




































Indian Journal of Finance and Banking 

 Vol. 9, No. 1; 2022 

                                       ISSN 2574-6081   E-ISSN 2574-609X 

Published by CRIBFB, USA 

 

1 

THE NONLINEAR ASYMMETRIC RELATIONSHIP AMONG 

IMPLIED VOLATILITY INDICES OF INDIAN STOCK MARKET, 

GOLD, AND OIL: EVIDENCES FROM NARDL MODEL 
 

 

Dr. Jyothi Chittineni 

Assistant Professor 

 Finance and Accounting 

IBS - Hyderabad, The ICFAI Foundation for Higher Education 

(Declared as Deemed-to-be University U/s 3 of the UGC Act 1956) 

Dontanapally Campus, Shanker Pally Road, Hyderabad, India 

E-mail: Jyothi.chittineni@ibsindia.org 

https://orcid.org/0000-0002-3838-6995 

 

 

Received: October 13, 2021       Accepted: November 15, 2021      Online Published: January 14, 2022  

 

DOI: 10.46281/ijfb.v9i1.1540            URL: https://doi.org/10.46281/ijfb.v9i1.1540 

 

 

ABSTRACT 

The paper aims to examine the nonlinear asymmetric relationship among the implied volatility indices 

of the Indian stock market, gold, and oil for the period from 2nd March 2009 to 29th October 2021. 

Nonlinear Autoregressive Distributed Lag (NARDL) model results provide evidence of asymmetric 

nonlinear relationship among the selected variables in the short-run and the long-run. The positive and 

negative shocks to gold and oil implied volatility indices have a positive and significant influence on the 

implied volatility of the Indian stock market. The expected volatility of gold has a short-term symmetric 

impact on expected stock market volatility in the short run. Whereas, the implied volatility of oil has a 

long-run asymmetric impact on the implied volatility of the stock market. Increasing volatility in oil 

prices can be viewed as a signal for the starting point for the volatility of the Indian stock markets. In 

the long run, positive shocks to gold volatility have more impact on the expected volatility of the Indian 

stock market than the negative. This indicates that investors are shifting their investments from gold to 

stocks for higher returns when the gold prices are fluctuating.  

 

Keywords: Nonlinear Autoregressive Distributed Lag, Implied Volatility Index, Asymmetric 

Relationship, Oil, Gold.  

 

JEL Classification Codes: G10, G11, G13, G15. 

 

INTRODUCTION 
Many economies liberalized their financial policies and trade policies to attract capital in-flows and to 

increase international trade volumes. These liberalized trade policies and financial policies integrated 

the economies as global villages. The positive side of these liberalized economies is that the developing 

economies could attract the capital inflow from developed economies. The other side of this integration 

is that the financial shocks and macroeconomic variables volatility is also transmitting from developed 

economies to developing economies.  

mailto:Jyothi.chittineni@ibsindia.org


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India being an emerging economy, it is largely depending on the developed economies for 

investments and trade. Indian economy is dependent on oil and gold markets because it is the biggest 

importer of oil and the consumer for the gold. India’s annual demand for gold is around 895 tonnes, 

which is 26% of the worldwide demand for physical gold. Gold has a very important role in Indian 

culture and rituals, during weddings and festivals buying gold is considered auspicious. Buying gold is 

a regular household expenditure, it is considered a symbol of status, wealth, sentiment, safety. India is 

the largest importer and the consumer of crude oil in the world. Lower crude oil prices narrow the fiscal 

deficit in India. An increase in crude oil has multiple impacts on the Indian economy.  

The Indian economy is more exposed to the price changes of these macroeconomic variables like 

oil and gold. The stock market prices and the inflation in the country are largely affected by the price 

changes of these resources. With this background, this paper aims to examine the impact of the future 

expected volatility of gold and oil on the future expected volatility of The Indian stock market. Unlike 

other papers, present paper uses expected future volatility as a central theme to understand the causality 

among these selected variables. 

There are several studies conducted to understand the bi-variate, bi-directional and dynamic 

relationship among stock prices, oil prices and gold prices. Most of these studies conducted on developed 

economies examined the linear relationship and presented mixed results about the oil, gold and stock 

prices interaction (Zhang & Wei, 2010), Most of the earlier studied used VAR and GARCH, DCC 

GARCH models. Interestingly, there is very little evidence of the causal relationship among the gold 

volatility index, oil volatility index and the Indian Implied volatility Indices. Therefore, the present study 

examines the non-linear causal interaction among implied volatility indices of gold, oil and Indian stock 

markets. Unlike earlier studies present study uses implied volatility indices to understand the non-linear 

causal interplay among selected variables. 

The paper results contribute to the literature in many ways. Firstly, this is one of the very few 

studies examined on implied volatility indices of stock markets, gold and oil and their interplay.  

Secondly, this paper uses a larger sample from 2nd March 2009 to 29th October 2021. Thirdly, the present 

study uses a non-linear autoregressive distributed lag model (NARDL) to understand the short-term and 

long-term responses to the shocks of one variable towards the other variables.  

The remaining part of the paper covers on review of literature, sample period and collection, 

model specification, empirical results discussions, implications of the study and the conclusions. 

 

REVIEW OF LITERATURE 

Understanding the interplay between the stock market and the alternative assets is very important for the 

policymakers to design the strategies for sustainable economic growth. Hence, the literature on these 

variables got attention from academicians, researchers, investors and policy makers.  Prior literature 

indicate that the fluctuations in the oil price has an impact on the economy because the oil price has 

direct impact on the cost of production and the profit margin (Hammoudeh & Choi, 2007). Fluctuation 

in the international oil prices leads to rupee value depreciating and hence the inflation in the country 

increase (Raj et al., 2008), when inflation increases investors are relying on the safe heaven gold to 

hedge their portfolio again inflation. The linkage between gold, oil and their movements influences the 

stock prices (Reboredo, 2013).  Sari et al. (2010) found a weak asymmetric relationship between gold 

and oil prices. Soytas et al. (2009) studied the influence of gold and silver price movements on the 

oil.  Zhang and Wei (2010) examined the relation between gold and oil prices and found a causal 

relationship between the variables. A nonlinear dynamic relationship between the oil and gold price 

examined by Lee and Lin (2012) found that the role of gold is determined by the oil price fluctuations. 

Contrary to the earlier studies, Chang et al. (2013) examined the interrelation between gold, oil and 

exchange rate and conclude that there is no relation between the selected variable.  Baur and McDermott 

(2010) highlighted that gold is not an effective hedging instrument for the BRIC nations during the stock 

market turmoil periods. Gurgun and Unalmis (2014) highlighted the hedging properties of gold for the 

Indian stock market. Concluded that there is a unidirectional spillover from gold returns to the Indian 

stock returns and there is no volatility spillover from the stock market to the gold.  Beckmann et al. 



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(2015) found that the gold is paying a safe haven role for the Indian stock markets and the author 

highlighted the need for non-linear modelling to understand the relationship between gold and the stock 

market. Chkili (2016) reported the evidence that gold can play a hedge role for the BRIC stock markets 

and holding the portfolios using gold can reduce the portfolio risk for emerging market 

portfolios.  Ghosh and Kanjilal (2016) reported that the non-linear co-integration between the Indian 

stock market and the oil. The results also revealed that there is a significant long-run association between 

the oil and Indian stock market.  Bouri, Roubaud, Jammazi, and Assaf (2017) reported a significant bi-

directional causality between gold and the Indian and Chinese stock markets. Bouri, Jain, Biswal, and 

Roubaud (2017) reported a significant relationship between the Indian stock market, gold and oil 

prices.  Miladifar, Mohamadi, and Moghadam (2020) employed a Markov switching Bayesian vector 

autoregressive model to understand the non-linear relationship between gold, oil and stock markets 

during upward and downward trends. The results reveal that there is a significant negative association 

between oil, gold and the stock markets. Lin, Kuang, Jiang, and Su (2019) reported a contagious effect 

from oil prices, gold prices to stock markets.  Tiwari, Adewuyi, and Roubaud (2019) examined the 

quantile regression on seven economies and reported a positive weak dependency between gold and the 

stock markets.  Wang, Ma, Niu, and He (2020) reported statistically significant association between oil 

prices on the stock markets.  Li, Semeyutin, Lau, and Gozgor (2020) confirm the interconnectedness 

between the emerging market volatility indices and the oil prices.  Enwereuzoh et al. (2021) observed 

that oil price shocks impact the stock markets of oil-importing nations and oil-exporting nations 

differently. Reported an interconnectedness between gold and the stock markets. From the prior studies 

it is evident that there is no conformity in the literature about the relationship between oil, gold and stock 

markets.  

 

DATA AND METHODOLOGY 

Data: the sample period is selected based on the availability of the data. The Indian implied volatility 

index is available from 2nd March 2009, hence daily closing prices for the Indian VIX (IVIX), gold 

implied volatility index (GVIX) and oil implied volatility index (OVIX) are used for the period from 2nd 

March 2009 to 29th October 2021. GVIX and OVIX data is collected from CBOE and IVIX data is 

collected from the Indian National Stock Exchange (NSE). 

 

METHODOLOGY 

Asymmetric non-linear ARDL (NARDL) model (Shin et al., 2014) is used to understand the non-linear 

relationship among the variables GVIX, OVIX and IVIX. The NRDL model is suitable for the stationary 

variables I(0), and the variables that are integrating at order one I(1). The model is not suitable if the 

variable are stationary at the second order I(2). The asymmetric non-linear ARDL model estimates both 

long-run and short-run co-integration among the variables in positive and negative directions. The 

advantage in using NARDL model is the co-integration can be estimated in a single equation framework. 

The following equation is used to estimate the long-run asymmetric relationship among the variables 

 

𝑌𝑡 = 𝛽+ ∑ ∆𝑡
𝑖=1 𝑋𝑖

+ + 𝛽− ∑ ∆𝑡
𝑖=1 𝑋𝑖

− + 휀𝑡 -------------------------------------------------------------------    (1) 

 

𝑌𝑡 is a dependent variables ; 𝛽+ and 𝛽− are the long-run parameters; 𝜕𝑡
+ and 𝜕𝑡

−  presents the positive 

and negative variation in the independent variable.  

 

Generalized form of Asymmetric non-linear ARDL equation is: 

 

∆𝑌𝑡 = 𝛼 + 𝛿𝑦𝑌𝑡−1 + 𝛿𝑥
+𝑋𝑡−1

+ + 𝛿𝑥
−𝑋𝑡−1

− + ∑ 𝛿𝑖
𝑚
𝑖=1 𝑌𝑡−𝑖 + ∑ (𝜃𝑖

+∆𝑋𝑡−𝑖
+ + 𝜃𝑖

−∆𝑋𝑡−𝑖
− ) + 휀1𝑡

𝑛
𝑖=0  ---------- (2)                                                          

 

Where,  𝛿+𝑎𝑛𝑑 𝛿− are the long-run asymmetric coefficients; ∆ represents the changes dependent 

variable Y; 𝜃+𝑎𝑛𝑑 𝜃− are the short-run asymmetric coefficients. The Long-run asymmetric coefficient 

https://www.sciencedirect.com/science/article/pii/S1057521921000739#bb0155
https://www.sciencedirect.com/science/article/pii/S1057521921000739#bb0205
https://www.sciencedirect.com/science/article/pii/S1057521921000739#bb0220
https://www.sciencedirect.com/science/article/pii/S1057521921000739#bb0150
https://www.sciencedirect.com/science/article/pii/S0301420721002087#bib31


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measures the direction of influence and the speed of adjustment of the independent variables on the 

dependent variable. The short-run nonlinear asymmetric analysis is used to understand the immediate 

influence of independent variables on the dependent variable. To test the null hypothesis of the long-run 

symmetry (𝜃+ = 𝜃−) the Wald test is employed. The positive and negative impact of exogenous 

variables on the dependent variables is measured by the changes in the long-run coefficients. The 

estimated parameters indicate the non-linear nexus between dependent and independent variables at the 

long-run equilibrium. Further, Wald test is used to test the short-run symmetry, null hypothesis (𝛿+ =
𝛿−). The positive and negative variations in the dependent variable is estimated by using the parameters. 

The estimated parameters indicate the positive and negative changes in the exogenous variables at the 

short-run equilibrium.  

 

EMPIRICAL ESTIMATES AND THE DISCUSSIONS 
Augmented Dickey-Fuller (ADF) and Phillip-Peron (PP) tests are employed to check the order of 

integration of the variables. All the variables are stationary after the first difference. Table 1 presented 

the unit root test results. 

 

Table 1. Unit root test results 

 

 IVIX GVIX OVIX 

ADF(Level) -0.8012 -0.345 -2.567 

PP (Level) -0.7634 -0.1865 -2.875 

ADF(First difference) 22.7654*** 28.567*** 26.4518*** 

PP(First difference) 27.0834*** 28.5891*** 36.6541*** 

*** is significant at 1 percent level of significance. 

 

The lag composition plays an important role, hence, Akaike Information Criterion (AIC) and 

Schwartz information criterion (SIC) is used to understand the appropriate lag length.  

To understand the co-integration among the selected variables, Nonlinear ARDL bound test is 

conducted and the results are presented in table 2. The F-statistic value higher than the critical value 

indicates the existence of non-linear asymmetric long-run co-integration among the variables. The test 

results indicate the existence of co-integration among the variables. The results are like Zhu et al. (2011), 

also reported that the stock markets and the oil markets are co-integrated for non-OECD and OECD 

economies in a panel framework.  

 

Table 2. The NARDL bound test results 

 

Variables F.Stat Cointegration 

IVIX 4.0121*** Cointegration 

GVIX 2.2981 No-cointegration 

OVIX 7.3821*** Cointegration 

*** is significant at 1 percent level of significance. 

 

The NARDL test results for understanding the long-run asymmetric nexus among OVIX, GVIX 

and IVIX are reported in table 3. When OVIX and IVIX are considered as dependent variables the F-

statistic value shows a significant asymmetric co-integration among the variables. The equation 

estimated with OVIX as a dependent variable, results indicates that IVIX does not influence the OVIX 

in the long-run. Current study results are contradicting to, Zhu et al. (2011), they have reported that the 



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stock market influences the oil in the long-run. The study results are coinciding with the findings of 

Kumar et al. (2019), they also reported that there is no significant co-integration existing between the 

stock market and oil in long-run. Whereas GVIX tends to have a statistically significant impact on 

OVIX. An increase (decrease) in GVIX causes (decrease) increase in OVIX, it indicates a statistically 

significant and negative asymmetric co-integration between GVIX and OVIX in long-run. This shows 

that the volatility shocks are transmitting from one market to the other. When markets are uncertain 

investors increase their trading volumes in gold because gold is considered as safe heaven. Increase in 

trading activity leads to price fluctuations and hence expected volatility. At the same time investors 

decrease their trading activity in oil markets, it leads to lower future expected volatility. Current study 

results indicate that the investors prefer to invest in gold compared to oil if gold prices are positively 

moving.  

IVIX as a dependent variable, the estimated equation results are statistically significant and 

confirm the asymmetric nonlinear association among OVIX, GVIX and IVIX in the long run. The 

fluctuation in the expected future volatility of the oil market and the gold markets influence the future 

volatility of the Indian stock market positively. The study results also indicate that the IVIX has no 

impact on OVIX. This unidirectional relation indicates that the level of dependency of oil-importing 

nation’s stock market volatility on the oil price volatility. Further, results indicate that an 

increase/decrease in GVIX causes a decrease/increase in IVIX. The results indicate that the Indian stock 

market’s future volatility is sensitive to the expected future volatility of the gold and oil markets. The 

volatility shocks from these two commodities markets transmit to the Indian stock markets’ expected 

future volatility.  

 

Table 3. NARDL estimated coefficients for the long-run co-integration 

 

OVIX equation estimated results IVIX equation estimated results 

Variables Coefficients T stat Variables Coefficients T stat 

IVIX+ 0.7635 1.1367 GVIX+ 0.1763*** 4.8128 

IVIX- 0.7865 1.1381 GVIX- 1.4528** 2.5001 

GVIX+ -0.0945** 2.3412 OVIX+ 0.9812*** 3.8102 

GVIX- -0.2387*** 3.5128 OVIX- 1.4623*** 4.1002 

C 2.864 *** 4.1291 C 1.7231*** 3.712 

*** is significant at 1 percent level of significance. ** indicates the level of significance is 5%,* 

indicates the level of significance is 10% 

 

The estimated values for the error correction model are presented in table 4. The error correction 

model results for OVIX are negative and statistically significant. The coefficient value is very small (-

0.0642). These results highlight that the oil volatility will subside after the shock, but the adjustment 

speed is very slow. The error correction equation estimated for IVIX is also negative and statistically 

significant. The smaller coefficient values indicate that the speed of adjustment for the IVIX is low and 

IVIX values will stabilize after the shocks.  

The study results show that the fluctuation in GVIX significantly influences the OVIX in the 

short run. A positive shock to GVIX causes a contemporaneous negative adjustment in OVIX. The 

OVIX undergoes a negative adjustment for a positive shock to GVIX at lag 1 and 2. The OVIX 

undergoes a positive adjustment for a positive shock to GVIX at lag 3. A negative shock to GVIX causes 

a positive adjustment in OVIX.  

The error correction model estimated for IVIX suggests that the GVIX and OVIX have a 

significant influence on IVIX in the short run. The IVIX undergoes a positive adjustment for the shock 

to IVIX at lag 2, 3 and 4. The IVIX demonstrates a negative contemporaneous adjustment to the positive 



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shock to GVIX at lag 1 and 2. A negative shock to GVIX causes a negative contemporaneous price 

adjustment in IVIX in the short-run. IVIX exhibits a positive adjustment to the positive stock to OVIX. 

The IVIX demonstrates a positive adjustment to the negative and positive shocks to the OVIX.  

 

Table 4. Error correction for NARDL model estimated results 

 

Error correction results for NARDL model 

(OVIX) 

Error correction results for NARDL model 

(IVIX) 

Variables Coefficients T stat Variables Coefficients T stat 

OVIX t-1  -0.1873 *** -3.8710 IVIX t-1  0.8723  1.9842 

OVIX t-s  -0.0129** -4.0086 IVIX t-2  0.3481** 2.0981 

GVIX +  -0.0321  -0.6823 IVIX t-3  1.7823*** 4.6528 

GVIX + t-1  -0.1287** -2.001 IVIX t-4  0.9821*** 3.9812 

GVIX + t-2  -1.9187 *** -4.981 GVIX+  -1.7635 -1.9823 

GVIX + t-3 0.9534 *** 2.4123 GVIX+ t-1  -0.9126 ** -2.1348 

GVIX-  0.5328** 0.0961 GVIX+ t-2  -1.9812*** -3.1287 

GVIX- 
t-1  3.2341 0.9128 GVIX-  -0.6381 -1.6522 

GVIX-
t-2  2.0981  -6.7218 GVIX- t-1  -.07623** -2.9912 

ECM (-1)  -0.0642***   OVIX +  2.001*** 3.9741 

      OVIX + t-1  3.1260*** 4.6914 

      OVIX-  0.3971*** 3.001 

      ECM (-1)  -0.0489*** -9.3912 

*** is significant at 1 percent level of significance.** indicates the level of significance is 5%,* indicates 

the level of significance is 10% 

 

The Wald test estimated results for short-term and long-term symmetric is presented in the 

table5. The Wald test estimated results are presented in table 5. The long-run (WLR) and short-run 

(WSR) result indicates that the OVIX has a long-run symmetric relationship with IVIX and the short-

run symmetric relationship with GVIX.  The IVIX exhibits a short-term symmetric relationship with 

GVIX and OVIX. 

 

Table 5. Wald test results for symmetric long-term and short-term cointegration 

 

Wald Test Results for OVIX Wald Test Results for IVIX 

variable WLR WSR Variables WLR WSR 

GVIX 7.6162  2.716** GVIX 11.6352 2.7634** 

IVIX 11.8372*** 7.3291 OVIX        11.84 7.323** 

*** is significant at 1 percent level of significance. ** indicates the level of significance is 5%,* 

indicates the level of significance is 10% 

 

CONCLUSIONS AND IMPLICATIONS 

The present study conducted on GVIX, OVIX and IVIX for the period from 2nd March 2009 to 29th 

October 2021 revealed the asymmetric long-run and short-run association among the selected variables.  



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The uniqueness of this study lies with the usage of implied volatility indices to test the asymmetric non-

linear association among gold, oil and the Indian stock markets. In the sense, current study results 

indicate the forward-looking uncertainty due to the uncertainty among the other selected variables.  

The empirical evidence from the study indicate short-run, long-run association among implied 

volatility of gold, oil and the Indian stock market. The results are similar to the findings of Jain and 

Biswal (2016). The current study reports the existence of asymmetric association among the selected 

variables when implied volatility index of oil and the Indian stock markets are considered as dependent 

variables. The NARDL co-integration test for the long-run indicates a statistically significant and 

negative asymmetric co-integration between GVIX and OVIX in long-run. This indicates that the 

investors are moving their trading activity from oil markets to gold during the uncertain market 

conditions. 

The current study results confirm that there is a contemporaneous asymmetric nonlinear 

association among OVIX, GVIX and IVIX in long-run. The fluctuation in the expected future volatility 

of the oil market and the gold markets influence the future volatility of the Indian stock market 

positively. The results indicate that the Indian stock market’s future volatility is sensitive to the expected 

future volatility of the gold and oil markets. India being the importer of these two commodities, the 

volatility shocks from these two commodities markets transmit to the Indian stock markets’ expected 

future volatility. So Investors may make use of the results to enter into appropriate derivative contacts 

to hedge their portfolio.  

The symmetric test for long term and short term association indicates that OVIX has the long-

run symmetric relationship with IVIX and the short-run symmetric relationship with GVIX.  The IVIX 

exhibits short-term symmetric relationship with GVIX and OVIX. It shows that the implied volatility of 

Indian stock market is influencing the expected volatility of oil and gold in the short-run symmetrically. 

The stock market performance as the barometer for the Indian economic activity, higher the economic 

activity higher the demand for oil. The higher demand from the biggest consumer may influence the oil 

prices positively in short-run. The results are important to the managers to enter into derivative contracts 

to hedge against the increasing production cost due to increasing oil prices.  

Further study should focus to understand, whether the relationship among implied volatility 

indices of oil, gold and the Indian stock market changes with the regime-switching behaviour of these 

indices or not.  

 

AUTHOR CONTRIBUTIONS 

Conceptualization: Jyothi Chittineni 

Data Curation: Jyothi Chittineni 

Formal Analysis: Jyothi Chittineni 

Funding Acquisition: Jyothi Chittineni 

Investigation: Jyothi Chittineni 

Methodology: Jyothi Chittineni 

Project Administration: Jyothi Chittineni 

Resources: Jyothi Chittineni 

Software: Jyothi Chittineni 

Supervision: Jyothi Chittineni 

Validation: Jyothi Chittineni 

Visualization: Jyothi Chittineni 

Writing – Original Draft: Jyothi Chittineni 

Writing – Review & Editing: Jyothi Chittineni 

 

CONFLICT OF INTEREST STATEMENT 

The author declare that he has no competing interests.  

 

 



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ACKNOWLEDGEMENT 

I would like to thank Mr. Narasimha Rao Kurra for his review suggestions and his support in conducting 

this study. 

 

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