Return and volatility spillovers Vietnamese and some Asian markets

Abstract Purpose - This thesis investigates the interdependence between the Vietnamese stock market and other nine Asian markets in terms of return and volatility spillovers during thre

UNIVERSITY OF ECONOMICS HOCHIMINH CITY

HO CHI MINH CITY, 2012

Acknowledgement

Foremost, I would like to express my sincere gratitude to my advisor Dr Võ Xuân Vinh for the continuous support of my thesis, for his patience, motivation, enthusiasm, and immense knowledge His guidance helped me in all the time of research and writing of this thesis

I would like to thank professors at Faculty of Business Administration and Postgraduate Faculty, University of Economics Ho Chi Minh City for their teaching, their guidance and support during my MBA course

I wish to thank my family for the love, support and constant encouragement I have got over the years

Abstract

Purpose - This thesis investigates the interdependence between the Vietnamese

stock market and other nine Asian markets in terms of return and volatility spillovers during three periods: pre-crisis, crisis and post-crisis

Methodology - Long run and short run integration are examined through

Johansen cointegration and Granger causality test respectively Vector autoregressive model is used to estimate the conditional return spillover among these indices Volatility spillover is studied through BEKK and AR-GARCH Model

Findings - We find evidence of the integration of Vietnamese market with

statically significant correlation, cointegration, return spillover and volatility spillover with other markets The crisis has strong impacts to market interdependence with higher correlation, cointegration and spillovers In the current period, there may be long run benefits from portfolio diversification to Vietnamese stocks

Originality/Value - The thesis points out the return and volatility between

Vietnamese stock market and other nine Asian Markets and suggests potential benefits from diversification

Key words - Return spillover, Volatility spillover, VAR, BEKK, VAR-GARCH,

Cointegration, Granger causality

Contents

Acknowledgement i

Abstract ii

Contents iii

List of Figures v

List of Tables vi

Chapter 1 Introduction 1

1.1 Background 1

1.2 Purpose and scope 1

1.3 Basic definition 3

1.3.1 Stock index 3

1.3.2 Return 3

1.3.3 Volatility 4

1.3.4 Return spillover 4

1.3.5 Volatility spillover 4

1.3.6 Time series 4

1.3.7 Cointegration 5

1.3.8 Granger causality 5

1.4 Research questions 5

1.5 Structure 6

Chapter 2 Literature review 7

Chapter 3 Methodology 12

3.1 Data 12

3.2 The model and methods 12

3.2.1 Introduction 12

3.2.2 Unit root and stationary test 13

3.2.3 Johansen’s cointegration techniques 14

3.2.4 Granger causality analysis 16

3.2.5 VAR Model 18

3.2.6 Bivariate BEKK Model 18

3.2.7 GARCH Model 20

Chapter 4 Data Description, Results and Analysis of Results 22

4.1 Descriptive statistics and correlation matrix 22

4.1.1 Opening and closing time of Indices 22

4.1.2 Descriptive statistics of Indices 23

4.1.3 Descriptive statistics of Indices’ return 24

4.1.4 Correlation matrix 25

4.2 Long-run interdependence 26

4.2.1 Unit root test 26

4.2.2 Johansen’s cointegration 27

4.3 Short-run interdependence 31

4.3.1 Granger causality analysis 31

4.3.2 VAR Model for estimation of return spill over 34

4.4 Volatility spill over 40

4.4.1 BEKK model 40

4.4.2 VAR – GARCH model 43

Chapter 5 Conclusions 49

Figure 51

References 53

List of Figures

Figure 1 Index timings by UTC Time 22Figure 2 Index closing price 51Figure 3 Index return 52

List of Tables

Table 1 Indices and their origination 2

Table 2 Descriptive statistics of Indices in pre-crisis period 23

Table 3 Descriptive statistics of Indices in crisis period 23

Table 4 Descriptive statistics of Indices in post-crisis period 23

Table 5 Descriptive statistics of Indices’ return in pre-crisis period 24

Table 6 Descriptive statistics of Indices’ return in crisis period 24

Table 7 Descriptive statistics of Indices’ return in post-crisis period 24

Table 8 Correlation Matrix between Indices' returns in pre-crisis period 25

Table 9.Correlation Matrix between Indices' returns in crisis period 26

Table 10.Correlation Matrix between Indices’ returns in post-crisis period 26

Table 11 Unit root test result on Indices 27

Table 12 Unit root test results on Indices' return 27

Table 13 Johansen's cointegration test for pre-crisis period 30

Table 14 Johansen's cointegration test for crisis period 30

Table 15.Johansen's cointegration test for post-crisis period 31

Table 16 Granger causality test results for pre-crisis period 33

Table 17 Granger causality test results for crisis period 33

Table 18 Granger causality test results for post-crisis period 34

Table 19 Bivariate VAR Model (VNIndex and other Indices) estimates of model on indices return in pre-crisis period 37

Table 20 Bivariate VAR Model (VNIndex and other Indices) estimates of model on indices return in crisis period 38

Table 21 Bivariate VAR Model (VNIndex and other Indices) estimates of model on indices return in post-crisis period 39

Table 22 Parameters estimates of BEKK model for pre-crisis period 42

Table 23 Parameters estimates of BEKK model for crisis period 42

Table 24 Parameters estimates of BEKK model for post-crisis period 43

Table 25 Volatility spillover estimates of AR(1) GARCH(1,1) model for pre-crisis period 46

Table 26 Volatility spillover estimates of AR(1) GARCH(1,1) model for crisis period 47

Table 27 Volatility spillover estimates of AR(1) GARCH(1,1) model for post-crisis period 48

Chapter 1 Introduction 1.1 Background

Currently, the globalization of domestic market becomes an evident trend The equity markets attract capital not only from domestic but also from international investors who expect to reduce the risk via diversification This trend would reduce the isolation of domestics markets and the markets can react quickly to international news and shocks

The information transmission across market has been widely studied in two different faces First, the long term interdependence and causality among markets are considered as strong signal of information transmission And secondly, the volatility transmission across markets gets more studies these days because it becomes important as a good measure of the risk of internationally diversified portfolio which very helpful in deciding the asset diversification strategy

Vietnamese stock market was formed a decade ago and now attracts valuable investment However, there have been relatively few studies on the linkages of Vietnamese equity market with international markets, especially the Asian markets

1.2 Purpose and scope

This study attempts to investigate interactions in terms of price and volatility spillover amongst Vietnamese equity market and other nine Asian markets (India, Hong Kong, Indonesia, Malaysia, Japan, Philippines, China, Singapore and Taiwan)

The return spillovers are examined with Johansen co-integration (for long term spillovers) and Granger causality test (for short term spillovers) Meanwhile, the bivariate BEKK and AR-GARCH model is used to evaluate the volatility spillovers

Both the return spillovers and volatility spillovers are considered through three periods: the pre-crisis period (from 03rd January 2005to 31st December 2007), the crisis period (from 01st January 2008 to 30th June 2010) and the post-crisis period (from 1st July 2010 to 31st August 2012) The evaluation based on these three periods would indicate the effect of financial crisis to the return and volatility spillovers between Vietnamese stock market and other nine Asian markets

The markets are presented by their Indices as following:

Table 1 Indices and their origination

The reason for selecting these markets is that they represent the developed and emerging economies of Asian stock markets and they have potential effect to Vietnamese stock market Moreover the chosen indices are widely accepted benchmark indices

- Hong Kong and Japan are regarded as one of the mature financial centers

in Asia and play important role in the regional economy with high transaction volume and high influences to other markets

- China is the fastest developing economy in the world and gains stronger position today in financial market; furthermore Vietnam shares same border with China and the trade among Vietnam and China gets large

BSESN BSE Sensex Index India

HIS Hang Seng Index Hong Kong

JKSE Jakarta Composite Index Indonesia

KLSE FTSE Bursa Malaysia Malaysia

Nikkei 225 Nikkei 225 Index Japan

PSEI Philippines Stock Exchange PSEi index Philippines

SSE SSE Composite Index China

STI Straights Times Index Singapore

TWII TSEC weighted index Taiwan

VNIndex Vietnam Index Vietnam

portion of the Vietnamese international trading, so we expect information transmission among China and Vietnam

- Other markets (Indonesia, Malaysia, Philippines and Singapore) are in the same ASEAN (Association of Southeast Asian Nations) organization as Vietnam ASEAN is the ninth largest economy in the world and is growing with more and proven integration between its members

1.3 Basic definition

1.3.1 Stock index

A stock index or stock market index is a method of measuring the value of a section of the stock market It is computed from the prices of selected stocks (sometimes a weighted average) It is a tool used by investors and financial managers to describe the market, and to compare the return on specific investments

1.3.2 Return

Most financial studies involve returns, instead of prices, of assets Campbell et al (1996) give two main reasons for using returns First, for average investors, return of an asset is a complete and scale-free summary of the investment opportunity Second, return series are easier to handle than price series because the former have more attractive statistical properties

There are several definitions of an asset return, and in this thesis, we use the word ‘return’ in means of continuously compounded return

Continuously compounded return

The natural logarithm of the simple gross return of an asset is called the continuously compounded return or log return:

𝑟𝑡 = 𝑙𝑛𝑃𝑃𝑡

𝑡−1 = ln(𝑃𝑡) − ln (𝑃𝑡−1)

where 𝑃𝑡 is the price/index value at time t, and 𝑟𝑡 is the log return

1.3.3 Volatility

Volatility is a statistical measure of the dispersion of returns for a given security

or market index Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index Commonly, the higher the volatility, the riskier the security

1.3.4 Return spillover

The return spillover is considered in the sense that the return of one index may have some impact on the return of other index, in the term that it would make other index’s return increase or decrease

1.3.5 Volatility spillover

The volatility spillover is considered in the sense that the volatility of one index’s return may have some impact on the volatility of other index’s return, in the term that it would increase or decrease the volatility of targeted index’s return

1.3.6 Time series

Time series is a sequence of data points, measured typically at successive time instants spaced at uniform time intervals In this thesis, the daily indices’ closing and theirs daily returns are considered as time series

Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data This study explores the time series analysis to answer the proposed questions in this section However with the time series analysis we confront some problems, for example the unit root Unit root can cause problems in statistical inference if it is not adequately dealt with Often, ordinary least squares (OLS) is used to estimate the slope coefficients of the auto-regressive model Use of OLS relies on the stochastic process being stationary When the stochastic process is non-stationary

or has the unit root, the use of OLS can produce invalid estimates.Granger & Newbold (1974) called such estimates spurious regression results: high R2 values and high t-ratios yielding results with no economic meaning

We discuss in details the Granger causality test in chapter three

H1: There is no return spillover between Vietnam and other markets

The second research question is answered with the following null hypothesis an alternative hypothesis:

H0: There is volatility spillover between Vietnam and other markets

H1: There is no volatility spillover between Vietnam and other markets

In order to assess how the spillovers response to the financial crisis, we study the research questions through three time frames as earlier discussed

1.5 Structure

The rest of this thesis is organized as follows Chapter two gives a brief and critical review of existing literature review relevant with this thesis Chapter three continues with the comprehensive description of the methodology applied

in the study The results are presented and discussed in chapter four, and finally the study is concluded in chapter five

Chapter 2 Literature review

The market integration in terms of price spillover between equity markets has been widely studied Grubel (1968) studied the co-movement and correlation between different markets from a US perspective for gains of international diversification Eun & Shim (1989) investigated the international transmission mechanism of stock market movements and found a substantial amount of multi-lateral interaction among national stock markets King & Wadhwani (1990) constructed a model in which "contagion" between markets occurs as a result of attempts by rational agents to infer information from price changes in other markets The authors offered supporting evidence for contagion effects using two different sources of data Jon (2003) provided evidence of transmission of information from the U.S and Japan to Korean and Thai equity markets during the period from 1995 through 2000 Berben & Jansen (2001) investigated the shifts in correlation patterns among international equity returns at the market level as well as the industry level from Germany, Japan, the UK and the US in the period 1980-2000

The volatility spillovers also gained focus of various authors Hamao, Masulis &

Ng (1990) found evidence of price volatility spillovers from New York to Tokyo, London to Tokyo, and New York to London was observed but no price volatility spillover effects in other directions is found for the pre-October 1987 period Karolyi (1995) examined the short-run dynamics of returns and volatility for stocks traded on the New York and Toronto stock exchanges with a multivariate GARCH model The main finding of the study was that inferences about the magnitude and persistence of return innovations that originate in either market and that transmit to the other market depend importantly on how the cross-market dynamics in volatility are modeled

Chelley-Steeley (2000) investigated the equity market volatility between countries and found that the correlation between the conditional variances of major equity markets has increased substantially over the last two decades Baele

(2003) quantified the magnitude and time-varying nature of volatility spillovers from the aggregate European (EU) and US market to 13 local European equity markets

In Asian markets context, Johnson & Soenen (2002) investigated the integration

of 12 equity markets in Asia and found that the equity markets of Australia, China, Hong Kong, Malaysia, New Zealand, and Singapore are highly integrated with the stock market in Japan and that these Asian markets became more integrated over time, especially since 1994 Tatsuyoshi (2003) examined the magnitude of return and volatility spillovers from Japan and the US to seven Asian equity markets Author found that only the influence of the US is important for Asian market returns; there is no influence from Japan; but the volatility of the Asian market is influenced more by the Japanese market than by the US; and there exists an adverse influence of volatility from the Asian market

to the Japanese market

Singh, Kumar & Pandey (2010) examined both price and volatility spillovers across 15 North American, European and Asian stock markets using a VAR model for the returns and an AR-GARCH for volatility They concluded that the direction of both return and volatility spillover was primarily from the US market

to Japanese and Korean markets, then to Singapore and Taiwan, and then to Hong Kong and Europe before returning to the US They also reported that the Japanese, Korean, Singapore, and Hong Kong markets were the markets with the greatest influencing power within the Asian markets

Worthington & Higgs (2004) indicated the presence of large and predominantly positive mean and volatility spillovers between three developed markets (Hong Kong, Japan and Singapore) and six emerging markets (Indonesia, Korea, Malaysia, Philippines, Taiwan and Thailand) Nevertheless, mean spillovers from the developed to the emerging markets are not homogeneous across the emerging markets, and own-volatility spillovers are generally higher than cross-volatility spillovers for all markets, but especially for the emerging markets Gamini &

Lakshmi (2004) pointed a high degree of volatility co-movement between Singapore, US, UK and Hong Kong market

Chuang, Lu & Tswei (2007) investigated the interdependence of volatility in six East Asian markets using the VAR-BEKK The results showed that the interdependence of equity market conditional variances was high; the Japanese market is the most influential in transmitting volatility to the other East Asian markets Lee (2009) used [VAR(p)-GARCH(1,1)] model to examine the volatility spillover effects among six Asian country stock markets (India, Hong Kong, South Korea, Japan, Singapore and Taiwan) and found the statistically significant volatility spillover effects within the stock markets of these countries Sariannidis, Konteos & Drimbetas (2010) analyzes the volatility linkages among three Asian stock exchange markets including India, Singapore and Hong Kong, during the period July 1997 to October 2005 The empirical analysis showed that the markets exhibit a strong GARCH affect and are highly integrated reacting to information which influences not only the mean returns but their volatility as well Giampiero & Edoardo (2008) explored the transmission mechanisms of volatility between markets using the Markov Switching bi-variate model The results show plausible market characterizations over the long run with a spillover from Hong Kong to Korea and Thailand, interdependence with Malaysia and co-movement with Singapore

Other authors including Jang & Sul (2002), In et al (2001), Yilmaz (2010), Alethea et al (2012), Matthew, Wai-Yip Alex & Lu (2010), Indika, Abbas & Martin (2010), concentrated the interdependence and volatility spillover during financial crisis periods

In et al (2001) examined dynamic interdependence, volatility transmission, and market integration across selected stock markets during the Asian financial crisis periods 1997 and 1998 with the VAR-EGARCH model The authors stated that Hong Kong played a significant role in volatility transmission to the other Asian markets The data also indicated market integration in that each market reacted to

both local news and news originating in the other markets, particularly adverse news

Alethea et al (2012) applied graphical modeling to the S&P 500, Nikkei 225 and FTSE 100 stock market indices to trace the spillover of returns and volatility between these three major world stock market indices before, during and after the

2008 financial crisis Authors found that the depth of market integration changed significantly between the pre-crisis period and the crisis and post- crisis period Matthew, Wai-Yip Alex & Lu (2010) investigated the spillover of financial crises by studying the dynamics of correlation between eleven Asian and six Latin American stock markets vis-a-vis the US stock market There was evidence

of contagion from the US stock market to markets in the two regions during the global financial turmoil The magnitude of the contagion effect to both regions in the global financial crisis is very similar, albeit their different economic, political and institutional characteristics

Indika, Abbas & Martin (2010) examined the interplay between stock market returns and their volatility, focusing on the Asian and global financial crises of 1997-98 and 2008-09 for Australia, Singapore, the UK, and the USusing MGARCH model The research could not find any significant impact on returns arising from the Asian crisis and more recent global financial crises across these four markets However, both crises significantly increased the stock return volatilities across all of the four markets

Yilmaz (2010) studied the extent of contagion and interdependence across the East Asian equity markets since early 1990s and compares the ongoing crisis with earlier episodes The study shows that there is substantial difference between the behavior of the East Asian return and volatility spillover indices over time While the return spillover index reveals increased integration among the East Asian equity markets, the volatility spillover index experiences significant bursts during major market crises, including the East Asian crisis The fact that both return and volatility spillover indices reached their respective peaks

during the current global financial crisis attests to the severity of the current episode

Zhou, Zhang & Zhang (2012) proposed measures of the directional volatility spillovers between the Chinese and world equity markets It was found that the

US market had dominant volatility impacts on other markets during the subprime mortgage crisis The volatility interactions among the markets of China, Hong Kong, and Taiwan were more prominent than those among the Chinese, Western, and other Asian markets were

Sang & Seong (2011) found unidirectional volatility spillovers from Hong Kong, Korea and Singapore markets to the Chinese markets in the pre-crisis period of the financial crisis in 2008; and found strong volatility linkages between the Chinese market and the other Asian markets and that the Chinese stock market has become an important information source among Asian emerging

However, there is not much study on the price and volatility spillover within the Vietnamese market context The aim and the main contribution of this study are

to fill up this gap

- Long-run integration is tested through Johansen co-integration techniques

If two or more series are found to be-cointegrating, then they are said to have common stochastic trends They tend to move together in the long run but may divergence in short run

- Short-run dynamics is examined through Granger causality test and Vector autoregressive model Because Granger causality test does not explain whether there is a positive or negative relation between endogenous variable, if any; this is investigated through VAR model The return spillover is also tested via VAR model

- BEKK model and AR-GARCH model and are applied to investigate volatility spillover

3.2.2 Unit root and stationary test

ADF method (Dickey & Fuller (1979)) is widely used for the unit root and stationary test in financial time series

Denote the series by xt, to verify the existence of a unit root of xt, we may perform the test with null hypothesis H0: β = 1 versus the alternative hypothesis H1: β <1 using the regression

𝑥𝑡 = 𝑐𝑡+ 𝛽𝑥𝑡−1+ � ∅𝑖∆𝑥𝑡−1

𝑝−1

𝑖=1

+ 𝑒𝑡

where 𝑐𝑡is a deterministic function of the time index t

∆𝑥𝑡−1 = 𝑥𝑡− 𝑥𝑡−1is the differenced series of 𝑥𝑡

In practice, 𝑐𝑡 can be zero or a constant or 𝑐𝑡 = 𝜔0+ 𝜔1𝑡

The ADF test value is calculated as:

𝐴𝐷𝐹 − 𝑡𝑒𝑠𝑡 = 𝛽̂ − 1

𝑠𝑡𝑑(𝛽̂)where 𝛽̂ denotes the least-squares estimate of 𝛽, is the well-known augmented

Dickey–Fuller (ADF) unit-root test

Hypothesis for the ADF Test

- H0: the series has unit root (β = 1)

- H1: the series has no unit root (β <1)

To decide the result, we use the following rules:

- If ( ADF value> ADF critical value )

 we fail reject the null hypothesis,

 the unit root exist

- If ( ADF value < ADF critical value )

 we reject the null hypothesis,

 There is no unit root in the time series

3.2.3 Johansen’s cointegration techniques

The Johansen multivariate cointegration procedure (Johansen (1988)) is widely used to perform the co-integration analysis If the two or more series are found to

be co-integrating, then they are said to have common stochastic trend: they tend

to move together in the long run but may divergence in short run

Consider a k-dimensional VAR (p) time series 𝑥𝑡with possible time trend so that the model is

𝑥𝑡 = 𝜇𝑡 + Φ1𝑥𝑡−1+ ⋯ + Φ𝑝𝑥𝑡−𝑝+ 𝑎𝑡

where the innovation 𝑎𝑡is assumed to be Gaussian and 𝜇𝑡 = 𝜇0+𝜇1𝑡, where 𝜇0

and 𝜇1 are k-dimensional constant vectors

An error correction model (ECM) for the VAR(p) process 𝑥𝑡is

∆𝑥𝑡 = 𝜇𝑡 + Π𝑥𝑡−1+ Φ1∗Δ𝑥𝑡−1+ ⋯ + Φ𝑝−1∗ Δ𝑥𝑡−𝑝+1+ 𝑎𝑡

With П = αβ′ = −Φ(1) Three cases are of interest in considering the ECM

1 If 𝑅𝑎𝑛𝑘(𝝅) = 0 This implies 𝑥𝑡 is not cointegrated

2 If 𝑅𝑎𝑛𝑘(𝝅) = k This implies 𝑥𝑡 contains no unit roots and 𝑥𝑡 is stationary process

3 If 0<𝑅𝑎𝑛𝑘(𝝅) = m < 𝑘 This implies 𝑥𝑡 is cointegrated with m linearly independent cointegrating vectors and has k - m unit roots that give k - m common stochastic trends of 𝑥𝑡

Two likelihood ratio tests are used to test the long run relationship: the trace test and the maximum eigenvalue test

The trace test

Consider the hypothesis

H0: Rank(𝛑) = m or there is m cointegrating vector, versus

H1: Rank(𝛑) > 𝑚, or there is more than m cointegrating vector

Johansen (1988) proposes the likelihood ratio (LR) statistic (trace value) to perform the test

To decide the result, we use the following rules:

- If Trace Value < Critical value :

 we fail to reject the null hypothesis H0

 there is m cointegrating vector

- If Trace Value > Critical value :

 we can reject the null hypothesis H0

 there is more than m cointegrating vector

The maximum eigenvalue test

Consider the hypothesis

H0: Rank(𝛑) = m or there is m cointegrating vector, versus

H1: Rank(𝛑) = m + 1 or there is m+1 cointegrating vector

The LR ratio test statistic, called the maximum eigenvalue statistic, is

To decide the result, we use the following rules:

- If max eigenvalue < Critical value :

 we fail to reject the null hypothesis H0

 there is m cointegrating vector

- If max eigenvalue > Critical value :

 we can reject the null hypothesis H0

 there is m + 1cointegrating vector

3.2.4 Granger causality analysis

Short run interrelationship is examined through Granger Causality test (Granger (1969; Granger (1988)) The Granger (1969) approach to the question of whether

X causes Y is to see how much of the current Y can be explained by past values

of Y and then to see whether adding lagged values of X can improve the explanation

Y is said to be Granger-caused by X if X helps in the prediction of Y, or equivalently if the coefficients on the lagged X’s are statistically significant Two-way causation is frequently the case; X Granger causes Y and Y Granger causes X

It is important to note that the statement “Granger causes” does not imply that is the effect or the result of Granger causality measures precedence and information content but does not by itself indicate causality in the more common use of the term

Let y and x be stationary time series To test the null hypothesis that x does not Granger-cause y, one first finds the proper lagged values of y to include in a uni-variate auto regression of y:

of x are retained in the regression

- If F-statistics value < Critical value :

 we fail to reject the null hypothesis Ho

 the X does not Granger cause Y

- If F-statistics value > Critical value :

 we can reject the null hypothesis Ho

 the X Granger cause Y

3.2.5 VAR Model

The vector auto regression (VAR) is commonly used for forecasting systems of interrelated time series and for analyzing the dynamic impact of random disturbances on the system of variables The VAR approach sidesteps the need for structural modeling by treating every endogenous variable in the system as a function of the lagged values of all of the endogenous variables in the system The mathematical representation of a VAR(p) is:

𝑦𝑦 = 𝐴1𝑦𝑡−1+ + 𝐴𝑝𝑦𝑡−𝑝+ 𝐵𝑥𝑡 + 𝜀𝑡where 𝑦𝑡is a k vector of endogenous variables,

𝑥𝑡is a d vector of exogenous variables,

p is the number of lag,

𝐴1, … , 𝐴𝑝 and B are matrices of coefficients, and 𝜀𝑡 is a vector of innovation

3.2.6 Bivariate BEKK Model

The VAR (k)-BEKK (1, 1) model to estimate volatility spillover is explained below

Let endogenous 𝑌𝑡is Nx1 vector with the mean equation:

𝑌𝑡 = 𝐶 + 𝐵1𝑌𝑡−1+ … + 𝐵1𝑌𝑡−𝑘+ 𝐸𝑡The error term has multinomial normal distribution as

𝐸𝑡|𝜓𝑡−1~ 𝑁(0, 𝐻𝑡) The BEKK(p,q) representation of the variance of error term 𝐻𝑡

𝐻𝑡 = 𝐶𝑜′𝐶0+ � 𝐴𝑖′𝜀𝑡−𝑖𝜀′

𝑡−𝑖𝐴𝑖 𝑞

𝑖=1

+ � 𝐵𝑖′𝐻𝑡−𝑖𝐵𝑖 𝑝

𝑖=1

Where 𝐴𝑖 and 𝐵𝑖 are kxk parameter matrix

𝐶0is kxk upper trangular matrix

Based on the symmetric parameterization of the model, 𝐻𝑡 is almost surely

positive definitive provided that A’A is positive definitive The BEKK (p,q) with

k variables requires 𝑘2(𝑞 + 𝑞) + 𝑘(𝑘 + 1)/2 parameters which increases rapidly with p and q

The BEKK (p=1, q=1) with 10 variables requires 255 parameters and the optimization will be tedious So, we use the bivariate BEKK (1, 1) which requires only 11 parameters to examine the volatility spillovers between two markets The method to handle the volatility spillover between more than two markets is discussed in section 3.2.7

The bivariate VAR (k) BEKK(1, 1) model can be written as

𝐻𝑡 = 𝐶𝑜′𝐶0+ �𝑎𝑎11 𝑎12

21 𝑎22�′� 𝜀1,𝑡−12 𝜀1,𝑡−1𝜀2,𝑡−1

𝜀1,𝑡−1𝜀2,𝑡−1 𝜀1,𝑡−12 � �𝑎𝑎11 𝑎12

21 𝑎22�+ �𝑏𝑏11 𝑏12

Where ℎ11, ℎ12 are the conditional variances of market 1 and 2 respectively

ℎ12 is the conditional covariance of market 1 and 2

In the BEKK representation of volatility, the parameter 𝑎21 is the volatility

spillover from market 2 to market 1and 𝑎12 indicates the spillover from market 1

to market 2 Hence, the statistical significance of these parameters tells about the volatility spillover among the two markets

3.2.7 GARCH Model

We employ the two-stage GARCH approach to examine the volatility spillover across all indices In this method we also considered the same day effect and estimated the partial coefficient of the parameters

First stage: in this stage we fit the AR (1) - GARCH (1, 1) model to each index

and obtain the residuals from the mean equations

𝑟𝑗,𝑡 = 𝑎 + 𝑏𝑗 ∗ 𝑟𝑗,𝑡−1+ 𝜀𝑗𝑡

where𝜀𝑡|𝜓𝑡−1~ 𝑁(0, 𝜎𝑗𝑡2) and

𝜎𝑗𝑡2 = 𝛼0+ 𝛼𝑗 ∗ 𝜀𝑡−12 + 𝛽𝑗 ∗ 𝜎𝑡−12

where𝑟𝑗,𝑡 is the return of the jth index at time t

𝜀𝑗 is the error or unexpected return of the jth index,

𝜎𝑗𝑡2 is the variance – which presents the volatility– of the jth index

Second stage: the residuals are then used in the GARCH equation of the other

𝑛=1

where k: number of the indices open/close before the jth index

l: number of the indices open/close after jth index

The coefficients 𝜑𝑗𝑘, 𝜑𝑗𝑙 is the volatility spillover from market k and l

respectively to the market j Hence the values of these coefficients and theirs statistical significance provide useful information about the volatility spillovers Consider the GARCH variance equation of VNIndex: three indices Nikkei, SSE, TWII open/close before VNIndex and we expect there are volatility spillovers within the same day; so the same day residuals of these three indices are used in the GARCH equation Meanwhile; other six indices BES, HIS, JKSE, KLSE, PSE, STI open/close after the VNIndex; the volatility spillovers, if any, would happen in the next day so the one lag day residuals of these six indices are used

in the equation

Chapter 4 Data Description, Results

and Analysis of Results

Chapter four will report the results and provide an analysis of the results based

on the methodologies we present in the previous chapter We use Eviews and RATS application to generate the results, and the details analysis are also discussed here with main findings

4.1 Descriptive statistics and correlation matrix

The brief descriptive statistics of indices and returns are described as followings:

4.1.1 Opening and closing time of Indices

The opening and closing timing of the indices by UTC time are presented in Figure 1 This information is necessary to determine which index would have potential effect on other indices in the same day or within next day For example, the Nikkei index opens and closes before the VNIndex, so the former index would have potential effect to VNIndex in the same day; and the VNIndex may have effect to Nikkei, if any, after one day lag

Figure 1 Index timings by UTC Time

4.1.2 Descriptive statistics of Indices

Table 2, 3 and 4 present the descriptive statistics of the studied indices All

skewness and kurtosis exhibit larger values and the J-B test statistics is highly

significant at the l% level (expect the VNIndex in the post crisis period),

indicating the distribution of all the prices is not distributed normally

Table 2 Descriptive statistics of Indices in pre-crisis period

BSESN HIS JKSE KLSE N225 PSEI SSE STI TWII VNINDEX Mean 11,463 18,139 1,564 1,057 15,178 2,590 2,332 2,731 7,141 590

Table 3 Descriptive statistics of Indices in crisis period

BSESN HIS JKSE KLSE N225 PSEI SSE STI TWII VNINDEX Mean 14,635 19,727 2,179 1,151 10,692 2,670 2,903 2,555 6,924 475

Table 4 Descriptive statistics of Indices in post-crisis period

BSESN HIS JKSE KLSE N225 PSEI SSE STI TWII VNINDEX Mean 17,920 21,167 3,738 1,516 9,361 4,382 2,568 2,985 7,959 439