SYMMETRIC AND ASYMMETRIC VOLATILITY MODELLING FOR CRUDE OIL PRICES IN INDIA ABSTRACT

Transcription

1 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: , Mobile: , prasadpq@gmail.com maheshrajgopal@yahoo.com 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 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

2 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

3 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 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.

4 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 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 thirdlargest 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 assess price volatility of crude oil To offer an overview of Indian using appropriate GARCH family petroleum industry/crude oil - gas models sector To ascertain the existence of leverage To explore the significant concepts of effect in crude oil price returns crude price volatility

5 To identify the best model for crude oil price volatility based on diagnostic tests III OVERVIEW OF INDIAN PETROLEUM INDUSTRY Upstream segment - exploration & production Midstream segment storage & transportation Downstream segment refining, processing & marketing State-owned ONGC dominate the upstream segment, It is the largest upstream company in the Exploration and Production (E&P) segment, accounting for approximately per cent of the country s total oil output (FY15) 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 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 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 Source: TechSci Research & India Brand Equity Foundation 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 Customers Customers have low/nonexistent bargaining power Customers are price-taker not a price maker Future opportunities Upstream segment Midstream segment Downstream segment Locating new fields for Expansion in the transmission India is already a refining hub with exploration: 78 per cent of the network of gas pipelines 21 refineries and expansions country s sedimentary area is yet to LNG imports have increased planned for tapping foreign be explored significantly; this provides an investment in export oriented Development of unconventional opportunity to boost production infrastructure, including product resources: CBM fields in the deep capacity pipelines and export terminals sea In light of mounting LNG Development of City Gas Opportunities for secondary production, huge opportunity lies Distribution (CGD) networks, /tertiary oil producing techniques for LNG terminal operation, which are similar to Delhi and Higher demand for skilled labor engineering, procurement and Mumbai s CGDs and oilfield services and equipment construction services Expansion of the country s petroleum product distribution network Source: TechSci Research & India Brand Equity Foundation

6 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

7 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 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 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.

8 VI EMPIRICAL ANALYSIS Table No. 1 Descriptive Statistics & Normality Test Particulars Spot price returns Futures price returns Mean Std. Dev Maximum Minimum Skewness Kurtosis Jarque-Bera Probability Observations 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 heavyfatter 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.

9 Stationarity Test [Unit Root Test] Figure No. 1 Figure No. 2 SPLR FPLR From the graphical analysis it has been observed that both returns series have shown time-varying fluctuations during Jan, 2006 Dec, 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 Prob.* (p-value) Critical value 1% % Test equation coefficient SPLR(-1) & FPLR(-1) -6.22E E E E-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 nonstationary & times series data have a unit root has been justified. Therefore it is concluded that, both the returns series are

10 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 ARCH-LM Heteroskedasticity Test for Crude oil Spot price return series Crude oil Futures price return series F-statistic Prob. F(1,2957) F-statistic Prob. F(1,2957) Obs*R-squared Prob. Chi-Square(1) Obs*R-squared Prob. Chi-Square(1) Source: Compiled, edited data from MCX & computed using EViews 7 Figure No. 3 Figure No Residual Actual Fitted Residual Actual Fitted 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

11 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) (0.2599) (0.7518) λ (Risk premium) (0.5156) Coefficients of Variance Equation ω (Constant) (0.0018) (0.0018) α (ARCH effect) (0.2210) (0.8760) (0.6030) (0.0093) (0.0095)

12 β (GARCH effect) α + β Log likelihood AIC SIC ARCH-LM Test Result Test statistics Prob. Chi-Square (1) 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 ( & ) are highly significant with positive value and it illustrates that information related to past volatility has an influence of current volatility. GARCH effect coefficients ( & ) 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 & 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

13 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 ( & ) are extremely significant with positive value and it explains the impact of past volatility information on current volatility. GARCH effect coefficients ( & ) 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

14 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 Normal (Gaussian) Student s t distribution Model TGARCH(1,1) EGARCH(1,1) TGARCH(1,1) EGARCH(1,1) Coefficients of Mean Equation μ (Constant) (0.7071) (0.3686) (0.4509) (0.3658) Coefficients of Variance Equation ω (Constant) (0.0014) (0.0085) α (ARCH effect) (0.0172) (0.0049) β (GARCH effect) γ (Leverage effect) (0.0004) (0.0001) (0.0002) α + γ Log likelihood AIC SIC ARCH-LM Test Result Test Statistics Prob. Chi Square(1) 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.

15 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 & 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.

16 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) (0.1676) (0.8044) (0.5055) (0.3514) λ (Risk premium) (0.5390) (0.4410) Coefficients of Variance Equation ω (Constant) (0.0252) (0.0238) (0.0346) (0.0320) α (ARCH effect) β (GARCH effect) α + β Log likelihood AIC SIC ARCH-LM Test Result Test statistics Prob. Chi-Square (1) 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

17 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

18 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 Normal (Gaussian) Student s t distribution Model TGARCH(1,1) EGARCH(1,1) TGARCH(1,1) EGARCH(1,1) Coefficients of Mean Equation μ (Constant) (0.5856) -7.37E-05 (0.9978) (0.6091) (0.7429) Coefficients of Variance Equation ω (Constant) (0.0239) (0.0452) α (ARCH effect) (0.1038) (0.0076) β (GARCH effect) γ (Leverage effect) (0.0001) (0.0009) α + γ Log likelihood AIC SIC ARCH-LM Test Result Test Statistics Prob. Chi Square(1) 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

19 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

20 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 nonnormality 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.

21 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 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

22 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 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: , pp Bollerslev T., 1986, Generalized Autoregressive Conditional Heteroscedasticity, Journal of Econometrics, 31 (3): 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 Bollerslev T. & Jeffrey M. Wooldridge, Quasi maximum likelihood estimation and inference in dynamic models with time varying covariances, Econometric Reviews, 11, pp 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 Chou R. Y., 1988, Volatility Persistence and Stock Valuations: Some Empirical Evidence Using GARCH, Journal of Applied Econometrics, 3 (4), pp 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 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 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