Empirical studies on the volatility of china stock market

逢 甲 大 學
金融博士學位學程
博士論文

中國股市波動之實證研究
Empirical studies on the volatility of China stock market

指導教授：吳仰哲教授
: 翁慈青 教授
研 究 生 ：王氏香江

中華民國一百一十年一月


Empirical studies on the volatility of China stock market

ACKNOWLEDGEMENTS
I would like to express my sincere thanks to the Chair of the Ph.D. Finance
program, the Director of Finance College, Feng Chia University’s administration
for creating all favorable conditions for me to complete this thesis. Most important,
I would like to thanks both Professors. Yang-Che Wu and Tzu-Ching Weng guided
enthusiastically me to carry out my thesis step by step. During my studying
process in Taiwan, I highly appreciate their contributions for time, subsidies, and
inspiration ideas to me. They taught me a lot of knowledge in the finance and
accounting fields. Especially, they have always encouraged and supported me to
perform the Ph.D. Finance program. Their successes and passion for researching
inspired me to complete my thesis.
I appreciate Professor Richard Lu, Li-Jiun Chen, Nathan Liu, Thomas Chinan
Chiang, Wei-Feng Hung, Yi-Ting Hsieh, Shin-Heng Michelle Chu. Their classes
provided me with a lot of specialized knowledge about econometrics and finance.
Professor. Richard Lu who always welcomes all students if we need any helps. I

am very impressed with his outdoor trips for all Ph.D. students to give memorable
memories in Taiwan country.
I would like to express my sincere thanks to my classmate, namely, Huu Manh
Nguyen for his help and collaborative assistance in the thesis. During two
academic years, he taught me basic knowledge in the financial field that I have
ever not known because before my studies focus mainly on the accounting field.
In our teamwork, he always enthusiastically guided me to how present in my
studies, my presentations in the best way. With his bits of help, I obtain more
knowledge, better skills in my research.
For the MATLAB code, Uyen Kim Nguyen who graduated Master IT program
a Feng Chia University has significant contributions to my empirical results. She
helps me how to write code in MATLAB software to solve the ICSS algorithm in
the methodology sector of the first study. I appreciate her time and her effort in
my thesis.
I would like to thank Finance College’s assistant who was ready to help with
any works related to us in Taiwan and arranged this thesis defense. Because of
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Empirical studies on the volatility of China stock market

language limits, I cannot write exactly her name but I hope that she may get my
gratefulness.
About the final defense, I am grateful to committee members: Professor. YangChe Wu, Professor. Tzu-Ching Weng, Professor. Tsang-Yao Chang, Professor. YuChih Lin and Professor. Meng-Fen Hsieh for their time, attention, and insightful
suggestions for completing this thesis.
Finally, I express all thanks to my family in Vietnam. I am so grateful for my
parents who encourage me to pursue the Ph.D. Finance program at Feng Chia
University. Especially for my mother who helps me to take care of my daughter
during the long period of the Ph.D. Finance program. I am so appreciated. Thank

you for all!
Vuong Thi Huong Giang
Feng Chia University
January 2021

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ABSTRACT
The volatility of the stock market returns needs to be carefully considered
because it relates closely to the degree of risking contagion between the equity
markets and the adjustment on the capital structure of listed firms.
In the macro aspect, the first study examines the bidirectional volatility
spillovers between the US and China stock markets in the post-2000 period. We
employ a variant model of EGARCH (1,1) with controlling the excessive volatility
points that are detected by the ICSS algorithm. Our results imply the barriers in the
bilateral US-China relationship and foreign investment’s restrictions in China’s
financial market have distinctly influenced the bidirectional volatility infections.
Most crucially, we indicate that the global financial crisis exposed the majority
volatility contagion from the US to China stock market while the Covid-19
pandemic strongly promoted the volatility infection from China to the US equity
market in March 2020.
In a micro aspect, an essential issue of listed firms is adjusting their market
leverages as the volatility of the stock market returns increases. Our paper examines
this concern on the biggest stock exchange of China market covering 2008 to 2018
in a panel model. The volatility of Chinese stock market returns immediately has
positive impacts on both total market leverage and short-term market leverage, but

a negative influence on the long-term market leverage of Chinese listed firms. We
indicate that in this situation, Chinese listed firms adjust their debt structure by
employing more bank debts and cutting trade credit. Finally, we present robust
evidence that the proportion of bank debts in total debts visibly increases while the
ratio of trade credit in total debts distinctly reduces. Furthermore, we implement
robust tests regarding potential issues such as sample selection, model selection,
endogenous factors, and apply quantile regression (QR) to enhance the robustness
of our empirical results.
Keywords: US stock market, China stock market; Bidirectional volatility spillovers;
ICSS algorithm; EGARCH (1,1) model; Capital structure; Panel model.

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CONTENTS
ACKNOWLEDGEMENTS.................................................................................. i
ABSTRACT .........................................................................................................iii
CONTENTS ......................................................................................................... iv
LIST OF FIGURES ........................................................................................... vii
LIST OF TABLES .............................................................................................viii
STUDY I: .............................................................................................................. 1
THE BIDIRECTIONAL VOLATILITY SPILLOVERS BETWEEN THE US
AND CHINA STOCK MARKETS ..................................................................... 1
1.1. Introduction ................................................................................................... 1
1.1.1. Research background ............................................................................... 1
1.1.2. Research motivations and Research contributions .................................. 4
1.1.3. Research structure .................................................................................... 6

1.2. Literature review ........................................................................................... 6
1.3. Sample, Methodology and Empirical models ............................................. 9
1.3.1. Sample ..................................................................................................... 9
1.3.2. ICSS algorithm to detect structural breakpoints in the variance of volatility
source’s returns .................................................................................................. 9
1.3.3. Modeling the bidirectional volatility spillovers between the US and China
stock markets ................................................................................................... 11
1.4. Analyzing empirical results on the bidirectional volatility spillovers
between the US and China stock markets ....................................................... 13
1.4.1. Basic analysis......................................................................................... 13
1.4.2. Empirical results on the volatility spillovers from the US to China stock
market .............................................................................................................. 15
1.4.2.1. Modeling the volatility of Shanghai Composite’s returns by using
structural breakpoints in the variance of US stock market returns ............. 15
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1.4.2.2. Modeling the volatility of Shenzhen Composite’s returns by using
structural breakpoints in the variance of US stock market returns ............. 17
1.4.2.3. Modeling the volatility of Chinese stock market returns by using the
variance of US stock market returns ........................................................... 18
1.4.3. Empirical results on the volatility spillovers from the China to US stock
market .............................................................................................................. 19
1.4.3.1. Modeling the volatility of S&P500’s returns by using structural
breakpoints in the variance of Chinese stock market returns ...................... 19
1.4.3.2. Modeling the return volatility of other US indexes by using structural
breakpoints in the variance of Chinese stock market returns ...................... 20

1.4.3.3. Modeling the volatility of US stock market returns by using the
variance of Chinese stock market returns ................................................... 21
1.5. Conclusion and Recommendation ............................................................. 23
References ........................................................................................................... 24
Appendix A. I ...................................................................................................... 37
Appendix B. I ...................................................................................................... 30
STUDY II: ........................................................................................................... 43
THE VOLATILITY OF CHINESE STOCK MARKET RETURNS AND
CAPITAL STRUCTURE OF CHINESE LISTED FIRMS .......................... 44
2.1. Introduction ................................................................................................. 44
2.1.1. Research background ............................................................................. 44
2.1.2. Research motivations and Research contributions ................................ 46
2.1.3. Research structure .................................................................................. 48
2.2. Literature review ......................................................................................... 48
2.3. Data, Empirical models and Variables ...................................................... 52
2.3.1. Data ........................................................................................................ 52
2.3.2. Empirical models and Variables ............................................................ 52
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2.4. Analyzing the volatility impact of Chinese stock market returns on the
adjusting capital structure of Chinese listed firms ......................................... 55
2.4.1. The volatility impact of Chinese stock market returns on market leverages
of Chinese listed firms ..................................................................................... 55
2.4.2. The volatility impact of Chinese stock market returns on bank debts of
Chinese listed firms ......................................................................................... 58
2.4.3. The volatility impact of Chinese stock market returns on trade credit of

Chinese listed firms ......................................................................................... 61
2.4.4. Robust checks ........................................................................................ 63
2.4.4.1. Sample selection ............................................................................. 63
2.4.4.2. Model selection .............................................................................. 64
2.4.4.3. Endogenous factors ........................................................................ 65
2.4.4.4. Using quantile regression (QR) ...................................................... 66
2.5. Conclusion and Recommendation ............................................................. 67
References ........................................................................................................... 68
Appendix A. II .................................................................................................... 72
Appendix B. II .................................................................................................... 73

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LIST OF FIGURES
LIST OF FIGURES IN STUDY I ..................................................................... 27
Figure 1.1. Examining the bidirectional volatility spillovers between the US and
China stock markets ............................................................................................. 27
Figure 1.2. The structural breakpoints in the variance of US stock market returns
are detected by the ICSS algorithm (2001–10/2020) ........................................... 28
Figure 1.3. The structural breakpoints in the variance of Chinese stock market
returns are detected by the ICSS algorithm (2001–10/2020) .............................. 29
LIST OF FIGURES IN STUDY II ................................................................... 72
Figure 2.1. The volatility of Chinese stock market returns per year and annual
China’s lending interest rate (2001-2019) ........................................................... 72

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LIST OF TABLES
LIST OF TABLES IN STUDY I ........................................................................30
Table 1.1: Descriptive statistics ............................................................................30
Table 1.2: Unit root tests .......................................................................................31
Table 1.3: Break dates corresponding to structural breakpoints are detected in the
variance of stock market returns using the ICSS algorithm (2001-10/2020) .......32
Table 1.4: Modeling the volatility of stock market returns without using the
detected structural breakpoints (2001-10/2020) ...................................................34
Table 1.5: Modeling the volatility of SSEC’s returns using structural breakpoints
in the variance of US stock market returns (2001-10/2020) .................................35
Table 1.6: Modeling the volatility of SZSC’s returns using structural breakpoints
in the variance of US stock market returns (2001-10/2020) .................................37
Table 1.7: Modeling the volatility of Chinese stock market returns by using the
variance of US stock market returns .....................................................................39
Table 1.8: Modeling the volatility of S&P500’s returns using structural breakpoints
in the variance of Chinese stock market returns (2001-10/2020) .........................40
Table 1.9: Modeling the volatility of DJIA’s returns using structural breakpoints in
the variance of Chinese stock market returns (2001-10/2020) .............................41
Table 1.10: Modeling the volatility of Nasdaq Composite’s returns using structural
breakpoints in the variance of Chinese stock market returns (2001-10/2020) .....42
Table 1.11: Modeling the volatility of US stock market returns by using the
variance of Chinese stock market returns .............................................................43

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LIST OF TABLES IN STUDY II .......................................................................73
Table 2.1: Definition of variables .........................................................................73
Table 2.2: Firms in different industries .................................................................74
Table 2.3: Descriptive statistics and correlation of variables ...............................75
Table 2.4: The volatility impact of Chinese stock market returns on market
leverages of Chinese listed firms (2008-2018) .....................................................77
Table 2.5: The volatility impact of Chinese stock market returns on debts of banks
and financial institutions in of Chinese listed firms (2008-2018) ........................78
Table 2.6: The volatility impact of Chinese stock market returns on trade credit of
Chinese listed firms (2008-2018) ..........................................................................79
Table 2.7: The volatility impact of Chinese stock market returns on market
leverages of Chinese listed firms excluding utility firms (2008–2018)................80
Table 2.8: The volatility impact of Chinese stock market returns on market
leverages of Chinese listed firms using a sample of Shenzhen Stock Exchange
(2008–2018) ..........................................................................................................81
Table 2.9: The volatility impact of the lag of Chinese stock market returns on
market leverages of Chinese listed firms (2008-2018) .........................................82
Table 2.10: Controlling for an endogenous factor (2008–2018) – IV regression 83
Table 2.11: Estimated results using quantile regression (2008-2018) ..................84

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STUDY I:
THE BIDIRECTIONAL VOLATILITY SPILLOVERS BETWEEN THE
US AND CHINA STOCK MARKETS
1.1. Introduction
1.1.1. Research background
Globalization results in increasing interdependence on capital markets (Baele,
2005). A large of studies indicate that the rise in financial integration leads to the
stock return transmission and volatility spillover between stock markets in the
world (Baele, 2005; Sui and Sun, 2016; Lien et al., 2018; Vo and Tran, 2020). At
present, emerging markets appear more and get more attention in the integrated
context of stock markets (Moon and Yu, 2010). Volatility spillovers between stock
markets are usually related to the variance of stock returns and investment risks in
equity markets (Vo and Tran, 2020). In addition, volatility spillovers indicate the
level of integration between stock markets (Mukherjee and Mishra, 2010).
Therefore, the important issues are to find out the source of volatility, the moment
of volatility, and the degree of volatility spillovers in the international equity
market.
The volatility transmission from advanced markets to emerging markets seems
like a natural issue shown by a large number of empirical results (Ng, 2000;
Worthington and Higgs, 2004; Chow, 2017; Vo and Tran, 2020) implying that
emerging markets are excitable by the small fluctuations from developed markets,
however, the contagion from developed markets to emerging markets varies across
different markets (Worthington and Higgs, 2004). Developing equity markets are
less likely to be affected by shocks from their developed counterparts if the
linkages between emerging markets and developed markets are weak. Inversely,
if emerging equity markets are absolutely dependent on advanced equity markets,
the volatility of emerging markets is also pointed out in the developed markets.
These recent studies address the impact of the global financial crisis in 2008 on
the relationships between international equity markets (Lien et al., 2018; Hung,
2019; Vo and Tran, 2020), overall, their empirical results show that financial

shocks expose substantially the contagion between stock markets.
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On the other hand, Li and Giles (2015) show the volatility spillovers from
emerging markets in Asia area to developed markets during the currency crisis
(1997), their findings imply that the volatility effects are also likely to exist
bidirectionally between equity markets but do not only appear from advanced
markets to emerging markets. Most recently, the Covid-19 pandemic sourced from
China market at the end of 2019 impacts terribly and rapidly on the entire
international market (Zhang et al., 2020), it occurs the worst in the US market.
The major stock indexes in the world simultaneously bottomed out at the end of
Q1-2020.
Despite the great changes in the global text, the positions of “big players” in the
international stock market have not yet varied. The US stock market accounts for
nearly 44.33% total market value of the international stock1. While the closest
competitor, China, is only still 1/5th of the market value of the US, however, China
is the largest emerging stock market of both the Asian stock market and the global
stock market. According to the STATISTA2, the first and the second-largest stock
exchanges in the world come from the US stock market, listed by the market
capitalization of listed firms in 20203. The fourth position belongs to the Shanghai
Stock Exchange of China stock market. China’s economy is distant from other
developing countries and China’s GDP has been continuously growing up from
1990 to the current year. Following the Purchasing Power Parity (PPP) Index,
China has been become the second-largest economy in 2004, but, by 2010
according to the GDP Index. Also, the China stock market is a promised emerging
market with potential linkages to the international markets. With its developed

speed, China is expected to get over the US equity market and turn into the largest
stock market in 2030 (Liu et al., 2013). The US is a large exporting market of
China, also, China is the second-biggest foreign creditor of the US country
(Morrison, 2010). On the other hand, the bilateral nexus between the US and China
are quite complex and tense during the Korean War, the Vietnamese War,

Data is published by World Bank, calculated at the end of 2018.
STATISTA is German enterprise operating in providing market database.
3
The figures are updated until 31th March, 2020
1
2

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Taiwanese, and Hong Kong issues. The most noticeable is the trade war between
the US and China in 2018. The mutually commercial allegations between the US
and China are on the intensively risen. The US has suffered criticisms from its
Chinese partner due to its importing restrictions on the high-tech products of China.
Inversely, the US side expresses views related the intellectual property rights,
commercial surplus. Moreover, both the US and China severely competitive to
increase their influence on the Asian markets. The government intervention
likelihoods to impact the open market and the integration between equity markets
(Uludag and Khurshid, 2019), hence the integrated degree between the US and
China stock market is more likely to be significantly dominated by the government
policies from two sides. Additionally, due to the restrictions on China’s foreign

investment, the volatility of Chinese stock market returns is less likely to be
significantly impacted by the market volatility of counterparts (Zhou et al., 2012).
In the first study, we provide comprehensive evidence on the bidirectional
volatility spillovers between the US and China stock markets over nearly 20 years
by applying a new methodology on large samples. We mainly survey the
bidirectional volatility spillovers between the Standard & Poor’s 500 (S&P500)
Index of the US stock market and the Shanghai Composite (SSEC) Index of the
China stock market in long term. Moreover, we use two other US stock indexes
(Nasdaq Composite Index, Down Jones Industrial Average Index) and another
Chinese stock index (Shenzhen Composite Index) to reinforce our empirical
results. Our research contents are shortly illustrated in Figure.1. Data is collected
from Thomson Reuters Eikon in the period January 2001-October 2020. The
research period consists of the global financial crisis in 2008 derived from the US
market and the Covid-19 pandemic originated from China country. Firstly, we
employ the ICSS algorithm to detect structural breakpoints of the volatility source
(Inclan and Tiao, 1994). Secondly, we use a variant form of the EGARCH (1,1)
model with the detected breakpoints to model the volatility spillovers from the US
to China stock market (Vo and Tran, 2020), and vice versa in the period January
2001- December 2020. In brief, empirical results show that China stock market is
the largest developing market in the Asia-Pacific area, however, its volatility was
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not frequently affected by the volatility of the US stock market returns. On
otherwise, we find out the substantial volatility spillovers from the US to China
stock market appear during the global financial crisis in 2008 and perform
obviously on the day of Leman Brother group’s collapse. In the opposite direction,

the volatility of China stock market has impacted persistently but weakly on the
volatility of US stock markets for the period from 2004 to 2020. We detected that
the Covid-19 pandemic that originated from China considerably promoted the
volatility spillovers from China to the US stock market at the end of March 2020.
Our findings are robust to a large volume of stock indexes in both the US and
China markets. In addition, we provide certainty evidence by another volatility
measure of S&P500’s returns, as well as, SSEC’s returns.
[Insert Figure 1.1 here]
1.1.2. Research motivations and Research contributions
This research is motivated by a large number of the following reasons.
Surveying the volatility in emerging markets becomes more and more important
in the financial field because these markets are young and likely to be more highly
sensitive to fluctuations from developed markets. Emerging markets have been
asserted their position in the international market, an outstanding example is the
China market. The volatility of developing markets has a high ability to influence
advanced equity markets. Secondly, the US and China stock markets are the two
largest stock markets in the world, they respectively represent a developed market
and an emerging market. Therefore, it’s quite essential to examine in detail the
bidirectional volatility spillovers from the US to China stock market in the longterm based on the barriers in bilateral nexus between the US and China, as well as,
foreign investment’s restrictions in China’s financial market in the recent two
decades. Thirdly, the international equity market witnesses two great crashes in
the period post-2000, the first shock is the global financial crisis in 2008 sourced
from the US and the second one is the Covid-19 pandemic originated from China
at the end of March 2020, both of them might significantly promote the volatility
spillovers between the US-China equity markets. Fourth, the majority of previous
research related to the volatility effects between the US and China stock markets
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turn around the currency crisis (1997) and the global financial crisis (2008) in the
period 1994-2015 while the recent impact of the Covid-19 has not yet mentioned.
Therefore, our study uses a new methodology compared with previous studies on
similar topics to solve a list of the research hypotheses regarding the bidirectional
volatility spillovers between the US and China stock markets in the post-2000
period, as follows:
- Research question 1: Whether the volatility spillovers from the US to China
stock market in the period January 2001-October 2020? and vice versa?
- Research question 2: Which degrees of volatility spillovers from the US to
China stock market and vice versa are at different moments?
- Research question 3: Does the global financial crisis in 2008 promote the
spillover effect from the US to China stock market to become more powerful? and
vice versa?
- Research question 4: Whether the recent Covid-19 pandemic substantially
motivate the volatility spillovers from China to the US stock market? and vice
versa?
More specifically, we implement the ICSS algorithm (Inclan and Tiao, 1994) to
detect excessive volatility breakpoints of daily stock market returns covering
January 2001 to October 2020. Then, we estimate a variant form of EGARCH (1,1)
with breakpoint dummy variables (Vo and Tran, 2020) to survey the volatility
spillovers from the US to China stock market and vice versa. Our research
overcomes weak points of the previous studies and robustly responds to the entire
our research hypotheses as follows: Investigating a large sample with different
stock indexes in both the US and China stock markets; Expanding the research
period that covers the global financial crisis in 2008 which is originated from the
US market and the Covid-19 pandemic derived from China country; Clearly
indicating the source of volatility, the broken volatility moments as well as their
degrees of volatility spillovers from the US to China stock market and vice versa;

Emphasizing the dominant role of the huge shocks in the volatility spillovers
between equity markets; Confirming of the integrated level between the US and
China stock markets for nearly two decades.
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1.1.3. Research structure
The introduction is presented in the first part. The remainder of this study
includes Part 2 summarizes the literature review of volatility spillovers. Sample,
Methodology, and Empirical models are introduced in Part 3. In the fourth part,
we analyze the main results on the bidirectional volatility spillovers between the
US and China stock markets using the S&P500 Index of the US stock market and
the SSEC Index of China stock market, as well as, the empirical results of robust
tests. The final part gives conclusions and recommendations.
1.2. Literature review
The volatility spillovers and interdependence between equity markets in the
world are undeniable. Besides the existence of volatility spillovers from developed
markets to developing markets, the volatility contagion is largely found among the
affiliate stock markets such as European stock markets (Kanas, 1998), East Asia
stock markets (Yilmaz, 2010), Asian stock markets (Joshi, 2011), North American,
European and Asian stock markets (Singh et al., 2010) or even volatility
transmission from East Asia stock markets to Southeast Asia stock markets (Wu,
2020) suggesting that the global integration sets the stage for volatility spillovers.
Especially, the spillover effects originating from the US stock market have been
popularly demonstrated in European stock markets (Baele, 2002), Islamic stock
markets (Majdoub and Mansour, 2014), BRICS stock markets (Sui and Sun, 2016;
Mensi et al., 2016), ASEAN stock markets (Vo and Tran, 2020). A lot of evidence

state that the volatility of US stock market is related strongly to the volatility of
Asian stock markets. For instance, Liu and Pan (1997) show the significant
volatility linkages between the US stock market and Asian stock markets such as
Hong Kong, Singapore, Taiwan, and Thailand. Li and Giles (2015) indicate the
volatility spillovers from the US to Asian emerging stock markets (including
China) are considerably unidirectional during the Asian crisis in 1997.
Additionally, Lien et al. (2018) find out the strong volatility spillovers from the
US stock market to Southeast Asian stock markets and East Asian stock market
(excluding China) during two crises in 1997 and 2008.
Meanwhile, there is little direct evidence regarding the volatility spillovers
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between the US and China stock markets. The first study investigates the linkage
among the US and China stock markets from January 2000 to August 2005 and
insists that there is no direct spillover effect from the US to China stock market by
using a multivariate GARCH model (Li, 2007). Then, Moon and Yu (2010) extent
their research period from January 1999 to June 2007, in order to survey the
volatility spillovers from the US to China stock market. Different from Li's (2007)
study, they use Andrews (1993)’s method to find out a single structural breakpoint
in the mean of Chinese stock market returns. Then, they employ GARCH-m (1,1)
model and prove that the volatility spillover from the US stock market to China
stock market only exists in the post-breakpoint period (December 2, 2005) but it
doesn’t appear in the pre-breakpoint period. In addition, the volatility spillovers
from the US to China stock markets are not also clearly indicated in the period
1994-2004 (Wang and Wang, 2010). The later studies mostly emphasize the role
of the global financial crisis. Zhou et al. (2012); Uludag and Khurshid (2019);

Mensi et al. (2016) largely focus on the dominated volatility spillovers from the
US to China stock market and other equity markets in two years (2007 and 2008).
On the other hand, since 2004, China’s economy has been the second-largest
economy (after the US) defined by the PPP index that event proves the efficiency
of Chinese innovative policy during three decades. Although China is only an
emerging market, its equity market has also substantial impacts on other equity
markets. Employing the VAR model, Zhou et al. (2012) show that since 2005, the
volatility transmissions from the China stock market to Hong Kong and Taiwan
stock markets have been more remarkable than to European and other Asian equity
markets. Hung (2019) proves the energetic volatility effects from China stock
market to the Southeast Asian stock market in the period July 2000 – July 2018
using the GARCH-BEKK model. Allen et al. (2013) use a variety of time series
models and find out some evidence on the volatility spillovers from China stock
market to advanced stock markets in the period pre-global financial crisis. On the
other hand, they indicate that the volatility of the US stock market returns strongly
impacts forward on China stock market during the global financial crisis in 2008.
Investigating a sample in the period 1993 to 2012, Li and Giles (2015) show that
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the volatility of China stock market has significant spillovers to the US stock
market during the currency crisis in 1997. Additionally, Uludag and Khurshid
(2019) prove that the volatility spillovers bi-directionally appear between China
stock market and G7 equity markets, as well as, E7 stock markets from 1995 to
2015 by the VAR (1) – GARCH (1) model. However, in their study, the
bidirectional volatility effects between the US and China stock markets are not
clearly shown while empirical results largely focus on the volatility spillovers

between the US and other equity markets.
In odds with the classical theory on the volatility transmission from the
advanced markets to emerging counterparts, the recent results suggest that the
volatility of China stock market not only influences the volatility of emerging
partners but also developed counterparts. However, there haven’t had any studies
that directly focus on the bidirectional volatility spillovers between the US and
China equity markets during the near two decades. Most importantly, the role of
the Covid-19 pandemic in the volatility spillovers from China stock market to
other equity markets is not still mentioned due to the objective reason while the
effects of the global financial crisis get more attention. In other respects, the
previous studies regarding the volatility spillovers between the US and China
stock market exist several limits. For instance, the volatility source originates from
the US stock market but most of the literature didn’t clearly indicate that these
volatilities sourced from the US stock market, and which their spillover degrees
to China stock market across different moments. Inversely, a single structural
breakpoint in the mean of Chinese stock market returns is found and prove that
this structural breakpoint is related to the volatility of the US stock market returns
(Moon and Yu, 2010). Secondly, Andrews's (1993) method only helps to detect a
single structural breakpoint based on the average stock returns. While multiple
structural breakpoints in the variance of the volatility source are more likely to be
detected by the ISCC algorithm (Inclan and Tiao, 1994), they are closely related
to the market risks. Hence, if the time series is observed in the long term, the
degree of volatility spillovers at different moments and the continuity of volatility
spillovers between equity markets are likely to be more exactly considered.
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Thirdly, the US stock market is usually surveyed by a representative stock index
(S&P500 Index) and omitted the rest stock indexes (Down Jones Industrial
Average, Nasdaq Composite) while the Shenzhen Composite Index is also an
important indicator of China stock market.
1.3. Sample, Methodology and Empirical models
1.3.1. Sample
The purpose of the first study is to examine the bidirectional volatility spillovers
between the US and China stock markets from January 2001 to October 2020. Our
research period includes the global financial crisis in 2008 that originated from the
US market and the Covid-19 pandemic derived from the China stock market. We
use three US stock indexes including the Standard & Poor’s 500 Index (hereafter
S&P500), Nasdaq Composite Index, and Down Jones Industrial Average Index
(hereafter DJIA), among them, the S&P500 Index is the best representative index
of the US stock market. Regarding the China stock market, both the Shanghai
Composite Index and Shenzhen Composite Index are employed, therein, the
Shanghai Composite Index as a major proxy for China stock market. Daily stock
prices are download from Thomson Reuters Eikon in the period January 2001October 2020.
1.3.2. ICSS algorithm to detect the structural breakpoints in the variance of
volatility source’s returns
According to the first dimension, we examine the volatility spillovers from the
US to China stock market implying that the US stock market is the volatility
source. In this direction, the US stock market is defined to be the volatility source.
We employ the iterative cumulative sum of squares (ICSS) algorithm so as to
determine the structural breakpoints in the variance of the US stock market returns
based on IT statistics (Inclan and Tiao, 1994). Then, we test their effects on the
volatility of Chinese stock market returns by a variant form of the EGARCH (1,1)
model (Vo and Tran, 2020).
The ICSS algorithm gives an alternative hypothesis that unconditional variance
is stationary over the period which is separated by the volatility breakpoints. We
summary briefly of steps in the ICSS algorithm to detect structural breakpoints, as

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follows:
Assuming that N is the total observations of time series, K is the number of
volatility breakpoints in the volatility of US stock market’s returns, C1 < C2 < …
< C k are k breakpoints. During the observed period, the unconditional variance of
stock returns in the US market is illustrated in the Formula (I.1):
σ20 1 < t ≤ C1
2
var(rtUS ) = σ1 C1 < t ≤ C2
…
…
2
{σk Ck−1 < t ≤ Ck

𝐹𝑜𝑟𝑚𝑢𝑙𝑎 (𝐼. 1)

j

CRSSj = ∑ e2t

𝐹𝑜𝑟𝑚𝑢𝑙𝑎 (𝐼. 2)

t=1

where j = 1,2, …, N; CRSSj is the cumulative residual sum of squares from the

starting of the time series to the jth date, presented in Formula (I.2). Assuming that
j equals to N, CN is the residual sum of squares of the whole observations. Dj is
used for testing statistics at jth break date is defined by Formula (I.3):
Dj = [

Cj
j
]−
CN
N

𝐹𝑜𝑟𝑚𝑢𝑙𝑎 (𝐼. 3)

D0 = DN = 0 meaning the first test statistic and the last test statistic
corresponding to the first and the last observations, respectively, equal zero. If
unconditional variance has no change (Null hypothesis H0: No breakpoint), the
test statistic (Dj ) will softly volatile around the “zero” value. Following the Null
hypothesis, Dj fluctuates between lower and upper bounds that are critical values.
If the absolute value of Dj exceeds the critical values meaning that we reject the
Null hypothesis (H0) meaning that volatility breakpoint exists. We repeat this
process over sub-samples to maybe discover multiple breakpoints in a long time
series. That is an advantage of the ICSS algorithm compared with the Andrews's
(1993) method, however, the ICSS algorithm is used only in unconditional
variance (Smith, 2008). In our research, MATLAB software is used to implement
the ICSS algorithm to recognize the volatility breakpoints in the volatility of the
US stock market returns. For the second dimension, we also carry out the ICSS
algorithm to detect the structural breakpoints in the variance of Chinese stock
market returns.
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After that, we survey the volatility effects from the US to China equity market
through a variant form of EGARCH (1,1) model with the US volatility breakpoints
in the volatility equation of US stock market returns. In the opposite direction, we
also control the volatility breakpoints of Chinese stock market returns in the
volatility equation of US stock market returns by the variant model of EGARCH
(1,1). The details of experimental models are introduced in Section 1.3.3.
1.3.3. Modeling the bidirectional volatility spillovers between the US and
China stock markets
Nelson (1991) succeeded in building the EGARCH (Exponential Generalized
ARCH) model to measure and forecast the volatility of stock returns. The original
EGARCH (1,1) model has a following form:
log(ℎ𝑡 ) = 𝜔 + 𝛼 |

𝑢𝑡−1
√ℎ𝑡−1

| +𝛽

𝑢𝑡−𝑖
√ℎ𝑡−𝑖

+ 𝜃log(ℎ𝑡−1 )

Eq. (I)

where: ℎ𝑡 is the variance of stock returns, 𝜔 is constant, 𝛼 expresses the ARCH

effect, 𝜃 shows the GRACH effect, 𝛽presents the asymmetric effect. In the case,
ß<0 that means the bad news (negative shocks) generates larger volatility than
good news (positive shocks).
Reyes (2001) uses a bivariate AR (1)-EGRCH (1,1) model to detect the
volatility transmission in the Tokyo stock market between different size stock
indexes. Krause and Tse (2013) also employ a bivariate EGARCH (1,1) model to
find out the spillover effect from the US stock market to the Canadian stock market.
The AR (1) model is adjusted for the return series. Hence, we use the combination
AR (1) model and a variant form of EGARCH (1,1) model so as to investigate
whether the volatility of Chinese stock market returns is affected by the volatility
breakpoints of the US stock market returns, and vice versa. The experimental
models are respectively built in Equation (I.1) and Equation (I.2), as follows:
r_CNt = α0 + α1 r_CNt−1 + ϵt ~N(0, v_CNt )
log(v_CNt ) = β0 + β1 |

ϵt−1
√v_CNt−1

| + γj USbreakpoint j + β2 log(v_CNt−1 )

r_USt = а0 + а1 r_USt−1 + ϵt ~N(0, v_USt )
log(v_USt ) = ϐ0 + ϐ1 |

ϵt−1
√v_USt−1

Eq. (I.1)

Eq. (I.2)

| + πj CNbreakpoint j + log(ϐ2 v_USt−1 )
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where: r_CNt and r_USt are the stock returns at (t) day, respectively, in China
stock market and the US stock market; v_CNt and v_USt are the variance of stock
returns at (t) day, respectively, in China stock market and the US stock market;
USbreakpoint j is a volatility breakpoint dummy variable (j) at a structural
breakpoint (jth ) in the variance of US stock market returns. CNbreakpoint j is a
volatility breakpoint dummy variable (j) at a structural breakpoint (jth ) in the
variance of Chinese stock market returns. A volatility breakpoint dummy variable
(j) equals 1 the beginning from a breakpoint (j − 1)th to breakpoint (jth ) and
equals 0 in other where. The coefficients (γj ) and (πj ) respectively indicate the
impacts of volatility breakpoint (jth ) of the US stock market on China stock market,
and vice versa. The ICSS algorithm and two empirical Equations (I.1), (I.2) are
applied for three US stock market indexes (S&P500, DJIA, Nasdaq Composite)
and two China stock market indexes (Shanghai Composite, Shenzhen Composite).
By another volatility measure of the stock market returns, we mainly focus on
the S&P500 Index of the US stock market and the SSEC Index of China stock
market. In Equation (I.3) and Equation (I.4), the variance of the US stock market
returns (VOL_S&P500) and the variance of Chinese stock market returns
(VOL_SSEC) are included in the variance equation of the EGARCH (1,1) model
to replace respectively for breakpoint dummy variables in Equation (I.1) and in
Equation (I.2), as follows:
r_SSECt = α0 + α1 r_SSECt−1 + ϵt ~N(0, v_SSECt )
log(v_SSECt ) = β0 + β1 |

ϵt−1
√v_SSECt−1

Eq. (I.3)

| + ∅VOL_S&P500 + β2 log(v_SSECt−1 )

where: r_SSECt is the stock return of SSEC Index at (t) day; v_SSECt is the
variance of SSEC’s returns at (t) day; VOL_S&P500 is the variance of the
S&P500’s returns and the ∅ coefficient represents the impact of the variance of
US stock market returns on the volatility of Chinese stock market returns.
To enhance the robustness of empirical results, we use sub-samples
corresponding with the different sub-periods regarding the global financial crisis
in 2008 including the pre-financial crisis (January 2001-June 2007), during the
financial crisis (July 2007-July 2009) and post-financial crisis (August 2009–
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October 2020)4.
r_S&P500t = а0 + а1 r_S&P500t−1 + ϵt ~N(0, v_S&P500t )
log(v_S&P500t ) = ϐ0 + ϐ1 |

ϵt−1
√v_&P500t−1

Eq. (I.4)

| + ΩVOL_SSEC + log(ϐ2 v_S&P500t−1 )

r_S&P500t is the stock return of the S&P500 Index at (t) day; v_S&P500 is the
variance of S&P500’s returns at (t) day. VOL_SSEC is the variance of the Shanghai
Composite’s returns and the Ω coefficient represents the impact of variance of
Chinese stock market returns on the volatility of US stock market returns.
We use the sub-samples corresponding to the pre-2004 period5 and post-2004
period to clearly examine the degree of volatility spillovers from China to the US
stock market after the China economy become the second-largest economy in
2004 according to the PPP Index. In addition, we use a sub-sample regarding the
global financial crisis in 2008 to affirm the volatility effects from China to the US
stock market in this period. We use the EVIEW 10.0 software to estimate the AR
(1)-EGARCH (1,1) models.
1.4. Analyzing empirical results on the bidirectional volatility spillovers
between the US and China stock markets
1.4.1. Basic analyses
Table 1.1 presents the descriptive statistics for the whole of stock market returns
in both the US and China markets including the S&P500’s returns (R_S&P500),
Nasdaq Composite’s returns (R_IXIC), DJIA’s returns (R_DIJ), Shanghai
Composite’s returns (R_SSEC), and Shenzhen Composite’s returns (R_SZSC).
Overall, the mean values of stock returns in the US and China stock markets
positively range from 0.0001 to 0.0003. The standard deviation (Std. dev)
indicators show that the Chinese stock market returns (SSEC’s returns, SZSC’s
returns) are less stable than the US stock market returns (the S&P500’ returns,
Nasdaq Composite’s returns, DJIA’s returns) implying that the emerging stock
markets are more volatile than developed stock markets.
[Insert Table 1.1 here]

4
5

Following Lien et al. (2018), the global financial crisis period took place from July 2007 to July 2009.
The pre-2004 period is determined from January 2001 to December 2003.
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Table 1.2 reports the results of stationary tests for the stock return series in both
the US and China stock markets. We employ three tests for the stationarity of time
series including the Augmented Dickey–Fuller (1979) – ADF test, Phillip – Perron
(1988) – PP test, and Kwiatkowski et al. (1992) – KPSS test. In which, the results
of ADF and PP tests reject the non-stationarity of the Null hypothesis (H0) for both
the US stock market returns and Chinese stock market returns at a 1% significant
level. Moreover, the results of the KPSS test can’t dismiss the stationarity of the
Null hypothesis (H0) for both the US stock market returns and Chinese stock
market returns at any significant level. All stationary tests give a consensus
conclusion that all stock returns in both the US and China stock markets are
stationary.
[Insert Table 1.2 here]
Next, we implement the ICSS algorithm by MATLAB software to detect
structural breakpoints in the variance of stock returns in both the US and China
markets. In the period from January 2001-October 2020, we observe a total of 28
structural breakpoints in the variance of the S&P500’s returns, 36 structural
breakpoints in the variance of the DJIA’s returns, 23 structural breakpoints in the
variance of the Nasdaq Composite’s returns, 26 structural breakpoints in the
variance of the Shanghai Composite’s returns and 22 structural breakpoints in the
variance of the Shenzhen Composite’s returns. Additionally, all break dates
corresponding to the detected breakpoints are respectively presented in Table 1.3.

[Insert Table 1.3 here]
Figure 1.2 illustrates the whole of structural breakpoints in the variance of US
stock market returns and Figure 1.3 describes the whole of structural breakpoints
in the variance of Chinese stock market returns by the red vertical lines.
[Insert Figure 1.2 here]
[Insert Figure 1.3 here]
Table 1.4 respectively reports the estimated results of the AR (1)-EGARCH (1,1)
model for the volatility of US stock market returns (S&P500 Index, DJIA Index,
Nasdaq Composite Index) and the volatility of Chinese stock market returns
(SSEC Index, SZSC Index) without using the volatility breakpoints detected in
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Table 1.3, as well as, the asymmetric effect.
[Insert Table 1.4 here]
1.4.2. Empirical results on the volatility spillovers from the US to China stock
market
1.4.2.1. Modeling the volatility of Shanghai Composite Index’s returns by
using breakpoints in the variance of US stock market returns
Firstly, we investigate the volatility spillovers from the US stock market to the
Shanghai Composite (SSEC) Index of the China stock market. Table 1.5
respectively reports the estimated results of the AR (1)-EGARCH (1,1) model with
28 volatility breakpoints of the S&P500’s returns in Column (1), 36 volatility
breakpoints of DJIA’s returns in Column (2), and 23 volatility breakpoints of
Nasdaq Composite’s returns in Column (3).
[Insert Table 1.5 here]
Overall, empirical results in Column (1) indicate that the volatility of SSEC’s

returns was not frequently affected but strongly by the volatility of the S&P500’s
returns. In the period 2001-2004, the volatility breakpoints of the US stock market
returns have no impact the volatility of SSEC’s returns that is consistent with the
previous findings (Li, 2007; Moon and Yu, 2010; Wang and Wang, 2010). During
the global financial crisis in 2008, the volatility of the SSEC Index seemed to be
strongly impacted by the volatility of the S&P500 Index. Clearly, in the variance
equation, dummy variables corresponding to the volatility breakpoints of the
S&P500’s returns in 2008 are significantly positive and have higher magnitudes
than the rest dummy variables. These empirical results suggest that the volatility
shocks of the S&P500’s returns in the recession period are involved significantly
in the volatility of the SSEC’s returns. A notable break date is on 15th September
2008, the coefficient of the dummy variable reaches the highest value and is
significant at a 1% level in the variance equation. It’s not surprising because, at
this time, the Lehman Brothers group declared collapse as one of the biggest
securities companies in the US market. It seems the biggest bankruptcy in US
economic history, hence, this event is more likely to impact the whole of the
international stock market.
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