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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016) 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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Page 1: SYMMETRIC AND ASYMMETRIC VOLATILITY MODELLING FOR CRUDE ... AND... · SYMMETRIC AND ASYMMETRIC VOLATILITY MODELLING FOR CRUDE OIL PRICES IN INDIA Mr. Prasad V. Daddikar, ... the impact

ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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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ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

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

-15

-10

-5

0

5

10

15

20

500 1000 1500 2000 2500

SPLR

-10

-5

0

5

10

15

20

500 1000 1500 2000 2500

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

-20

-10

0

10

20

-20

-10

0

10

20

500 1000 1500 2000 2500

Residual Actual Fitted

-10

-5

0

5

10

15

20

-10

-5

0

5

10

15

20

500 1000 1500 2000 2500

Residual Actual Fitted

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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.\

REFERENCES

Afees A. Salisu & Ismail O. Fasanya,

2012, “Comparative performance of

volatility models for oil price”,

International journal of energy

economics & policy, Vol. 2, No. 3, pp.

167-183.

Appenzeller, T., 2004, “End of cheap oil”

National Geographic magazine.

Aparna A., 2014, “Impact of Oil Prices on

the Indian Economy”, NMIMS

Management Review, Vol., XXIII,

ISSN: 0971-1023, pp. 141-147

Bollerslev T., 1986, “Generalized

Autoregressive Conditional

Heteroscedasticity”, Journal of

Econometrics, 31 (3): 307–27.

Bollerslev, T., Chou, R. Y., and Kroner, K.

F., 1992, “ARCH Modeling in

Finance: A Review of the Theory and

Empirical Evidence”, Journal of

Econometrics 52, pp. 5-59.

Bollerslev T. & Jeffrey M. Wooldridge,

“Quasi maximum likelihood estimation

and inference in dynamic models with

time varying covariances”,

Econometric Reviews, 11, pp. 143-

179.

Busayo, O., 2013, “Oil price and exchange

rate volatility in Nigeria”, Ota:

covenant University

C.O. Mgbame, P.A. Donwa & O.V.

Onyeokweni, 2015, “Impact of oil

price volatility on Economic growth:

Conceptual perspective”, International

Journal of Multidisciplinary Research

and Development, Volume: 2, Issue: 9,

PP 80-85

Chou R. Y., 1988, “Volatility Persistence

and Stock Valuations: Some Empirical

Evidence Using GARCH”, Journal of

Applied Econometrics, 3 (4), pp. 279-

94.

Dana AL-Najjar, 2016, “Modeling &

estimation of volatility using

ARCH/GARCH models in Jordan’s

stock market”, Asian journal of finance

& accounting, Vol. 8, No. 1

Daniel B. Nelson, 1991, Conditional

Heteroscedasticity in Asset Returns: A

New Approach, Econometrica, Vol.

59, No. 2, pp. 347-370.

Dickey D. A., and W. A. Fuller, 1979,

“Distribution of the Estimators for

Autoregressive Time Series with a

Unit Root”, Journal of American

Statistical Association, 74 (366), pp.

427–31.

Duong T Le, 2015, “Ex-ante Determinants

of Volatility in the Crude Oil Market”,

International Journal of Financial

Research, Vol. 6, No. 1.

Engle R. F., 1982, “Autoregressive

Conditional Heteroscedasticity with

Estimates of the Variance of UK

Inflation”, Econometrica, 50 (4), pp.

987–1007

Page 23: SYMMETRIC AND ASYMMETRIC VOLATILITY MODELLING FOR CRUDE ... AND... · SYMMETRIC AND ASYMMETRIC VOLATILITY MODELLING FOR CRUDE OIL PRICES IN INDIA Mr. Prasad V. Daddikar, ... the impact

ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

Engle, R.F., and T. Bollerslev, 1986,

“Modeling the Persistence of

Conditional Variances”, Econometric

Reviews, 5, pp. 1-50.

Engle, R. F., and Ng, V. K., 1993,

“Measuring and Testing the Impact of

News on Volatility”, Journal of

Finance, 48, pp. 1749-78.

Engle, R. F. and R. Susmel, 1993,

“Common Volatility in International

Equity Markets”, Journal of Business

and Economic Statistics, 11, pp. 167-

176.

Engle, R., 2002, “New Frontiers for

ARCH Models”, Journal of Applied

Econometrics, 17, pp. 425-446

Farhad Taghizadeh-Hesary, Ehsan

Rasolinezhad, and Yoshikazu

Kobayashi, 2015, “Oil Price

Fluctuations and Oil Consuming

Sectors: An Empirical Analysis of

Japan”, ADBI Working Paper Series,

No. 539.

Feng Ren and David E. Giles, 2007,

“Extreme Value Analysis of Daily

Canadian Crude Oil Prices”,

Econometrics Working Paper

EWP0708, University of Victoria

Glosten, L., Jaganathan, R. & Runkle, D.,

1993, “Relationship between the

expected value and volatility of the

nominal excess returns on stocks”,

Journal of Finance, 48(5), pp. 1779-

1802.

Hamilton, J. D., 2003, “What is an Oil

Shock?” Journal of Econometrics, 113,

pp. 363-98

Hamilton, J.D., 2009, “Causes and

consequences of the oil shock of 2007-

08”, Brookings Papers on Economic

Activity

Hojatallah G. & Ramanarayanan, C. S.,

2010, “Modeling and estimation of

volatility in the Indian stock market”,

International Journal of Business and

Management, 5(2), pp. 85-98.

Hojatallah G. & Ramanarayanan, C. S.,

2011, “Modeling Asymmetric

Volatility in the Indian Stock Market”,

International Journal of Business and

Management, Vol. 6, No. 3, pp. 221-

231.

India Brand Equity Foundation (IBEF)

James L. Williams, 1999-2016, WTRG

economics

Jarque, C.M., Bera, A.K., 1980, “Efficient

tests for normality, homoscedasticity

and serial independence of regression

residuals”, Economics Letters 6, pp.

225–259.

Jarque, C.M., & A.K. Bera, 1987, “A test

for normality of observations and

regression residuals”, International

Statistics Review, 55, pp. 163-172.

Karmakar M., 2005, “Modelling

Conditional Volatility of the Indian

Stock Markets”, Vikalpa, 30 (3), pp.

21–37.

Karunanithy Banumathy & Ramachandran

Azhagaih, 2015, “Modeling stock

market volatility: Evidence from

India”, managing global transitions,

Vol. 13, No. 3

Kolade Sunday Asesina, 2013, Modeling

stock market returns volatility:

GARCH evidence from Nigerian stock

exchange”, International journal of

financial management, Vol. 3.

Lutz Kilian, 2009, “Oil Price Volatility:

Origins and Effects”, WTO working

paper series, World Trade Report 2010

on Trade in Natural Resources:

Challenges in Global Governance

Manish Kumar, 2014, “The Impact of Oil

Price Shocks on Indian Stock and

Foreign Exchange Markets”, ICRA

Bulletin, Money & Finance

Multi commodity exchange (MCX), crude

oil prices for spot & futures from

2006-2015

Mhmoud A. S. & F. M. Dawalbait, 2015,

“estimating & forecasting stock market

volatility using GARCH models:

Page 24: SYMMETRIC AND ASYMMETRIC VOLATILITY MODELLING FOR CRUDE ... AND... · SYMMETRIC AND ASYMMETRIC VOLATILITY MODELLING FOR CRUDE OIL PRICES IN INDIA Mr. Prasad V. Daddikar, ... the impact

ELK ASIA PACIFIC JOURNAL OF FINANCE AND RISK MANAGEMENT

ISSN 2349-2325 (Online); DOI: 10.16962/EAPJFRM/issn. 2349-2325/2016; Volume 7 Issue 3 (2016)

Empiricla evidence from Saudi

Arabia”, International journal of

engineering research & technology,

Vol. 4, Issue 2.

Mittal A. K., D. D. Arora and N. Goyal,

2012, “Modelling the Volatility of

Indian Stock Market”, GITAM Journal

of Management, 10 (1), pp. 224–43.

Namit Sharma, 1998, “Forecasting Oil

Price Volatility”, Master’s thesis,

Virginia Polytechnic Institute and State

University

Niaz Bashiri Behmiri and José R. Pires

Manso, “Crude Oil Price Forecasting

Techniques”, Alternative Investment

Analyst Review

Ogiri, I., H., Amadi, S., N., Uddin, M., M.,

& Dubon, P., 2013, “Oil price and

stock market performance in Nigeria:

An empirical analysis” American

Journal of Social and Management

Sciences, 4(1), 20 – 41.

Olga Efimova, 2013, “Energy Commodity

Volatility Modelling using GARCH,

University of Calgary

Oriakhi, D. E., & Osazee, I. D., 2013, “Oil

price volatility and its consequences on

the growth of the Nigerian economy:

An examination (1970-2010)”, Asian

Economic and Financial Review, 3(5),

683-702.

Oil & Gas sector report, 2016, India brand

equity foundation, www.ibef.org

Petroleum Annual Report 2015, Ministry

of Oil & Natural Gas, India

Phillips P. C. B. and P. Perron, 1988,

“Testing for a Unit Root in Time

Series Regression”, Biometrika, 75 (2),

pp. 335–346.

Pirog, R., 2004, “Natural gas prices and

market fundamentals”, CRS Report for

Congress Congressional Research

service.

Robert S. Pindyck, 2004, “Volatility in

natural Gas and Oil markets”, The

journal of energy and development,

Vol. 30, No.1

Robert S. Pindyck, 2001, “The Dynamics

of Commodity Spot and Futures

Markets: A Primer”, The Energy

Journal, 22, 3, pp. 1-29.

Sang Hoon Kang & Seong-Min Yoon,

“Volatility models and their

forecasting abilities”, Working paper

series, Pusan National University,

Busan, Korea

Sebastian Dullien & et all, 2010, The

Financial and economic crisis of 2008-

2009 and developing countries, united

nations conference on trade &

development

Syed Aun Hassan, 2011, “Modeling

Asymmetric Volatility in Oil Prices”,

The Journal of Applied Business

Research, Volume 27, Number 3.

Syed Aun Hassan & Hailu Regassa,

“Asymmetric behavior of volatility in

gasoline prices across different regions

of the United States”, Journal of

Finance and Accountancy

Zakoian, J. M., 1994, “Threshold

Heteroscedasticity models. Journal of

Economic Dynamics and Control”, 18,

(5), pp. 931–955.