‘Indian Stock Market Volatility’: A Study of Inter-linkages and Spillover Effects

Abstract

The article attempts to examine interdependence between Indian stock market and other domestic financial markets, namely, foreign exchange market, bullion market, money market, and also Foreign Institutional Investor (FII) trade and foreign stock markets comprising one regional stock market represented by Nikkei of Japan and other stock market for the rest of the world represented by Standard & Poor’s (S&P) 500 of the USA. Attempts are also made to examine asymmetric volatility spillover, first, between the Indian stock market and other domestic financial markets and second, between the Indian stock market and global stock markets (represented by Nikkei and S&P 500) along with the foreign exchange market. To measure linear interdependence among multiple time series of financial markets multivariate Vector Autoregression (VAR) analysis, Granger causality test, impulse response function and variance decomposition techniques are used. For estima-ting the volatility spillover among the aforesaid markets Dynamic Conditional Correlation-Multivriate-Threshold Autoregressive Condi-tional Heteroscedastic (DCC-MV-TARCH) (1, 1) model is applied on daily data for a quite long period of time from 01 April 1996 to 31 March 2012. The results of multivariate VAR analysis, Granger causality test, variance decomposition analysis and impulse response function estimation establish significant interdependence between domestic stock market and different other financial markets in India and abroad. The results of DCC-MV-TARCH (1, 1) model estimation further show signi- ficant asymmetric volatility spillover between the domestic stock market and the foreign exchange market and also from the domestic stock market to bullion market and changes in gross volume of FII trade. We also find (a) both way asymmetric volatility spillover between the domestic stock market and the Asian stock market and (b) its unidirectional movement from the world stock market to the domestic stock market. The results of the study may help market regulators in setting regulatory policies considering the inter-linkages and pattern of volatility spillovers across different financial markets.

JEL Classification: G15, G17

Keywords

Volatility spillover asymmetric volatility spillover VAR Granger causality impulse response function variance decomposition DCC-MV-TARCH (1,1)

1. Introduction

Economic liberalisation in the early 1990s along with deregulation of interest rates and introduction of floating exchange rate system have made Indian financial market gradually more integrated not only domestically but also internationally. Along with these, opening up of the domestic market for the foreign investors has become one of the most important reformatory steps leading to strong integration of the Indian stock market with that of the rest of the world. Although in the course of these years Indian financial markets have been benefited for the increased domestic and foreign financial market integration in different ways, but it has to be remembered that during these years Indian markets have also become vulnerable to global shocks as can be witnessed from sharp and asymmetrical movements of the Indian stock indices as a result of a number of contemporary catastrophic events, such as global financial meltdown and European debt crisis.

Liberalisation and globalisation influenced the relation among diff-erent components of domestic financial system as they brought before investors several opportunities for greater portfolio diversification as risk containment measures. Superior technology also enhanced the scope of portfolio diversification for the investors. Common news has been empirically recognised as an important cause of both inter and intra country financial market integration. Globalisation led to increased market for currencies in which the securities are denominated, thus, creating interdependence between stock returns and exchange rate changes. In the floating exchange rate regime and for increased volume of transactions, financial markets volatilities have also increased and there might be increased occurrence of volatility spillover. The causal relationship between stock prices and exchange rates are explained in theoretical models (the monetary models, the portfolio-balance model). The monetary models of exchange rate determination present a robust tool to link stock prices with foreign exchange rates where money supply, interest rate, price level and inflation are taken into account to predict exchange rate movements. Whereas, expectations regarding movements of financial asset prices play an important role affecting exchange rate dynamics in the portfolio-balance model. On the other hand, Dornbusch and Fischer (1986), Hekman (1985), Sercu and Vanhulle (1992) among others evidenced opposite direction of causality (i.e., the exchange rate is a vital indicator of the stock price). It seems important to understand empirically the volatility linkage between stock prices and exchange rates in emerging economies, like India. Again, it is observed that bullion (both gold and silver) is becoming an alternative area of investment domestically as well as internationally and we, therefore, have incorporated the gold bullion market in the study for examining volatility spillovers among domestic financial markets including stock market. Moreover, in the question of execution of monetary policy of an economy, money market plays a key role and it is expected that stock market movements would be taken into consideration behind the policy decisions because of their considerable impact on the economy. The money market is the key link in the transmission mechanism of monetary policy to financial markets, and finally, to the real economy (RBI, 2012). Call money rate (CMR) is an important indicator of the money market and interest rate structure of an economy is highly influenced by changes in the CMR. These have great influences on the decision of companies while arranging finance and thus the corporate profits, thereby affecting the stock market. Besides, with the opening up of the domestic economy for FII trade, foreign investors have become very influential for Indian financial markets. It is a popular belief that daily FII turnover is a major factor behind stock market volatility in India. Therefore, while addressing the issue of volatility spillover in India FII’s asset allocation has been taken into consideration.

Still the researchers are looking for the answers regarding the nature of the integration and the diffusion channels through which shocks disseminate. A few literatures can be found focusing exclusively on spillovers among different domestic asset prices while few others whose primary objective was to examine inter-country spillovers for individual asset prices alone. Apprehending greater domestic and international inter-linkages of asset markets we found it necessary to model and estimate the spillovers across select domestic as well as foreign financial markets in a more comprehensive way. This may help investors to find out efficient hedging and trading strategies. Better understanding of volatility spillover among the financial markets is beneficial for portfolio managers as it helps in reducing risk and derivative dealers are also benefited while determining the values of derivative securities as their payoffs are dependent not only on prices of multiple assets but also on their volatilities. Moreover, while setting regulatory policies the policymakers should consider the volatility linkage pattern among the financial markets because of their influence on investment and risk management decisions.

Although there are different studies showing that globally financial markets co-vary at a greater degree and there are asymmetries in volatility transmission as a result of some common news impact, like 1987 stock market crash, Asian currency crisis, etc., there are also literatures showing that such linkages exist even in normal situation. In this study we try to explore the impact of innovations in different segments of domestic financial market in India, namely money market, foreign exchange market, bullion market and capital market (represented by change in the gross value of net FII turnover), and also foreign stock market on the volatility of domestic stock market.

The rest of the article is organised in the following manner: Section 2 represents a brief literature survey relating to empirical research on financial market inter-linkages and spillover effects; Section 3 identifies the gap in the existing researches; Section 4 sets the objectives of the study; Section 5 describes the study period and data base used; Section 6 presents methodological framework used in empirical analysis; Section 7 shows analysis of results and findings of the study and finally Section 8 concludes the study mentioning some ideas for future research.

2. Brief Literature Survey

There are a number of studies addressing the issue of volatility linkages/transmission. A few of them also investigate the transmission mechanism of price and volatility spillover across the major stock markets in the world and obtain varying results mainly due to the use of particular techniques and data over different periods.

King and Wadhwani (1990) estimated their contagion model for the New York, London and Tokyo stock markets using high-frequency data and found evidence of market contagion. Karolyi (1995) found short-term price spillovers between the New York and Toronto stock markets while estimating bivariate Generalized Autoregressive Conditional Heteroscedastic (GARCH) model in their study. Koutmos and Booth (1995) estimated an extended multivariate Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH) model on the basis of daily open to close returns of New York, Tokyo and London stock markets and witnessed asymmetric volatility transmission across the three markets. Moreover, the authors found the evidence of more interdependence among the markets in the post 1987 crash period. Koutmos (1999) observed presence of leverage effect in stock index returns of emerging stock markets which means conditional variance is asymmetric due to faster adjustment of prices to past negative returns. Ng (2000) evidenced presence of volatility spillover from Japan (regional market) and US (world market) to the Pacific-Basin markets though world factors were found to be more influential. Hashmi and Xingyun (2001) estimated correlation and VAR models for examining inter-linkages among New York, Tokyo and five South East Asian stock markets and found increasing inter-linkages among the South East Asian markets in the post-crisis period. Moreover, the authors observed New York market to affect South East Asian market significantly in both the periods. The study also considers Singapore market to be the most influential in the region, even more than New York market. Kumar and Mukhopadhyay (2002) investigated short-run dynamic inter-linkages between the US and the Indian stock markets and observed significant volatility spillover from NASDAQ Composite index to NSE Nifty. Nath and Verma (2003) found evidence of no co-integration among Asian stock markets represented by India, Singapore and Taiwan and no presence of causality implying that the markets were not interlinked. Nair and Ramanathan (2003) observed evidence of unidirectional causality from NASDAQ composite index to NSE Nifty. A. Worthington and H. Higgs (2004) examined the transmission of equity returns and volatility among developed and emerging Asian equity markets using Baba-Engle-Kraft-Kroner (BEKK) form of multivariate GARCH model and evidenced sign of high integration among the Asian equity markets and no homogeneity in volatility spillovers from developed to different emerging markets. The authors also noticed that own volatility spillovers were relatively higher than cross volatility spillovers, especially in emerging markets, implying greater importance of domestic factors there.

Sheng-Yung Yang (2005) used Engle’s (2002) dynamic conditional correlation (DCC) model to examine stock market correlations between Japan vis-à-vis each of the Asian Four Tigers, namely, Taiwan, Singapore, Hong Kong and South Korea. The author found evidence of volatility contagion across markets and increasing bilateral correlations during the period of high market volatilities. Kim, Moshirian, and Wu (2005) used bivariate DCC-EGARCH model to examine the impact of initiation of the European Monetary Union (EMU) on the stock market integration dynamics and found visible regime shift in European stock market integration which, according to them, was the result of not only macroeconomic integration brought by the introduction of EMU but also the development of existing financial sector. Kuper and Lestano (2007) examined financial markets interdependence in and between Thailand and Indonesia in a DCC-MGARCH (Multivariate Generalized Autoregressive Conditional Heteroscedastic) framework and found evidence of time-varying correlations among financial markets both within country and also between countries for each financial market, which got intensified all through Asian financial crisis. Wang and Moore (2008) employed DCC-EGARCH method to investigate the extent of co-movement of three major Central Eastern European emerging markets with the aggregate euro zone market and found sufficient evidence of dynamic correlations among the markets especially during and after financial crisis. Siddiqui (2009) has examined associations between Standard & Poor’s (S&P) CNX Nifty and selected Asian and US stock markets, and found increasing interdependencies among the indices in the second period of his study. From the Granger causality he has found no clear direction of relationships among the markets, which, according to the author is the indication of decreasing influence of a few markets notably that of the USA. Durai and Bhaduri (2009) analysed the correlation structure of the Indian stock market with the world stock markets and found very low correlation and slow pace of integration between the Indian stock market with that of Asian and other developed markets.

A. Hakim and M. McAleer (2010) have used the VARMA(1,1)-AGARCH(1,1) model of Hoti, Chan, and McAleer (2002) to examine the mean and volatility spillovers across bond, stock and foreign exchange markets in Australia, Japan, New Zealand, Singapore and the USA. The authors have witnessed the evidence of international mean spillovers in individual markets to be more general rather than across markets, whereas, volatility spillovers have been found to be strong both across markets and within individual markets and in all the cases the USA has been observed to be the most influential one. Joshi (2011) has tried to examine the co-movement of stock markets of USA, Brazil, Mexico, China and India and found evidence of co-integration among the markets under study. The author has also witnessed relatively higher speed of adjustment of the Indian stock market. Li and Giles (2013) have used BEKK (1,1) model to examine the linkages of stock markets across the USA, Japan and six Asian developing countries (namely, China, India, Indonesia, Malaysia, Philippines and Thailand) and have found significant one-way shock and volatility spillover from the US market to both the Japanese and the Asian emerging markets except during the Asian financial crisis when there was stronger and both-way volatility spillover between the US market and the Asian markets. V. K. Natarajan, Robert, Singh, and Priya (2014) have investigated the mean-volatility spillover effects among five major national stock markets (namely, Australia, Brazil, Germany, Hong Kong and US) using the GARCH-mean model. The authors have found cross-mean and volatility spillovers from the USA market to the Australian and Germany markets; also, the past USA returns and volatility shocks have been found to have great effects on Germany and Australia with varying degrees of intensity. The authors have identified the US market as the most influential market among the markets under their study. Herrera, Salgado, and Ake (2015) have found evidence of one-way volatility spillovers from the World Market to Mexican market and the strong association between the Mexican and the World market indices has been observed not only during high volatility regime but also in low volatility period, reducing the potential diversification benefits in both the cases, which are unlikely to occur according to the standard models of international portfolio theory. Baek and Oh (2016) have examined the volatility spillover aspects of realised volatilities for the log returns of the Korea Composite Stock Price Index (KOSPI) and the Hang Seng Index (HIS) using Leverage Heteroskedastic Autoregressive Realised Volatility (LHAR) model and have found significant unidirectional daily volatility spillover from the HSI to the KOSPI.

There are few other studies also which explore the volatility linkages and spillovers among different asset types within an economy or different components of the same financial system for addressing the issue of domestic financial integration.

Fleming, Kirby, and Ostdiek (1998) used GMM for predicting volatility linkages between stock, bond and money markets and observed strong volatility linkages between the markets which were found become even stronger after 1987 stock market crash. Ebrahim (2000) investigated information transmission, if any, between foreign exchange (US/Canadian dollar, Deutsche mark and Japanese yen) and related money markets using trivariate GARCH estimation method and found strong evidence of volatility spillovers in all the three cases and volatility spillovers were found to be asymmetric in some cases. H. R. Badrinath and P. G. Apte (2005) used a multivariate EGARCH framework in their study and found asymmetric volatility spillover across stock, foreign exchange and call money markets in India where, stock market was found to have greatest asymmetric impact on the other two markets. Banerjee and Sarkar (2006) used FII trade as an exogenous variable while estimating different GARCH models and found no significant impact of increasing participation of FII on volatility of the Indian stock market. Xiong and Han (2015) have used Granger causality multivariate stochastic volatility (GC-MSV) model to examine volatility spillover effects between the foreign exchange and stock markets and found evidence of asymmetric bi-directional volatility spillover between the two markets, for both in the continued Ren Min Bi (RMB) appreciation and constant RMB shock stages, although in the second case the volatility spillover effects have not been found to be as significant as in the stage of continued RMB appreciation.

3. Research Gap

The existing literature reveals to the authors that in the context of India, there remains a scope for exploring the nature of volatility inter-linkages and examine the existence of asymmetric volatility spillovers, if any, between Indian stock market on the one hand and other components of domestic financial system and also the global stock markets on the other. Moreover, to the best of the authors’ knowledge the volatility spillovers among the domestic stock market, money market, bullion market and FII trade have not been so far analysed in India using daily data. In the existing studies on volatility spillover, it is observed that mainly multivariate model with constant conditional correlation (CCC) assumption has been used. But in reality the correlation structure does not remain constant over time; rather DCC is more appropriate postulate than CCC and our estimated model corroborates that. Moreover, we have found hardly any study in the Indian context that has tried to capture the feature of asymmetry in the volatility spillover process across domestic as well as foreign financial markets, which is also necessary as it is well evidenced (Black, 1976; Christie, 1982) that volatility is higher in a falling market (in response to negative news) than that in a rising market (having positive news). So we feel that not only the presence of volatility spillover with over time changed correlation structure, but also the presence of asymmetric feature in the volatility spillover process need to be examined in a multivariate setting in the Indian context, unlike other existing studies in this field. This study permits own market and cross-market innovations to have an asymmetric impact on the volatility of the market concerned. The news generated in one market can be evaluated both in terms of size and sign by the other markets in a dynamic setting.

4. Objectives and Significance of the Study

The objectives of the study are to address the following issues in relation with the Indian stock market:

Is there any evidence of interdependence between the stock market and different other components of domestic financial system (namely, foreign exchange market, bullion market, money market and change in gross volume of FII trade) in India and foreign stock markets?

If there is any evidence of volatility spillover between the stock market and different other domestic financial markets, are they asymmetric in nature?

Is there any evidence of asymmetric volatility spillover between the domestic stock market and foreign stock markets represented by a regional and a world stock market?

The knowledge regarding the volatility interdependence between the domestic stock market and different other components of domestic financial market as well as foreign stock markets is very important for taking any decision regarding investment or management of risk while hedging against shocks generated across markets. It also helps market regulators in fixing appropriate regulatory policies taking into consideration the pattern of volatility inter-linkages among different financial markets.

5. Study Period and Database

In view of measuring interdependence between different domestic and foreign financial markets and to examine asymmetric volatility spillover across the markets we have used daily closing prices of S&P CNX Nifty as representative of Indian stock market, collected from the website http://nseindia.com, and that of NIKKEI and S&P 500 as representatives of regional and world stock market respectively collected from the website http://finance.yahoo.com for the study period spanning from 1 April 1996 to 31 March 2012. Daily closing spot price of gold bullion in Mumbai and daily INR/USD exchange rate are used to represent the Indian bullion market and foreign exchange market, respectively, data of both of which are obtained from various daily issues of Economic Times, Mumbai. Domestic money market is represented by average daily CMR whose data is obtained from different issues of monthly bulletin of Reserve Bank of India though it is only available from 4 May 1998. Therefore, while examining volatility inter-linkages and volatility spillover of money market with other domestic financial markets our study period is shortened to 4 May 1998 to 31 March 2012. Moreover, daily gross volume of FII trade (sum of purchase and sales volume) is included in the study as it is now commonly believed to be an important determinant of the stock market volatility in India. The FII trade data is obtained from the website http://nseindia.com but only from 4 April 2006. Thus, when we examine volatility inter-linkages and volatility spillover between FII trade in India with other domestic and foreign financial markets, the span of our study period is reduced and effectively becomes 4 April 2006 to 31 December 2012. S&P CNX Nifty is currently the most popular stock index in India and it is a major player in the Indian stock market. Presently, NIKKEI, a stock market index for the Tokyo Stock Exchange (TSE), is the most extensively quoted average of Japanese equities and is used in our study as the representative of Asian stock market. On the other hand the S&P 500 is recognised worldwide as one of the most influential equity indices and is regarded as the best representative of the US stock market by many (Durai & Bhaduri, 2009; Engle & Sheppard, 2001; Hakim & McAleer, 2010; Joshi, 2011; Karolyi, 1995; Siddiqui, 2009). Therefore, S&P 500 index is used in the present study as the representative of world stock market, other than the Asian one. The accuracy and reliability of all these data has been checked also from other available sources.

The daily closing prices of all the financial variables have been transformed into daily continuous returns which are the logarithmic differences of prices of two successive periods, that is,

R_{i, t} = \log_{e} (P_{i, t} / P_{i, t - 1})

where R_i,t is continuous daily return at time t, and P_i,t_–1 and P_i,t are two successive daily closing prices of ith financial market. In case of the daily gross volume of FII trade we have transformed it into the change in gross volume of FII trade which is calculated as: R_FII,t = FII_t – FII_t–1, where FII_t–1 and FII_t are gross volumes of FII trade for two consecutive dates.

6. Methodology

Stationarity of all the return series has been checked by Augmented Dickey–Fuller (ADF) test (1979). To measure linear interdependence among multiple time series of financial markets, all of which have already been found stationary in the study, the multivariate VAR model is used and in the model all the market return series are used as endogenous variables. To understand the causal relationship between the returns in financial variables in pairs we carry out test for Granger causality. For explaining economic significance over and above the statistical significance we also analyse impulse response function and variance decomposition. It may be noted that impulse response function explains impact of an exogenous shock in one variable on the other variables of the system. Here we also use the impulse response function to analyse the impact of innovation (shock) of the ith market on the jth market return and vice versa. By variance decomposition we try to analyse how much variation in ith market return is explained by its own lag and how much is due to shocks to the other financial markets. We use econometric software package EViews7 for estimation of multivariate VAR, Granger causality, impulse response functions and variance decomposition analysis.

The dynamic relationships among all the data series are estimated using multivariate VAR model in which returns in all the markets are endogenous variables, as mentioned earlier.

Let R_i,t be the return in variable i at time t, [i = 1, 2, 3, 4, 5 where, 1 represents Gold Bullion (RTGOLD), 2 represents foreign exchange rate (RTEX), 3 represents S&P CNX Nifty (RTNIF), 4 represents S&P 500 (RTSP) and 5 represents NIKKEI (RTNIK)]. Further R_i,t–n be the return in variable i at time t  n (n being the length of lag which is taken either 1 or 2). Multivariate VAR model can be represented symbolically as follows:

\begin{matrix} R_{i, t} {=θ}_{i,0} + {\sum^{​}}_{10}^{j =1} {\sum^{​}}_{2}^{n =1} θ_{i, j, n} R_{j, t - n} {+ε}_{i, t}, for i = 1, 2..., 5. \\ j = 1, 2, 3, ..., 10. \\ n = 1, 2. \end{matrix}

where, ε_i,t’s are the stochastic errors, termed as impulses or shocks or innovations in VAR system. The maximum lag length (here 2) is chosen by using Akaike and Schwarz criteria. The coefficients _i,j,n’s represent the respective effects of own lagged returns and lagged returns of other markets on the present return of the market concerned. If the parameters are found to be significant, then there exists a bi-directional causal relation among the variables. The same model has been estimated separately to examine the influence of change in FII trade (with other five endogenous variables related to domestic as well as foreign markets) and also of change in CMR (with all three endogenous variables related to domestic markets only). Separate estimations have been made due to the consideration of different study periods as per availability of data and in case of CMR, unlike others, only domestic market variables have been considered deliberately to examine their mutual influences. To understand the dynamic relationship among the macroeconomic financial variables we report both the Granger causality test and VAR parameter estimates in our study.

The dynamic relationship is also investigated by analysing the impulse response function and variance decomposition. An impulse response function traces out the impact of a one standard deviation shock to one of the error terms [innovation] on current and future values of endogenous variables. A shock to the ith variable directly affects the ith variable and through the dynamic structure of VAR it is transmitted to all other variables in the system, for example, a change in ε_i,t will immediately affect R_1,t and also affect all future values of R₁, R₂, R₃ R₄, and R₅. By variance decomposition analysis, on the other hand, variation in an endogenous variable is decomposed into component shocks to the endogenous variables in the VAR system. From it we can get the relative importance of each random innovation to the VAR variables.

To measure asymmetric volatility spillover across the financial markets in our study the multivariate extension of Threshold GARCH [TARCH] (1, 1) model has been used under DCC assumption and therefore, can be named as DCC-MV-TARCH (1, 1) asymmetric volatility spillover model. With the help of this model the news generated in one market can be evaluated both in terms of size and sign by the other markets (Badrinath & Apte, 2005). In the study the DCC-MV-TARCH (1, 1) model has been used following Engle (2002) whose general specification is as follows:

There are i number of conditional mean equations in the model as specified below:

\begin{matrix} R_{i, t} {=θ}_{i,0} + \sum_{j} θ_{i, j,1} R_{j, t - 1} {+ε}_{i, t}, ε_{i, t} {/ψ}_{t - 1} ~ N (0, H_{i i, t}) \\ f o r 3 \leq i, j \leq 4 i n o u r s t u d y . \end{matrix}

(1)

where, ε_i,t is the stochastic error terms in the ith market, and _t–1 is the information set available at time t  1.

The variance equation with spillover and asymmetric effects is represented as:

H_{i i, t} = ω_{i 0} ​ + \sum_{j} a_{i j} ε_{j, t - 1}^{2} + b_{i} H_{i i, t - 1} + d_{j} ε_{j, t - 1}^{2} I_{ε \leq 0} {(ε}_{j, t - 1})

(2)

where ω_i0 >0 and the conditional variances are finite if b_i < 1. The volati-lity spillover effect from market j to market i is captured by a_ij, where i ≠ j. I is an indicator function for ε < 0 [negative residual]. Positive value of d_j implies that negative residuals (i.e., bad news) in market j tend to increase the volatility in market i (represented by H_ii,t) more than that of positive ones. On the other hand, if d_j is found to be negative, negative residuals in market j tend to increase the volatility in market i less than positive ones.

The conditional covariances in the DCC-MV-TARCH (1, 1) model are defined as:

H_{i j, t} = D_{t} R_{t} D_{t}

(3)

where D_t $=diagonal(\sqrt{h_{11, t,}} … … … ., \sqrt{h_{N N, t}})$ , h_ii,t is defined as univariate GARCH (1, 1) model and

R_{t} =diagonal (s_{11, t}^{- 1/2},… … … . s_{N N, t}^{- 1/2}) S_{t} diagonal(s_{11, t}^{- 1/2},… … … . s_{N N, t}^{- 1/2})

(4)

where the N×N symmetric positive definite matrix S_t[= (s_ij,t)] is given by:

S_{t} = (1 - α - β) \bar{S} + α u_{t - 1} u_{t - 1}^{/} + β S_{t - 1}

(5)

with u_t = ε_t/D_t

$\bar{S}$ is the N×N unconditional covariance matrix of standardised residual u_t, and ‘’ and ‘’ are nonnegative scalar parameters satisfying the condition  +  < 1. These two scalar parameters govern a ‘GARCH (1, 1)’ model on covariance matrix as a whole. The actual H matrix is generated by using univariate GARCH models for the variances along with the correlation matrix provided by the ‘S’ [Software Package RATS User’s Guide].

H_{i j, t} = D_{t} R_{t} D_{t} = \frac{s_{i j, t} \sqrt{h_{i i, t} . h_{j j, t}}}{\sqrt{s_{i i, t} s_{j j, t}}}

(6)

The maximum likelihood method is used to estimate the model and the log likelihood function following Engle (2002) and Engle ε<0 and Sheppard (2001) can be written as:

L (\emptyset)= - N T /2ln(2π) - 0 .5 \sum_{t =1}^{T} [ln {(R}_{t})+2ln| D_{t} |+ u_{t}^{/} R_{t}^{- 1} u_{t}]

(7)

where the parameter vector ‘Φ’ to be estimated contains the para‑ meter set of the univariate TARCH models along with the parameter set of dynamic correlation structure. u_t is the vector of standardised residuals (u_t = ε_t/D_t) at time t. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is used to produce the maximum likelihood estimates of parameters and their corresponding asymptotic standard errors.

7. Data Analysis and Findings

The ADF unit root test is performed to check the stationarity of daily return series of each representative of the domestic and foreign financial markets and the results of the test are presented in Table 1. From Table 1 it is visible that all the return series are stationary. To measure linear interdependence among multiple time series of financial markets which are all found to be stationary, the multivariate VAR model is used and in the model all the market return series are used as endogenous variables. The results of VAR estimation are presented in Table 2. Since our objective is to examine interdependence between domestic stock market and other domestic as well as foreign financial markets, we, therefore, like to report from the table concerned only the results related to Nifty. From the column of Nifty in Table 2 we find that individually only RTG at lag-2, RTSP at lag-1 and lag-2 and RTNIKKEI at lag-1 are statistically significant. But collectively F-statistic is found to be significantly different from zero and fairly high. So we cannot reject the hypothesis that collectively all the lagged terms are statistically significant.

Table 1.
Estimated Result of ADF Test of Return Series of Selected Domestic and Foreign Financial Markets

Market ADF Test Statistic*

Return in gold bullion market (RTG) -26.82840

Return in foreign exchange market (RTEX) -26.25317

Return in S&P CNX Nifty (RTNIF) -27.75388

Return in money market (RTCMR) -36.61062

Change in gross volume of FII trade (CHFII) -21.12778

Return in S&P 500 (RTSP) -30.49912

Return in Nikkei (RTNIK) -29.47499

Market	ADF Test Statistic*
Return in gold bullion market (RTG)	-26.82840
Return in foreign exchange market (RTEX)	-26.25317
Return in S&P CNX Nifty (RTNIF)	-27.75388
Return in money market (RTCMR)	-36.61062
Change in gross volume of FII trade (CHFII)	-21.12778
Return in S&P 500 (RTSP)	-30.49912
Return in Nikkei (RTNIK)	-29.47499

Source: Authors’ own calculations.

Note: *ADF test statistic is estimated by fitting the equation of the form: $Δ y_{t} = φ + δ y_{t - 1} + \sum_{j =1}^{4} θ_{j} Δ y_{t - j} + μ_{t} .$

Table 2.

Estimated Results of Multivariate VAR Model

	RTG	RTEX	RTNIF	RTSP	RTNIKKEI
RTG(−1)	0.016801	0.017325*	0.006884	0.012398	−0.032041
	(0.01591)	(0.00588)	(0.02787)	(0.02231)	(0.02328)
	(1.05632)	(2.94553)	(0.24700)	(0.55571)	(−1.37622)
RTG(−2)	−0.001200	−0.020059*	0.093065*	0.004679	0.009060
	(0.01589)	(0.00588)	(0.02785)	(0.02229)	(0.02326)
	(−0.07548)	(−3.41275)	(3.34155)	(0.20989)	(0.38943)
RTEX(−1)	0.040855	−0.019997	−0.032270	0.000942	−0.005797
	(0.04402)	(0.01628)	(0.07715)	(0.06175)	(0.06444)
	(0.92799)	(−1.22829)	(−0.41830)	(0.01526)	(−0.08996)
RTEX(−2)	−0.020133	−0.018811	−0.113049	−0.026500	−0.183427*
	(0.04299)	(0.01590)	(0.07533)	(0.06030)	(0.06293)
	(−0.46830)	(−1.18324)	(−1.50066)	(−0.43946)	(−2.91486)
RTNIF(−1)	0.006988	−0.034063*	0.017936	0.028040**	0.046965*
	(0.00943)	(0.00349)	(0.01652)	(0.01323)	(0.01380)
	(0.74100)	(−9.76797)	(1.08542)	(2.11992)	(3.40241)
RTNIF(−2)	−0.002952	−0.007935**	−0.038713**	0.008466	−0.003658
	(0.00950)	(0.00351)	(0.01664)	(0.01332)	(0.01390)
	(−0.31091)	(−2.25961)	(−2.32659)	(0.63560)	(−0.26319)
RTSP(−1)	−0.035411*	−0.061256*	0.273749*	−0.077741*	0.488100*
	(0.01166)	(0.00431)	(0.02042)	(0.01635)	(0.01706)
	(−3.03814)	(−14.2119)	(13.4034)	(−4.75527)	(28.6096)
RTSP(−2)	0.015445	0.008656***	0.082876*	−0.034503***	0.080298*
	(0.01297)	(0.00480)	(0.02273)	(0.01819)	(0.01899)
	(1.19072)	(1.80466)	(3.64630)	(−1.89645)	(4.22929)
RTNIKKEI (−1)	0.008913	0.018173*	−0.065266*	−0.031579**	−0.138951*
	(0.01119)	(0.00414)	(0.01961)	(0.01570)	(0.01638)
	(0.79641)	(4.39079)	(−3.32787)	(−2.01160)	(−8.48167)
RTNIKKEI (−2)	−0.004648	0.001607	−0.004707	−0.055717*	−0.055635*
	(0.01045)	(0.00386)	(0.01831)	(0.01465)	(0.01529)
	(−0.44494)	(0.41604)	(−0.25710)	(−3.80223)	(−3.63815)
C	0.000422*	0.000140**	0.000308	0.000168	−0.000444**
	(0.00015)	(5.5E-05)	(0.00026)	(0.00021)	(0.00022)
	(2.83189)	(2.53976)	(1.17900)	(0.80172)	(−2.03265)
R2	0.004052	0.089893	0.051186	0.012784	0.189670
Adj. R2	0.001545	0.087602	0.048798	0.010300	0.187631
Sum sq. resids	0.348307	0.047632	1.069504	0.685271	0.746283
Standard Error (S. E.) equation	0.009363	0.003462	0.016407	0.013133	0.013705
F-statistic	1.616468***	39.24185*	21.43318*	5.145046*	92.99423*
Log likelihood	12961.62	16924.87	10726.86	11613.57	11443.67
Akaike AIC	−6.501314	−8.490899	−5.379448	−5.824583	−5.739293
Schwarz SC	−6.483947	−8.473532	−5.362081	−5.807216	−5.721926
Mean dependent	0.000428	0.000102	0.000416	0.000191	−0.000290
Standard Deviation (S. D.)dependent	0.009370	0.003625	0.016823	0.013201	0.015206
Determinant residual covariance		7.72E-21
Log likelihood		63985.44
Akaike information criteria		−32.09359
Schwarz criteria		−32.00676

Source: Authors’ own calculations.

Notes: *, ** and *** indicate significance of the parameter at 1%, 5% and 10% significance levels, respectively. Standard errors & t-statistics in parentheses.

The results of pair wise Granger causality test for lag-1 and lag-2 are presented in Table 3. The results show that in lag-1 return in Nifty and return in gold bullion do not Granger cause one another but there is one way Granger causality running from return in Gold bullion to return in Nifty in lag-2. Return in Nifty is found to be Granger cause of return in exchange rate both in lag-1 and lag-2 but the converse is not true. Return in S&P 500 does Granger cause return in Nifty both in lag-1 and lag-2 but return in Nifty is not found to be Granger cause of return in S&P 500 in any lag. We find one way Granger causality running from return in Nifty to return in NIKKEI in both the lags.

Table 3.

Results of Pair Wise Granger Causality Test

Null Hypothesis	Obs	F-Statistic	Probability
Sample: 1 3986
Lags: 1
RTEX does not Granger cause RTG	3985	0.41701	0.51847
RTG does not Granger cause RTEX		12.7995*	0.00035
RTNIF does not Granger cause RTG	3985	0.33048	0.56541
RTG does not Granger cause RTNIF		0.60455	0.43689
RTSP does not Granger cause RTG	3985	9.62405*	0.00193
RTG does not Granger cause RTSP		0.39309	0.53071
RTNIKKEI does not Granger cause RTG	3985	1.11223	0.29166
RTG does not Granger cause RTNIKKEI		10.7621*	0.00104
RTNIF does not Granger cause RTEX	3985	109.618*	0.00000
RTEX does not Granger cause RTNIF		1.12944	0.28796
RTSP does not Granger cause RTEX	3985	248.987*	0.00000
RTEX does not Granger cause RTSP		0.19159	0.66162
RTNIKKEI does not Granger cause RTEX	3985	2.96079***	0.08538
RTEX does not Granger cause RTNIKKEI		12.9038*	0.00033
RTSP does not Granger cause RTNIF	3985	167.671*	0.00000
RTNIF does not Granger cause RTSP		1.41712	0.23395
RTNIKKEI does not Granger cause RTNIF	3985	1.13517	0.28674
RTNIF does not Granger cause RTNIKKEI		51.9237*	6.9E-13
RTNIKKEI does not Granger cause RTSP	3985	5.99561**	0.01438
RTSP does not Granger cause RTNIKKEI		858.881*	0.00000
Lags: 2
RTEX does not Granger cause RTG	3984	0.36662	0.69309
RTG does not Granger cause RTEX		13.9754*	8.9E-07
RTNIF does not Granger cause RTG	3984	0.18818	0.82847
RTG does not Granger cause RTNIF		6.05021*	0.00238
RTSP does not Granger cause RTG	3984	6.10466*	0.00225
RTG does not Granger cause RTSP		0.14126	0.86827
RTNIKKEI does not Granger cause RTG	3984	0.54757	0.57840
RTG does not Granger cause RTNIKKEI		5.46229*	0.00428
RTNIF does not Granger cause RTEX	3984	56.3533*	0.00000
RTEX does not Granger cause RTNIF		1.85412	0.15673
RTSP does not Granger cause RTEX	3984	126.124*	0.00000
RTEX does not Granger cause RTSP		0.10962	0.89618
RTNIKKEI does not Granger cause RTEX	3984	1.62668	0.19671
RTEX does not Granger cause RTNIKKEI		9.77661*	5.8E-05
RTSP does not Granger cause RTNIF	3984	87.3002*	0.00000
RTNIF does not Granger cause RTSP		1.88599	0.15181
RTNIKKEI does not Granger cause RTNIF	3984	0.41941	0.65746
RTNIF does not Granger cause RTNIKKEI		26.4413*	3.9E-12
RTNIKKEI does not Granger cause RTSP	3984	7.78459*	0.00042
RTSP does not Granger cause RTNIKKEI		441.251*	0.00000

Source: Authors’ own calculations.

Note: *, ** and *** indicate significance of the parameter at 1%, 5% and 10% significance levels, respectively.

From the variance decomposition results presented in Table 4, it is evident that any variation of return in Nifty is explained mainly by its own lagged return (>96% in lag-1, >92% in lag-2 and >91% thereafter) than by the lagged returns in other markets. It is also to be noted that (a) lagged return in exchange rate is able to explain more than 3 per cent and (b) lagged return in S&P 500 is able to explain more than 4 per cent variation of Nifty return. On the other hand, more than 99 per cent variation in exchange rate return is explained by its own lagged returns and that too by lag-1; thereafter it comes down to more than 91 per cent whereas lagged return in Nifty is able to explain more than 3 per cent and lagged return in S&P 500 is able to explain more than 4 per cent from lag-2 of the variation in exchange rate return. Variations in returns in Gold bullion, S&P 500 and Nikkei are also mainly explained by their own lagged returns. It is also observed that lagged return in Nifty explains more than 2 per cent of variation and lagged return in exchange rate explains more than 1 per cent of variation in S&P 500 return. Again lagged return in Nifty explains more than 3 per cent, lagged return in exchange rate explains more than 2 per cent and lagged return in S&P 500 explains more than 1 per cent in lag-1 but more than 17 per cent thereafter of variations in Nikkei return. These results broadly indicate evidence of interdependence among the financial variables supporting the earlier results of Granger causality test.

Table 4.

Estimated Results of Variance Decomposition

Period	S.E.	RTG	RTEX	RTNIF	RTSP	RTNIKKEI
Variance decomposition of RTG
1	0.009350	100.0000	0.000000	0.000000	0.000000	0.000000
2	0.009365	99.73255	0.029340	0.003975	0.218347	0.015789
3	0.009369	99.63877	0.037234	0.005842	0.298656	0.019501
4	0.009369	99.63831	0.037319	0.005848	0.298694	0.019827
5	0.009369	99.63778	0.037358	0.005888	0.298882	0.020092
6	0.009369	99.63776	0.037358	0.005892	0.298895	0.020095
7	0.009369	99.63776	0.037358	0.005892	0.298896	0.020097
8	0.009369	99.63776	0.037358	0.005892	0.298897	0.020097
9	0.009369	99.63776	0.037358	0.005892	0.298897	0.020097
10	0.009369	99.63776	0.037358	0.005892	0.298897	0.020097
Variance decomposition of RTEX:
1	0.003458	0.019082	99.98092	0.000000	0.000000	0.000000
2	0.003611	0.392754	91.75169	3.076358	4.337821	0.441381
3	0.003624	0.741652	91.12217	3.134526	4.551238	0.450411
4	0.003624	0.750104	91.10305	3.141486	4.551376	0.453987
5	0.003624	0.750196	91.10075	3.141845	4.551427	0.455784
6	0.003624	0.750220	91.10064	3.141891	4.551463	0.455784
7	0.003624	0.750221	91.10063	3.141891	4.551462	0.455793
8	0.003624	0.750221	91.10063	3.141891	4.551463	0.455793
9	0.003624	0.750221	91.10063	3.141891	4.551463	0.455793
10	0.003624	0.750221	91.10063	3.141891	4.551463	0.455793
Variance decomposition of RTNIF:
1	0.016384	0.001266	3.696235	96.30250	0.000000	0.000000
2	0.016777	0.014830	3.611957	92.02810	4.081364	0.263751
3	0.016816	0.289358	3.634490	91.67576	4.135667	0.264728
4	0.016820	0.290092	3.634872	91.62944	4.173364	0.272236
5	0.016821	0.290086	3.634940	91.62716	4.175581	0.272230
6	0.016821	0.290085	3.634925	91.62679	4.175679	0.272523
7	0.016821	0.290086	3.634924	91.62674	4.175731	0.272524
8	0.016821	0.290086	3.634925	91.62673	4.175731	0.272527
9	0.016821	0.290086	3.634925	91.62673	4.175732	0.272527
10	0.016821	0.290086	3.634925	91.62673	4.175732	0.272527
Variance decomposition of RTSP:
1	0.013115	0.475821	1.640269	2.573833	95.31008	0.000000
2	0.013167	0.490721	1.634347	2.579482	95.19520	0.100245
3	0.013197	0.491502	1.628829	2.575047	94.94884	0.355778
4	0.013199	0.492356	1.628700	2.576586	94.92905	0.373314
5	0.013200	0.492345	1.628905	2.576603	94.92739	0.374756
6	0.013200	0.492359	1.628948	2.576591	94.92734	0.374761
7	0.013200	0.492360	1.628951	2.576590	94.92732	0.374783
8	0.013200	0.492361	1.628951	2.576590	94.92732	0.374783
9	0.013200	0.492361	1.628951	2.576590	94.92732	0.374783
10	0.013200	0.492361	1.628951	2.576590	94.92732	0.374783
Variance decomposition of RTNIKKEI:
1	0.013686	0.012393	2.252465	3.018508	1.677935	93.03870
2	0.015163	0.264872	2.049805	3.375999	17.04221	77.26711
3	0.015192	0.276741	2.159313	3.366026	17.00100	77.19692
4	0.015203	0.278687	2.162337	3.361220	17.09553	77.10223
5	0.015204	0.279555	2.163113	3.361000	17.09799	77.09834
6	0.015204	0.279553	2.163078	3.360948	17.09879	77.09763
7	0.015204	0.279561	2.163090	3.360943	17.09892	77.09749
8	0.015204	0.279561	2.163090	3.360943	17.09892	77.09749
9	0.015204	0.279561	2.163090	3.360943	17.09892	77.09749
10	0.015204	0.279561	2.163090	3.360943	17.09892	77.09749

Source: Authors’ own calculations.

Note: Ordering: RTG > RTEX > RTNIF > RTSP > RTNIKKEI.

The impulse responses of returns in each variable to shocks in all the variables under study are presented in Figure 1. From Figure 1 it is found that all the returns in the study are mostly autoregressive but effective for only two lags supporting the result of VAR estimates. When we concentrate on impulse response of returns in Nifty to one standard deviation innovations in all the endogenous variables, the interdependence among the variables representing different financial markets is evident from Figure 1.

When we introduce changes in FII trade and CMR (of course, with different study periods as noted earlier) in our study regarding market interdependence, from the respective estimated results [results are not shown here to save space] of multivariate VAR analysis, Granger causality test, variance decomposition and impulse response function we, in general, observe the evidence of significant interdependence between domestic stock market and different other financial markets in India and abroad.

Figure 1.

Source: Authors’ own calculations.

Table 5 presents the results of the DCC-MV-TARCH (1, 1) model estimation with gold bullion, foreign exchange rate and Nifty. Since in this study we are interested in examining volatility spillovers from and to the domestic stock market only, the results related to domestic stock market are reported here. Here i, j = 1, 2, 3, where 1 represents gold bullion, 2 represents exchange rate and 3 represents Nifty. The values of the coefficients _i,j in the mean equation show that each of the three domestic markets are by and large autoregressive, though only for the foreign exchange market _2,3 is found to be statistically significant which indicates that there is influence of the return of the stock market in the previous period on the current period return of the foreign exchange market. It is observed in the variance equation that b_i < 1 for all the three markets indicating that variances are finite and volatilities are persistent in nature. The scalar parameters ‘’ and ‘’ are found to be significantly positive and less than one ( +  = 0.9948) satisfying the condition of positive definiteness of the time dependent conditional correlation matrix t. It can also be seen from Table 5 that among the parameters a_ij for i ≠ j, only a₃₂ is statistically significant (at 5% level) and coupled with it the significant negative value of d₂ (significant at 1% level) imply that negative residuals (bad news) in foreign exchange market has lesser impact on the volatility of the stock market compared to the effects of the positive residuals, that is, there is asymmetric volatility spillover from foreign exchange market to the stock market. There is no evidence of significant spillover from the gold bullion market and the stock market to other markets.

Table 5.

Maximum Likelihood Estimate of DCC-MV-TARCH (1, 1) Model for Gold Bullion, Foreign Exchange and Domestic Stock Market

Variable	Coefficient	Standard Error	T-statistic	Significance
Parameters of mean equation^?
q_1,0	2.0005e-004***	1.1929e-004	1.67690	0.09356184
q_1,1	0.0460*	0.0174	2.64100	0.00826618
q_1,2	0.0664	0.0417	1.59089	0.11163496
q_1,3	3.3814e-003	7.4635e-003	0.45306	0.65050564
q_2,0	1.8947e-007	2.1941e-005	0.00864	0.99311004
q_2,1	2.8033e-003	2.6414e-003	1.06130	0.28855258
q_2,2	-0.0377***	0.0196	-1.92192	0.05461572
q_2,3	-9.1427e-003*	1.3982e-003	-6.53900	0.00000000
q_3,0	5.7742e-004*	2.2093e-004	2.61361	0.00895925
q_3,1	0.0243	0.0262	0.92598	0.35445495
q_3,2	0.0462	0.0697	0.66348	0.50702498
q_3,3	0.0539*	0.0183	2.94404	0.00323961
Parameters of Variance Equation^??
w₁₀	1.2571e-006*	2.1321e-007	5.89579	0.00000000
w₂₀	1.1334e-007*	1.1827e-008	9.58358	0.00000000
w₃₀	7.2982e-006*	1.0666e-006	6.84252	0.00000000
a₁₁	0.1290*	0.0145	8.90355	0.00000000
a₁₂	5.7372e-003	0.0214	0.26753	0.78906438
a₁₃	3.8499e-003	4.6382e-003	0.83004	0.40651602
a₂₁	-7.3496e-003	4.8808e-003	-1.50582	0.13211452
a₂₂	0.4794*	0.0326	14.71962	0.00000000
a₂₃	1.8949e-003	1.5156e-003	1.25021	0.21122369
a₃₁	2.0964e-003	0.0160	0.13116	0.89564553
a₃₂	0.0934**	0.0402	2.32042	0.02031818
a₃₃	0.0514*	8.6833e-003	5.91445	0.00000000
b₁	0.9023*	9.9759e-003	90.44525	0.00000000
b₂	0.6905*	0.0137	50.33074	0.00000000
b₃	0.8741*	0.0101	86.63173	0.00000000
d₁	-0.0851*	0.0136	-6.23508	0.00000000
d₂	-0.1128*	0.0330	-3.41795	0.00063095
d₃	0.1125*	0.0167	6.73863	0.00000000
Parameters of DCC^???
a	0.0150*	5.1744e-003	2.89957	0.00373671
β	0.9798*	8.2653e-003	118.54137	0.00000000
Log likelihood = 43438.1740

Source: Authors’ own calculations.

Notes: 1 represents bullion market, 2 represents foreign exchange market and 3 represents Nifty.

† Mean equation: $R_{i, t} = θ_{i,0} + \sum_{j} θ_{i, j} R_{j, t - 1} {+ε}_{i, t} ε_{i, t} / ψ_{t - 1} ~ N (0, H_{i i, t}) .$

‡ Variance equation: $H_{i i, t} = ω_{i 0} + \sum_{j} a_{i j} ε_{j, t - 1}^{2} + b_{i} H_{i i, t - 1} + d_{j} ε_{j, t - 1}^{2} I_{ε \leq 0} {(ε}_{j, t - 1})$ and

†‡ H_ij,t = D_tR_tD_t, where D_t = $diag(\sqrt{h_{11, t}}, \sqrt{h_{22, t}}, \sqrt{h_{33, t}})$ and $R_{t} =diag (s_{11, t}^{- 1/2}, s_{22, t}^{- 1/2}, s_{33, t}^{- 1/2})$ $S_{t} diag(s_{11, t}^{- 1/2}, s_{22, t}^{- 1/2}, s_{33, t}^{- 1/2})$ , where $S_{t} =(1 - α - β) \bar{S} + α u_{t - 1} u_{t - 1}^{} /+ β S_{t - 1}$

*, ** and *** indicate significance of the parameter at 1%, 5% and 10% levels, respectively.

While examining the presence of asymmetric volatility spillover in DCC-MV-TARCH (1, 1) framework between Nifty, gold bullion, foreign exchange rate and CMR together [the results are not shown here to save space] for different study period, both way volatility spillovers between the stock and foreign exchange markets are observed though the volatility spillover is found to be asymmetric one only from the stock market to the foreign exchange market. We also observe significant asymmetric volatility spillover from the stock market to the bullion market but no significant spillover is observed between the stock market and the money market.

When the DCC-MV-TARCH (1, 1) model is estimated with gold bullion, foreign exchange, stock market and daily gross volume of FII trade (the results are not shown here to economise space) for different study period, as already mentioned, we find evidence of significant asymmetric volatility spillover from the domestic stock market return to change in gross volume of FII trade and return in bullion market. Significant volatility spillover from the foreign exchange market to the stock market is again observed here, though it is not found to be asymmetric.

After observing the existence of significant asymmetric volatility spillover between the domestic stock market and the foreign exchange market, now we also want to examine the asymmetric volatility spillover between the domestic stock market and global stock markets comprising a regional stock market represented by Nikkei and rest of the world stock market represented by S&P 500 along with the foreign exchange market. Here i, j = 1, 2, 3, 4 where 1 represents Nifty, 2 represents Nikkei, 3 represents S&P 500 and 4 represents exchange rate. The DCC-MV-TARCH (1, 1) model estimation for the global and domestic stock markets and the foreign exchange market together is done using Berndt–Hall–Hall–Hausman (BHHH) algorithm. The results of this estimation are presented in Table 6. We find significant a₁₂ and a₂₁ along with significantly positive d₁ and d₂ here which imply the existence of both way significant asymmetric volatility spillovers between the domestic and Asian stock markets. Significant a₁₃ and a₁₄ along with significantly positive d₃ and significant negative d₄ in the estimated result indicate the presence of asymmetric volatility spillovers from the world stock and foreign exchange markets to the domestic stock market. Thus, while examining the volatility spillover relation among the domestic, Asian and world stock markets along with the foreign exchange market both way significant asymmetric volatility spillovers between the domestic stock market and the Asian stock market is evidenced and there are also evidences of significant asymmetric volatility spillovers from the world stock market and the foreign exchange market to the domestic stock market.

Table 6.

Maximum Likelihood Estimate of DCC-MV-TARCH (1, 1) Model for Volatility Spillover Across Domestic Stock Market, Asian Stock Market, World Stock Market and Foreign Exchange Market

Variable	Coefficient	Standard Error	T-statistic	Significance
Parameters of mean equation^?
q_1,0	5.4354e-004**	2.1110e-004	2.57477	0.01003063
q_1,1	0.0440*	0.0168	2.62188	0.00874450
q_1,2	-0.0369**	0.0150	-2.45876	0.01394172
q_1,3	0.2190*	0.0170	12.90782	0.00000000
q_1,4	0.0795	0.0617	1.28829	0.19764388
q_2,0	-2.0838e-004	1.8102e-004	-1.15111	0.24968726
q_2,1	0.0334*	0.0110	3.03071	0.00243983
q_2,2	-0.0688*	0.0162	-4.24635	0.00002173
q_2,3	0.4279*	0.0142	30.20090	0.00000000
q_2,4	0.0200	0.0534	0.37451	0.70802802
q_3,0	1.8306e-004	1.5190e-004	1.20511	0.22815969
q_3,1	6.0515e-003	8.6994e-003	0.69562	0.48666664
q_3,2	-4.1034e-003	0.0108	-0.38036	0.70367598
q_3,3	-0.0571*	0.0178	-3.20038	0.00137244
q_3,4	0.0507	0.0469	1.08106	0.27967003
q_4,0	-2.0301e-006	1.9267e-005	-0.10537	0.91608604
q_4,1	-0.0102*	5.9594e-004	-17.06761	0.00000000
q_4,2	2.6831e-003**	1.1532e-003	2.32657	0.01998831
q_4,3	-8.0930e-003*	1.1392e-003	-7.10428	0.00000000
q_4,4	-0.0415**	0.0169	-2.45883	0.01393905
Parameters of Variance Equation ^??
w₁₀	7.1628e-006*	7.4667e-007	9.59296	0.00000000
w₂₀	4.0485e-006*	5.3131e-007	7.61977	0.00000000
w₃₀	2.0994e-006*	2.1086e-007	9.95681	0.00000000
w₄₀	9.1659e-008*	6.5795e-009	13.93102	0.00000000
a₁₁	0.0498*	6.8984e-003	7.21436	0.00000000
a₁₂	-0.0469*	8.4497e-003	-5.55316	0.00000003
a₁₃	0.0344*	9.1758e-003	3.74611	0.00017960
a₁₄	0.1191*	0.0370	3.22109	0.00127702
a₂₁	0.0147**	6.2145e-003	2.36853	0.01785911
a₂₂	0.0281*	7.0555e-003	3.98342	0.00006793
a₂₃	0.0131***	6.7831e-003	1.93376	0.05314241
a₂₄	0.0154	0.0258	0.59832	0.54962913
a₃₁	1.2312e-003	3.6229e-003	0.33984	0.73397337
a₃₂	-0.0152**	5.9111e-003	-2.57441	0.01004111
a₃₃	-0.0150*	5.6233e-003	-2.66031	0.00780688
a₃₄	0.0205	0.0206	0.99864	0.31797032
a₄₁	3.0912e-004	7.0190e-004	0.44040	0.65964458
a₄₂	-2.0858e-003***	1.1556e-003	-1.80493	0.07108608
a₄₃	0.0118*	2.0055e-003	5.85959	0.00000000
a₄₄	0.4973*	0.0172	28.84107	0.00000000
b₁	0.8792*	6.7586e-003	130.08791	0.00000000
b₂	0.8938*	6.2860e-003	142.19352	0.00000000
b₃	0.9218*	5.9141e-003	155.86060	0.00000000
b₄	0.6876*	5.9124e-003	116.29078	0.00000000
d₁	0.1108*	0.0112	9.92689	0.00000000
d₂	0.1043*	0.0111	9.35252	0.00000000
d₃	0.1608*	9.5625e-003	16.81180	0.00000000
d₄	-0.1014*	0.0214	-4.73570	0.00000218
Parameters of DCC^???
a	3.6721e-003*	6.2539e-004	5.87162	0.00000000
β	0.9960*	7.1662e-004	1389.91733	0.00000000
Log likelihood 54438.6562

Source: Authors’ own calculations.

Notes: 1 represents domestic stock market, 2 represents Asian stock market, 3 represents World stock market and 4 represents foreign exchange market.

† Mean equation: $R_{i, t} = θ_{i,0} + \sum_{j} θ_{i, j} R_{j, t - 1} {+ε}_{i, t} ε_{i, t} / ψ_{t - 1} ~ N (0, H_{i i, t});$

‡ Variance equation: $H_{i i, t} = ω_{i 0} + \sum_{j} a_{i j} ε_{j, t - 1}^{2} + b_{i} H_{i i, t - 1} + d_{j} ε_{j, t - 1}^{2} I_{ε \leq 0} {(ε}_{j, t - 1})$ and

*, ** and ***) indicate significance of the parameter at 1%, 5% and 10% levels, respectively.

8. Concluding Remarks

This article modestly tries to examine interdependence between Indian stock market and different other components of domestic financial system, namely, foreign exchange market, bullion market, money market and also gross volume of FII trade and foreign stock markets comprising a regional one (represented by Nikkei of Japan) and other for the rest of the world (represented by S&P 500 of the USA). Attempts are also made to examine asymmetric volatility spillover first, between the Indian stock market and other domestic financial markets and second between the Indian stock market and global stock markets represented by Nikkei and S&P 500 along with the foreign exchange market. To measure linear interdependence among multiple time series of financial markets multivariate VAR analysis, Granger causality test, impulse response function and variance decomposition techniques are used. DCC-MV-TARCH (1, 1) model is applied for estimating the volatility spillover relation between the aforementioned markets considering daily data for a relatively longer period of time from 1 April 1996 to 31 March 2012. The results of multivariate VAR analysis, Granger causality test, variance decomposition and impulse response function establish significant interdependence between domestic stock market and different other financial markets in India and abroad. The results of DCC-MV-TARCH (1, 1) model estimation show significant asymmetric volatility spillover between the domestic stock market and the foreign exchange market and also from the domestic stock market to bullion market and changes in gross volume of FII trade. We also find both way asymmetric volatility spillovers between the domestic stock market and the Asian stock market whereas it is found to be one way from the world stock market to the domestic stock market. The results do not show any evidence of volatility spillover between the domestic stock market and the money market.

The findings of the study have much practical significance. For instance, as the volatility of the US stock market is found to be spilled over to the Indian stock market significantly in our study, the Indian regulators in response to any US event (say, insolvency of Lehman Brothers) must be watchful and ready to take appropriate steps to lessen its volatility enhancing impact. The findings on volatility transmission among the financial markets may also provide international portfolio managers, speculators as well as hedgers in protecting their interest through enhanced informational efficiency in markets which are integrated with their spillover effects.

Nevertheless, the conclusions of the study are based on analysis of data of select domestic and foreign financial markets and therefore the results may vary for other set of markets. Moreover, the study has to depend on secondary sources of official data whose inherent limitations cannot be avoided. There is further scope of research in comparing the volatility spillovers among the domestic and foreign financial markets prior and following the global financial meltdown of 2007–2008 using high frequency intraday data instead of daily data.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

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