_{1}

The paper examines the spillover effects of return volatility among stock market index, foreign exchange market and WTI crude oil market across five emerging nations. Here a Trivariate Diagonal BEKK-GARCH model is used to estimate the time-varying conditional variance and to test the own-volatility spillover effects of returns among the three underlying variables. We find that significant own volatility spillover exists in the WTI returns followed by that of stock returns and forex returns. Further, fluctuations in WTI returns exert considerable influence over the stock market volatilities. The lagged variance of the variables as well as their lagged squared residuals from the mean equation has a positive and significant impact on the current volatility in most cases. The findings of the study are of pertinent importance to financiers, economists, investors and policymakers.

A flourishing stock market attracts capital inflows from foreign investors leading to an increase in the demand for a country’s domestic currency. The converse would happen in case of decreasing stock prices where the shareholders/investors try to sell off their stocks so as to evade further loss. As a result, upward and downward movement of stock prices would reflect itself through appreciation and depreciation in foreign exchange rates. However, appreciation in the domestic currency inversely affects the national stock market for an export dominant country while it positively affects the national stock market for an import dominant country.

Oil import/export constitutes a significant portion of the demand/supply for dollar in a country’s foreign exchange market. This contributes to the appreciation or depreciation of domestic currencies against US dollar. Moreover, exchange rates and oil prices are anticipated to have a positive and statistically significant impact on stock markets. However, some studies have also shown oil price changes to have no significant influence over stock market returns [

Understanding the influence of oil price changes/shocks on the financial as well as foreign exchange markets, particularly in the case of emerging economies would be of paramount importance as these economies are inclined to exert a greater influence over the global economy in the forthcoming years. Additionally, with the liberalization of the capital accounts and the integration of capital markets, investors’ world over would be anticipated to diversify their portfolios across international currencies as well as national stock markets. Further, the association between oil price fluctuations and the corresponding movements in the stock markets and foreign exchange rates has attracted the attention of investors and researchers alike over the past few decades, as crude oil prices exhibit exceptional volatility, leading to an increasing uncertainty in the whole economy and particularly in the financial and foreign exchange markets.

If the price returns and their volatilities thereof of these three variables, namely, WTI crude oil returns, corresponding stock market as well as forex returns are dynamically interrelated, then a random shock in the price return of any one of these variables will soon get reflected in the price returns and the return volatility of the other two variables as a result of an underlying relationship called as “spillover effect”. In most cases, the fluctuations in the prices of these macroeconomic variables are determined by the domestic as well as the global market forces leading to randomness in the underlying returns. This randomness in returns is popularly understood through the returns volatility which is otherwise known as returns with heteroscedastic variance. This volatility induced through a random shock may then persist over a longer period of time resulting in volatility clustering; a phenomenon wherein, a period of high returns is consequently followed by subsequent periods of higher returns and a period of low returns is consequently followed by subsequent periods of lower returns. With increasing global integration and unrestricted flow of capital across borders, shocks in financial markets tend to spread across other financial markets within and across national boundaries.

Since randomness is a natural outcome for a financial time series data, volatility of such series does not remain constant over time. Modeling this heteroscedastic variance required theories on dynamic volatility and this gap was duly filled by the ARCH (Autoregressive Conditional Heteroscedasticity) family of models. Subsequently, the ARCH/GARCH models were extensively used in volatility spillover studies. In our study, we try to analyze the own as well as cross volatility contagion effects across stock returns, crude oil returns and forex returns for five emerging economies, namely, Brazil, Indonesia, Malaysia, Pakistan and South Korea. We use the Diagonal BEKK GARCH model to assess the volatility contagion effects between the three underlying markets.

The economies that possess some characteristics of a developed market yet do not meet all the standards of a developed economy are called emerging economies. Such economies invest more on productive capacity and by way of which achieve rapid growth. With an ongoing strive to become more and more advanced, investments in emerging economies comes with higher return potential. Nevertheless, these economies also assume much higher risk because of the high volatilities in their financial markets.

The remaining part of the paper is organized as follows. Section two briefly discusses the literature existing in the area of study and highlights the gap which the present study attempts to fill. Section 3 describes the data that is employed in the study which is then followed by a subsequent section that gives a concise description of the econometric models used in meeting the study objectives. Section 5 gives the detailed analysis of the empirical exercise and Section 6 concludes the paper.

Wang M.L. et al. [

The literature documents a good number of research papers that study the nexus between various macro variables against the stock market returns, especially that of developed countries. There are, however, very few studies on the developing or the emerging economies. Adebiyi et al. [

However, Bartov and Bodnar [

Ma and Kao [

Though there are several research studies that explore the relationship between stock returns, foreign exchange returns, and oil price returns, most of the studies pertain to be bivariate in nature. In the modern oil dependent globalized economy, it is imperative to study the dynamic interaction and cross volatility spillover between the three markets in a trivariate fashion and our study aims to bridge this gap. Contrary to the common usage of low-frequency monthly data, the study employs a high-frequency daily time series data. Some of the similar studies are available in literature but by large, they pertain to that of the developed countries alone. The study also complements and enhances the existing literature on cross volatility spillovers between macroeconomic variables by comparing the interaction between the underlying variables across five emerging economies.

The present study employs five-day week, daily time series data on stock returns, forex returns and WTI crude oil returns for five emerging economies. The countries included in the analysis are Brazil, Indonesia, Malaysia, Pakistan, and South Korea. We choose a benchmark stock market index (closing) based on total market capitalization as a proxy for the market performance of a particular county. The data include daily closing prices of 5 representative indexes: Brazil (BOVESPA), Indonesia (JKSE), Malaysia (KLCI), Pakistan (KSE), and South Korea (KOSPI). Further, foreign exchange rates for five emerging economies are also obtained along with the benchmark oil market index i.e. West Texas Intermediate crude oil rates (WTI), all designated in dollar terms.

The data is collected for a period of five years from January 01 2010 through January 01 2015. The data for the oil price (WTI) is obtained from the database of International Financial Statistics (International Monetary Fund). The exchange rate refers to the number of units of local currency per one USD. The data for the exchange rate are compiled from the OANDA pages. The stock market index data of respective exchanges are obtained from yahoo finance website.

The data used is a financial time series data which has the inherent problem of being non-stationary in its level form leading to spurious regression if not made stationary. Hence, the daily return of all series was computed as logarithmic differences of successive observations viz. Rt = (ln Pt - ln Pt − 1) × 100. Then we conducted stationarity tests using ADF (Augmented Dickey-Fuller test) and Phillip Perron (PP) unit root tests to examine the time series properties of the model variables. With that, the data was found to satisfy the condition of stationarity.

The Diagonal BEKK GARCH model is employed in order to assess the volatility

Name of the variable | Symbol | Proxy used |
---|---|---|

Crude Oil Prices | WTI | West Texas Intermediate crude oil rates |

United States Dollar | USD | |

Brazilian Real | BRL | |

Indonesian Rupiah | IDR | |

Malaysian Rupee | MYR | |

Pakistan Rupee | PKR | |

South Korean Won | KRW | |

Brazil Stock Market | BOVESPA | Bolsa de Valores do Estado de São Paulo |

Indonesia Stock Market | JKSE | Jakarta Stock Exchange |

Malaysia Stock Market | KLCI | Kuala Lumpur Composite Index |

Pakistan Stock Market | KSE | Karachi Stock Exchange |

South Korea Stock Market | KOSPI | Korea Stock Exchange Composite Index |

contagion effects between the three underlying markets for each of the five economies. Diagonal BEKK is a multivariate GARCH model that allows for the explicit and dynamic parameterization of conditional covariances (Engle and Kroner, 1995). By restricting the parameter matrices to be diagonal, the model significantly reduces the number of parameters estimated and by ensuring that the conditional covariance matrix is always positive definite, it also effectively overcomes the difficulty with the alternative VECH model. The general Diagonal BEKK Equation is given as:

H t = Ω ′ Ω + A ′ ( u t − 1 u ′ t − 1 ) A + B ′ H t − 1 B

where, H t is an N ´ N conditional variance-covariance matrix, Ω is an upper triangular matrix of parameters, u t − 1 is an N ´ 1 disturbance vector, and, A and B are N ´ N diagonal parameter matrices. A trivariate Diagonal BEKK model can be described as follows.

The Ω ′ Ω matrix (3 × 3) equals:

Ω ′ Ω = [ ω 11 0 0 ω 12 ω 22 0 ω 13 ω 23 Ω ω 33 ] [ ω 11 ω 12 ω 13 0 ω 22 ω 23 0 0 ω 33 ] = [ ω 11 2 ω 11 ω 12 ω 11 ω 13 ω 11 ω 12 ω 12 2 ω 22 2 ω 12 ω 13 + ω 22 ω 23 ω 11 ω 13 ω 12 ω 13 + ω 22 ω 23 ω 13 2 ω 23 2 ω 33 ]

The H t matrix can be represented as:

H t = [ h 11 , t h 12 , t h 13 , t h 21 , t h 22 , t h 23 , t h 31 , t h 32 , t h 33 , t ]

Now, the BEKK Garch equation can be represented as:

[ h 11 , t h 12 , t h 13 , t h 21 , t h 22 , t h 23 , t h 31 , t h 32 , t h 33 , t ] = [ ω 11 2 ω 11 ω 12 ω 11 ω 13 ω 11 ω 12 ω 12 2 ω 22 2 ω 12 ω 13 + ω 22 ω 23 ω 11 ω 13 ω 12 ω 13 + ω 22 ω 23 ω 13 2 ω 23 2 ω 33 ] + [ α 11 0 0 0 α 22 0 0 0 α 33 ] ( [ u 1 , t − 1 u 2 , t − 1 u 3 , t − 1 ] [ u 1 , t − 1 u 2 , t − 1 u 3 , t − 1 ] ′ ) [ α 11 0 0 0 α 22 0 0 0 α 33 ] + [ β 11 0 0 0 β 22 0 0 0 β 33 ] [ h 11 , t − 1 h 12 , t − 1 h 13 , t − 1 h 21 , t − 1 h 22 , t − 1 h 23 , t − 1 h 31 , t − 1 h 32 , t − 1 h 33 , t − 1 ] [ β 11 0 0 0 β 22 0 0 0 β 33 ]

Thus, each conditional and covariance equation can be represented as:

h 11 , t = ω 11 2 + α 11 2 u 1 , t − 1 2 + β 11 2 h 11 , t − 1

h 12 , t = ω 11 ω 12 + α 11 α 22 u 1 , t − 1 u 2 , t − 1 + β 11 β 22 h 12 , t − 1

h 13 , t = ω 11 ω 13 + α 11 α 33 u 1 , t − 1 u 3 , t − 1 + β 11 β 33 h 13 , t − 1

h 22 , t = ω 12 2 ω 22 2 + α 22 2 u 2 , t − 1 2 + β 22 2 h 22 , t − 1

h 23 , t = ω 12 ω 13 + ω 22 ω 23 + α 22 α 33 u 2 , t − 1 u 3 , t − 1 + β 22 β 33 h 23 , t − 1

h 33 , t = ω 13 2 ω 23 2 ω 33 + α 33 2 u 3 , t − 1 2 + β 33 2 h 33 , t − 1

Under the assumption of conditional normality, the parameters of the multivariate GARCH models of any of the above specifications can be estimated by maximizing the log-likelihood function:

r t = μ + ε t where ε t ~ N ( 0 , H t )

L = − 1 2 ∑ t = 1 T ( log | H t | + ε ′ t H t − 1 ε t )

Our study employs a Trivariate Diagonal BEKK Specification. The conditional mean and variance/covariance are estimated simultaneously with a system of three equations.

From

As can be observed in

Coefficient/SR | Brazil | Indonesia | Malaysia | Pakistan | S Korea |
---|---|---|---|---|---|

Mean | −0.038 | 0.078 | 0.036 | 0.135 | 0.014 |

Median | −0.049 | 0.163 | 0.065 | 0.121 | 0.020 |

Maximum | 5.199 | 6.783 | 3.322 | 5.212 | 4.900 |

Minimum | −8.431 | −9.300 | −4.326 | −5.038 | −6.420 |

Std. Dev. | 1.612 | 1.400 | 0.691 | 1.086 | 1.207 |

Skewness | −0.198 | −1.051 | −0.485 | −0.025 | −0.384 |

Kurtosis | 4.869 | 10.907 | 7.575 | 5.824 | 5.919 |

Jarque−Bera | 133.26 | 2443.43 | 798.25 | 291.17 | 332.59 |

Probability | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

Observation | 1284 | 1284 | 1284 | 1284 | 1284 |

Coefficient/FX | Brazil | Indonesia | Malaysia | Pakistan | S Korea | WTI |
---|---|---|---|---|---|---|

Mean | 0.051 | 0.034 | 0.004 | 0.020 | −0.002 | −0.048 |

Median | 0.050 | 0.047 | 0.010 | 0.021 | −0.031 | 0.014 |

Maximum | 3.754 | 2.761 | 3.406 | 1.647 | 6.990 | 9.001 |

Minimum | −4.695 | −4.086 | −3.410 | −1.96 | −4.240 | −11.60 |

Std. Dev. | 0.843 | 0.547 | 0.501 | 0.367 | 0.639 | 1.972 |

Skewness | 0.037 | −0.634 | −0.111 | −0.37 | 1.465 | −0.471 |

Kurtosis | 6.642 | 12.390 | 9.842 | 6.176 | 22.797 | 7.088 |

Jarque-Bera | 484.302 | 3276.845 | 1710 | 388 | 14618 | 642.490 |

Probability | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

Observations | 1284 | 1284 | 1284 | 1284 | 1284 | 1284 |

probability for extreme values.

Jarque-Bera statistic tests the null hypothesis that data follow a normal distribution. By using probability values of Jarque-Bera statistics, the null hypothesis is rejected for all variables at 1% level of significance. This shows the non-normal distribution of the exchange rate returns, stock returns as well as WTI returns indicating randomness and inefficiency of the market

In this study, the Augmented Dickey-Fuller (ADF) and Phillip Perron (PP) unit root tests were employed to test for the time series properties of model variables. The null hypothesis is that the variable under investigation has a unit root against the alternative that it does not. The choice of lag length was based on Akaike and Schwartz-Bayesian information criteria. The decision rule is to reject the null hypothesis if the ADF and PP statistic value exceeds the critical value at a chosen level of significance. The ADF unit root test is performed with all three specifications namely, with intercept, with intercept and trend and none. Results of the model with intercept are presented in

The results of

Stock returns | Exchange rates | |||
---|---|---|---|---|

At Level | Ln Returns | At Level | Ln Returns | |

Brazil | −2.207 | −29.838* | 0.646 | −26.798* |

(0.204) | (0.000) | (0.990) | (0.000) | |

Indonesia | −1.522 | −19.802* | 0.786 | −30.286* |

(0.522) | (0.000) | (0.993) | (0.000) | |

Malaysia | −1.633 | −26.315* | −1.429 | −28.353* |

(0.465) | (0.000) | (0.569) | (0.000) | |

Pakistan | 1.251 | −27.105* | −0.781 | −33.452* |

(0.998) | (0.000) | (0.823) | (0.000) | |

S Korea | 0.134 | −28.475* | −2.288 | −21.97* |

(0.968) | (0.000) | (0.176) | (0.000) | |

WTI | At Level | −1.232 | Ln Returns | −19.182* |

(0.662) | (0.000) |

The market returns are influenced by multiple factors such as shocks and turbulence in markets, forces of demand and supply, socio-economic and political state of the country etc. The natural outcome of this is the randomness in returns. Such randomness in returns is called as volatility or returns with

WTI | BRL | IDR | MYR | PKR | KRW | BOVESPA | JKSE | KLCI | KSE | KOSPI | |
---|---|---|---|---|---|---|---|---|---|---|---|

WTI | 1 | −0.075 | −0.049 | −0.039 | 0.031 | −0.001 | 0.067 | 0.152 | 0.138 | 0.007 | 0.202 |

BRL | 1 | 0.22 | 0.489 | 0.071 | 0.371 | −0.261 | −0.236 | −0.309 | −0.113 | −0.283 | |

IDR | 1 | 0.383 | 0.059 | 0.333 | −0.159 | −0.135 | −0.165 | −0.029 | −0.09 | ||

MYR | 1 | 0.016 | 0.658 | −0.282 | −0.171 | −0.277 | −0.098 | −0.205 | |||

PKR | 1 | 0.032 | 0.033 | −0.07 | 0.022 | −0.026 | 0.002 | ||||

KRW | 1 | −0.281 | −0.188 | −0.299 | −0.123 | −0.24 | |||||

BOVESPA | 1 | 0.347 | 0.365 | 0.144 | 0.428 | ||||||

JKSE | 1 | 0.517 | 0.19 | 0.521 | |||||||

KLCI | 1 | 0.213 | 0.495 | ||||||||

KSE | 1 | 0.193 | |||||||||

KOSPI | 1 |

heteroscedastic variance. Now, the volatility may persist over a period of time (i.e. a period of high returns are followed by subsequent periods of higher returns and a period of low returns are followed by subsequent periods of lower returns), resulting in volatility clustering and may spread across various financial markets resulting in what is called as volatility spillover. Indeed, if the clusters of volatility are removed from the data, the returns would be approximately log-normal.

The plots of market volatility can act like an electrocardiogram, reflecting the pulse of the underlying markets.

Figures A1-A6 show evidence of volatility clustering in returns across all stock markets and international crude oil market. In financial literature, this phenomenon is called ‘time-varying conditional volatility’. The stylized facts of volatility clustering mean that stock market risk and WTI crude oil price risk are not constant over time (at least as measured by volatility) and while their prices, except for a long-term upward trend are not predictable, their volatility is somewhat predictable. It is also observed that when volatility clusters, stock returns are typically, but not always, low or negative (the largest of the extreme negative moves are usually larger on average than the largest extreme positive moves). This is probably because the news events that affect stock market prices are more often bad news rather than good news. Such kind of an inference cannot be made in the case of crude oil returns as large extreme positives moves as well as large extreme negative moves occur simultaneously at almost equal intervals.

Further, just by looking at the Figures A2-A6, we can observe that a positive shock in stock market volatility is preceded by a higher positive shock in WTI returns and a negative shock in stock market volatility is preceded by a higher negative shock in WTI returns. Hence, we can roughly interpret that huge fluctuations/shocks in WTI returns exert considerable influence over the stock markets of all the countries resulting in stock markets responding to such WTI shocks in a similar trend with a small time lag.

As observed in Figures A1-A6, the returns data exhibit volatility clustering, validating the presence of conditional heteroscedasticity in the data. Thus we can introduce Autoregressive Conditional Heteroscedasticity (ARCH) or Generalized Autoregressive Conditional Heteroscedasticity (GARCH) class of models to match and analyze the data series. Here, a trivariate Diagonal BEKK GARCH model is used to estimate the time-varying conditional variance and to test the own-volatility spillover effects of returns of the stock index, the West Texas Intermediate crude oil prices and the bilateral exchange rate between the US dollar and the local currency of each country.

The estimation of a multivariate GARCH model involves the joint estimation of both mean and variance equations. We specify the Diagonal BEKK GARCH model used in the study as stated below:

Mean Equation:

y = m u + l a m b d a ∗ H + r e s

Variance Equation:

H = o m e g a ′ ∗ o m e g a + a l p h a ′ ∗ r e s ( − 1 ) ∗ r e s ( − 1 ) ′ ∗ a l p h a + b e t a ′ ∗ H ( − 1 ) ∗ b e t a

S e r i e s y 1 = S t o c k R e t u r n s

S e r i e s 2 = W T I R e t u r n s

S e r i e s 1 = F o r e x R e t u r n s

The mean equation results are presented in

Brazil | Indonesia | Malaysia | Pakistan | S Korea | |
---|---|---|---|---|---|

Stock Returns | 0.118496 | 0.038691 | 0.140773 | 0.099914 | 0.006898 |

(0.2167) | (0.0006)* | (0.0564) | (0.4895) | (0.8321) | |

WTI Returns | 0.039813 | 0.050932 | 0.166028 | 0.121527 | 0.103896 |

(0.387) | (0.1717) | (0.3074) | (0.2933) | (0.8946) | |

Forex Returns | 0.020874 | 0.161458 | −0.03463 | 1.382328 | 0.078812 |

(0.7881) | (0.0339)** | (0.8967) | (0.0921) | (0.568) |

value of returns for JKSE and IDR is found to be influenced by their own past volatilities. In all the other cases, the volatility fluctuations in the markets do not exert a significant impact on their respective mean returns. That is to say, mean spillover is found not to exist in all financial markets except for the Jakarta Stock Exchange and the Indonesian Rupiah. However, as regards to volatility spillovers, it was observed that the lagged variance of the variables (GARCH effect) as well as their lagged squared residuals from the mean equation (ARCH effect) has a positive and significant impact on the current volatility.

The conditional variance-covariance equations as stated by the Diagonal BEKK specification are as follows.

h 11 , t = ω 11 2 + α 11 2 u 1 , t − 1 2 + β 11 2 h 11 , t − 1

h 12 , t = ω 11 ω 12 + α 11 α 22 u 1 , t − 1 u 2 , t − 1 + β 11 β 22 h 12 , t − 1

h 13 , t = ω 11 ω 13 + α 11 α 33 u 1 , t − 1 u 3 , t − 1 + β 11 β 33 h 13 , t − 1

h 22 , t = ω 12 2 ω 22 2 + α 22 2 u 2 , t − 1 2 + β 22 2 h 22 , t − 1

h 23 , t = ω 12 ω 13 + ω 22 ω 23 + α 22 α 33 u 2 , t − 1 u 3 , t − 1 + β 22 β 33 h 23 , t − 1

h 33 , t = ω 13 2 ω 23 2 ω 33 + α 33 2 u 3 , t − 1 2 + β 33 2 h 33 , t − 1

Based on the equations above, the ARCH and GARCH coefficients are computed and are consolidated in

The results above stands evidence for the presence of strong GARCH effect, while it corroborates the presence of a very weak ARCH effect among the variables. It can be deduced from the equations that there exists a statistically significant co-variation in return volatilities that are dependent more on its lags rather than on past errors. Arch coefficients from

ARCH Coefficient | GARCH Coefficient | ||||||
---|---|---|---|---|---|---|---|

Brazil | Variables | BOVESPA | WTI | BRL | BOVESPA | WTI | BRL |

BOVESPA | 0.0511 | 0.0431 | 0.0668 | 0.8727 | 0.9101 | 0.8764 | |

WTI | 0.0426 | 0.0562 | 0.9374 | 0.9139 | |||

BRL | 0.0871 | 0.8799 | |||||

Indonesia | Variables | JKSE | WTI | IDR | JKSE | WTI | IDR |

JKSE | 0.0974 | 0.0787 | 0.1612 | 0.8838 | 0.9001 | 0.8015 | |

WTI | 0.0426 | 0.1302 | 0.9374 | 0.8162 | |||

IDR | 0.2668 | 0.7268 | |||||

Malaysia | Variables | KLCI | WTI | MYR | KLCI | WTI | MYR |

KLCI | 0.1459 | 0.0539 | 0.0818 | 0.7393 | 0.8325 | 0.7879 | |

WTI | 0.0426 | 0.0302 | 0.9374 | 0.8873 | |||

MYR | 0.0419 | 0.8399 | |||||

Pakistan | Variables | KSE | WTI | PKR | KSE | WTI | PKR |

KSE | 0.0726 | 0.0556 | 0.1005 | 0.8007 | 0.8544 | 0.5412 | |

WTI | 0.0426 | 0.0769 | 0.9374 | 0.5775 | |||

PKR | 0.1390 | 0.3658 | |||||

S Korea | Variables | KOSPI | WTI | KRW | KOSPI | WTI | KRW |

KOSPI | 0.1049 | 0.0176 | 0.1269 | 0.8504 | 0.9055 | 0.8089 | |

WTI | 0.0426 | 0.0213 | 0.9374 | 0.8614 | |||

KRW | 0.1535 | 0.7696 |

(All the alpha and beta coefficients were found to be significant at 1% level of significance. In the table above, the ARCH and GARCH coefficients were computed using the Diagonal BEKK GARCH specifications).

innovations on the current volatility is very small in all the cases. It is interesting to note that among the three underlying markets, the forex returns tend to have the maximum own-volatility spillover effect, followed by the stock returns and the WTI crude returns for all the countries under study except for Malaysia, where KLCI has a larger own volatility spillover while MYR has the least. These coefficients show the volatility persistence for each market in terms of its own past errors.

As for cross-volatility ARCH effects, consistent with the previous observations, the past innovations in the forex returns exert the greatest influence on the current volatility of stock returns followed by that of the WTI. Therefore, the above results suggest that the past innovations in the forex returns have a positive and significant impact on the future volatility in case of their respective stock returns.

Now, the GARCH effect tends to be a very strong factor in determining the future volatilities of all the three variables. As is highly intuitive, WTI returns tend to exhibit extremely high own-volatility GARCH effect with 94 percent of the future variance being determined by the past variance. In other words, WTI exhibits a huge dependence of current volatility on their own one period lagged volatility. Hence, WTI volatility is by and large highly predictable just by looking at the one time period lagged variance. Except for KLCI with 73 percent own-volatility GARCH effect, all the other stock markets show strong evidence of variance spillovers within a range of 80 to 87 percent. However, the own-volatility GARCH effects for forex returns show mixed results with spillovers as high as 88 percent in the case of BRL to as low as 37 percent in the case of PKR.

The cross volatility GARCH effect is highest between WTI and stock markets for all the economies except Malaysia where the highest influence on KLCI is exerted by the MYR. The observations state a strong causal relationship between oil price fluctuations and stock returns. The above observations show that any fluctuations in the international crude prices will soon get reflected in the domestic stock prices for all the countries with an immediate and strong lag effect. The cross volatility GARCH effect is the weakest for the KLCI as the Malaysian stock market is still in its growth phase. It is also interesting to observe that PKR is not affected largely by fluctuations in both KSE and WTI. This is mostly because of the high volatile nature of the PKR along with a less competent stock market and little dependence on oil imports by volume.

Therefore the volatility of each variable does not affect the mean value of their respective returns. However, the lagged variance of the variables as well as their lagged squared residuals from the mean equation has a positive and significant impact on the current volatility. The results of the conditional variance equations depict the presence of significant conditional heteroscedasticity in the return series of stock market and forex market of all five countries. The same holds for the WTI crude oil market as well. Significant own volatility spillover exists in the WTI returns followed by stock returns and forex returns. Past returns in variables have a greater effect on current returns, validating the time-varying co-movement of returns as a leading forecasting factor.

It is of paramount importance to understand the impact of oil price shocks on financial and foreign exchange markets particularly in the case of emerging economies as they are expected to exert a larger influence over the global economy over the coming years. As a result of globalization and liberalization of capital markets, the investors are anticipated to diversify their portfolios across international currencies and national stock markets. Since exchange rate risk and its relationship with the domestic stock market is an important determinant of the overall portfolio risk, this trend is expected to link the forex market and stock market more closely. Such linkages manifest themselves in the form of cross volatility spillovers, over and above the mean returns spillover. At this juncture, the own and cross volatility spillover analysis would help investors in predicting the market movement to a larger precision irrespective of the impact of other macroeconomic variables on the price behavior of the underlying variable. The evidence presented in this paper does indeed bear out such an expectation.

We find that huge fluctuations in WTI returns exert considerable influence over the stock markets. Further, significant own volatility spillover exists in the WTI returns followed by stock returns and forex returns. Past returns in variables have a greater effect on current returns, validating the time-varying co-movement of returns as a leading forecasting factor. The lagged variance of the variables as well as their lagged squared residuals from the mean equation has a positive and significant impact on the current volatility in most cases.

The findings of the study are of great importance to financiers, economists, investors, and policymakers. A proficient understanding of the volatility spillover among crude oil market, stock market and foreign exchange market returns, and subsequently the degree of their integration, would increase the information set available to multinational corporations, policymakers, and international as well as domestic investors for better decision making. This would also help in the pricing of securities, optimizing portfolios as well as in developing hedging strategies. The study would also complement the existing literature on how the behavior of returns and volatility spillover in one economy compares with those of other emerging economies.

Varghese, G. (2018) Within and Cross Volatility Contagion Effects among Stock, Crude and Forex Returns: Empirical Evidence from Five Emerging Economies. Theoretical Economics Letters, 8, 1475-1492. https://doi.org/10.4236/tel.2018.88095