial correlation in the residual’.
Therefore, on the basis of insignificant
diagnostic tests results it is validated that
model specification was precise.
Therefore, based on the empirical results it
was found that crude oil prices in India are
subjected to significant volatility. For
selection of best model of asymmetric
GARCH family, the AIC & SIC standards
were used. The AIC & SIC principle
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demands, best model should have lower
AIC & SIC value with respect to error
distribution and optimization algorithm for
iterative process. From table no. 8, it is
learnt that EGARCH (1,1) with student’s t
distribution is the best model in
asymmetric class to estimate the daily
crude oil futures price volatility for the
sample data used in this paper.
VII FINDINGS
India has become the third-largest crude
oil consumer in 2015 as per techsci report.
India’s dependency on crude oil imports is
likely to increase further due to rapid
economic growth and limited domestic
production. State-owned oil companies
undertake most of the upstream drilling
and exploration work of crude oil in India.
India has 19 refineries in the public sector
and 3 in the private sector for crude oil.
Indian government has permitted 100%
FDI in exploration & production projects
of crude oil and 49% in refining
companies under the automatic route.
Crude oil spot price returns have
evidenced lower price decline with
greater standard deviation as compared
to near month expiry futures contract
price returns of crude oil.
Kurtosis demonstrated leptokurtic
nature with heavy-fatter tailed
distribution and Jarque-Bera test is
significant at 1% level, it denotes non-
normality of data.
Spot & futures crude oil price returns
have changed over time due to
influence of long memory and
illustrated volatility clustering for
financial returns series.
Spot & futures crude oil price returns
are stationary at levels, representing
the mean reverting feature of time
series.
The normality and heteroscedasticity
tests were highly significant, hence it is
concluded that residuals are not
conditionally normally distributed in
time series.
The risk premium parameter is
insignificant & there is no risk/return
trade-off for crude oil prices
ARCH effect coefficients are highly
significant with positive value and it
explains that information related to
past volatility has an influence of
current volatility.
The significant ARCH & GARCH
values in symmetric models also
suggest the influence of internal
dynamics on crude oil price volatility.
The combined effect of ARCH &
GARCH in symmetric models
validates persistent volatility that
would endure in future periods too for
a longer duration.
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Leverage effect in asymmetric
TGARCH model is positively
significant and it suggest bad news
have a bigger impact on volatility and
bad news may increase the future
volatility.
Asymmetric EGARCH model is
negatively significant and it specifies
presence of leverage effect in return
series and reporting diverse impact of
previous periods good & bad news on
the volatility.
Diagnostic tests revealed insignificant
results for all symmetric & asymmetric
GARCH family models and it proves
the model fit prerequisites related to
crude oil price volatility modelling.
AIC & SIC principles reveals that
GARCH (1,1) and EGARCH(1,1)
models with student’s t distribution are
found to better analyze the symmetric
& asymmetric volatility estimation for
near month expiry futures contract
crude oil price returns.
VIII CONCLUSION
This paper is prepared in order to
empirically analyze the crude oil price
return volatility patterns employing both
the symmetric & asymmetric GARCH
family models using time series data of
daily spot & near month expiry futures
contract price of crude oil traded on multi
commodity exchange (MCX) from
January 2006 to December 2015. Based on
results it has been realized that GARCH
(1,1) and EGARCH(1,1) models with
student’s t distribution were better able to
capture the symmetric & asymmetric
volatility estimates of near month expiry
futures contract crude oil price returns.
The risk premium parameter revealed
positive & insignificant result indicating
absence of risk/return trade-off in crude oil
price return series. The leverage effect is
significant with negative result which
suggests varied impact of past periods
good & bad news on the volatility.
Asymmetric effect is positively significant
exhibiting bigger impact of bad news on
return series volatility than good news.
The paper supports the behavior of crude
oil prices observed during the past decade
as the crude oil prices were exposed to
global economic crisis, geo-political unrest
in MENA, natural calamities and most
importantly commodity cycle bust. All
these factors have substantially influenced
the crude oil prices and prices have
recorded both highs & lows indicating
extreme level of volatility. The results are
beneficial to crude oil stakeholder’s who
needs to recognize the influence of internal
factors or news on oil return series
volatilities before strategizing their future
course of activities to protect the bottom
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lines of their undertakings. Lastly, the
empirical outcomes are also significant to
our country’s policy makers since our
country depends on crude oil imports to
fulfill the consumption requirements of
domestic & commercial entities. Therefore
it is imperative to maintain a right balance
between demand and supply of crude oil in
order to mitigate the adverse price
risk/volatility impact on macro & micro
economic entities. The future studies may
undertake modelling of crude oil price
volatility with intraday price frequency,
impact of external factors like foreign
exchange, gold prices on oil volatility and
other outstanding aspects are left for
further empirical research.\
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