Thesis I.J. Furda

Volatility Spillovers Across Stock Indices:
Empirical Evidence from Developed Markets
I.J. Furda
Master’s thesis, MSc. Finance
ABSTRACT
This study aims to investigate volatility spillovers between global equity markets. Five major
equity indices, United States (S&P 500), Canada (Toronto 300 Composite), United Kingdom
(FTSE 100), Germany (DAX 30) and Japan (Nikkei 225) are being investigated over the years
2002 to 2015. Main findings are that during the great financial crisis overall linkages and spillovers
between the five indices intensified. Strong evidence is found that market linkages, and thereby
volatility spillovers, are increasing over time.
JEL codes: C22, F21, F65, G01, G15
Keywords: volatility spillovers, market linkages, contagion, financial crisis, MGARCH-DCC
Date Thesis: 14/01/2016
Author: Ivo Jurriën Furda
Student ID number: s1854356
Student email: i.j.furda@student.rug.nl
Name Supervisor: Marnix Reijenga

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Table of Contents
Introduction..................................................................................................................................... 3
1. Literature review...................................................................................................................... 5
Introduction...................................................................................................................... 5
Information flow .............................................................................................................. 5
Economic fundamentals versus market contagion........................................................... 5
Financial crises................................................................................................................. 7
Interlinkages between the foreign exchange market and the stock market...................... 7
Empirical methods............................................................................................................ 8
2. Hypotheses............................................................................................................................. 10
Introduction.................................................................................................................... 10
Hypotheses ..................................................................................................................... 10
3. Data & Methodology............................................................................................................. 12
Introduction.................................................................................................................... 12
Sample collection........................................................................................................... 12
Correlations.................................................................................................................... 13
Intraday volatilities......................................................................................................... 13
Overnight and daytime rate of return ............................................................................. 14
Descriptive statistics....................................................................................................... 14
ARCH family of statistical models ................................................................................ 16
Volatility spillover effects.............................................................................................. 17
Multivariate Dynamic Conditional Correlation Model.................................................. 19
4. Results ................................................................................................................................... 21
4.1 Introduction.................................................................................................................... 21
4.2 Correlations.................................................................................................................... 21

2
4.3 Intraday volatilities......................................................................................................... 24
4.4 Volatility spillover effects.............................................................................................. 25
4.5 Multivariate Dynamic Conditional Correlation Model.................................................. 27
4.6 Conclusion...................................................................................................................... 30
5 Discussion & Conclusion ...................................................................................................... 32
5.1 Introduction.................................................................................................................... 32
5.2 Discussion ...................................................................................................................... 32
5.3 Limitations ..................................................................................................................... 33
5.4 Future research ............................................................................................................... 33
5.5 Conclusion...................................................................................................................... 34
Appendix....................................................................................................................................... 35
References..................................................................................................................................... 43
Acknowledgments: I would like to sincerely thank my supervisor Marnix Reijenga for all of the
help and guidance given throughout the course of producing this dissertation.

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Introduction
The last decades have shown an increased globalization of financial markets. It can be argued that
globalization makes the overall system more efficient and leads to lower prices for consumers,
however it definitely causes difficulties as well. As within a globalized system market movements
become more intertwined, creating a well-diversified portfolio suddenly seems a lot more
complex. As an example, if volatility easily transmits from one market to another, there is no real
reason for investors to include both markets within the same portfolio.
Not only does higher integration among capital markets make it harder for investors to
diversify risks, it also makes the system more vulnerable to a financial crisis (Büttner, 2011). As
global trade among countries, nowadays, is expanding at a rapid pace, better knowledge about
volatility spillovers between markets seems rather important. It directly affects the private and
professional investors of this world but also yields important implications for politicians and
multinational firms. According to one source “the importance of investigating volatility spillovers
is, therefore, self-evident” (Mozumder, 2015, p. 44).
This study employs daily open and close data of five stock indices, for the years 2002 to 2015,
chosen from the G-7 countries. The five stock markets used for this research are the S&P 500
(United States), Toronto 300 Composite (Canada), FTSE 100 (United Kingdom), DAX 30
(Germany) and Nikkei 225 (Japan). For a more detailed picture about the data and criteria being
used, see Chapter 3. The main research question of this thesis yields:
“Is volatility of a stock market leading the volatility of other stock markets?”
Besides addressing this question the thesis constitutes three sub questions (derived and related to
the main research question). The sub questions being addressed are:
(1) Do volatility spillovers between stock indices increase during a financial crisis?
(2) Are volatility spillovers between stock indices increasing within the long-run?
(3) Is geography still a determinant factor for co-movements between equity markets?
More detailed explanations on why these questions have been chosen can be found in Chapter 2.

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The thesis is structured as follows. Chapter 1 provides the reader a literature overview on
where and how volatility spillovers do originate. Chapter 2 outlines the hypotheses. Chapter 3
describes the process of data collection and the methodology being used for the research of
volatility spillovers between the five stock indices. Chapter 4 depicts and reflects on the results of
the analyses. Chapter 5 discusses and concludes on the results of this study.

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1. Literature review
Introduction
In this chapter the conceptual framework of this research is being developed. First we take a look
at what explains volatility. Secondly we analyze how it evolves, during crises for instance and over
time. The chapter concludes with a brief literature coverage of how volatility spillovers between
financial markets can be researched.
Information flow
Volatility and risk are interrelated. When an asset or index shows greater movements, stability of
returns becomes more uncertain and thereby risk of the initial investment increases. According to
Ross (1989) price volatility equals information volatility. “Volatility is often related to the rate of
information flow” (Ross, 1989, p. 16). As information often comes in clusters, e.g. central bank
announcements or earnings figures, these are the moments when volatility should be greatest. In
other words, it implies that volatility is greatest when most information is released within the
system. Investigating volatility spillovers among global equity indices therefore not only depicts
the overall vulnerability of the system to new information, it also reveals the speed of market
adjustments to this new information. If there would not be volatility spillovers between equity
markets, it implies that the information is only important to that specific market, market-specific
fundamentals might explain the local shock (Hong, 2001). An example of this can be a change in
legislation which only applies to the local economy.
Economic fundamentals versus market contagion
Previous research has shown that there exist two main theories explaining market linkages and
spillovers between stock indices. The first theory is related to fundamentals (e.g. Solnik, 1974).
Common fundamental variables; such as an overlap in business cycles, central bank policies,
exchange rates and the overall inflation environment, might affect stock markets on a global level
(Dumas et al, 2003). In 1974 Solnik published a research in which an equilibrium model was
derived consistent with a single world market concept. The general idea of Solnik’s research is
that in an international capital market many consumption preferences are not restricted to national
output (Solnik, 1974). Grauer et al. (1976) support this theory and argue that multiplicative utility
functions are often affected by the same economic fundamentals. One should keep in mind

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however that the theory of a single world market concept depends upon restrictive assumptions
about homogenous expectations, perfect capital markets and consumption preferences.
The second theory is market contagion. Grubel and Fadner (1971) were among the first to
embark on the theoretical explanation of contagion. In their paper it is hypothesized that correlation
between equity markets is merely a function of the share of an industries’ domestic consumption.
More recently King and Wadhwani (1990) came up with a theory called the Market Contagion
Hypothesis. Foreign market price changes might reveal important information for the domestic
market as well as it shows the willingness of foreign investors to pay for certain assets. “An
individual trading in London may feel that information is revealed by the price changes in the New
York and Tokyo stock exchanges” (King and Wadhwani, 1990, p. 7). According to King and
Wadhani the rather complex structure of mapping signals leads to a ‘non-fully revealing
equilibrium’ in which price changes in a domestic market are depended upon the price changes in
foreign markets through ‘structural contagion coefficients’. Engle, Ito and Lin in 1990 conducted
a research in which informational effects on the yen/dollar exchange rate are examined. Market
dexterity, a form of market efficiency, which requires stock prices in different markets to react
simultaneously to new information, was tested throughout their research. According to Engle, Ito
and Lin (1990) if a market is dexterous and no new news comes out there will be no price
movement within this market. If this is not the case volatility spillovers are evidence against the
market dexterity hypothesis. Their empirical results reflect that the yen/dollar foreign exchange
market is not dexterous and is affected by volatility spillovers.
In 2000 Allen and Gale published a paper dedicated to financial contagion. It was found
that, due to banks holding interregional claims on other banks, a small liquidity preference shock
in a single region can lead to contagion to an arbitrarily number of n regions. More recently Forbes
and Rigobon (2002, p. 2) classified contagion as “a significant increase in cross-market linkages
after a shock to one country or group of countries”. Forbes and Rigobon state that co-movements
can only be considered as contagion if cross-market co-movements between markets increase
significantly, if this is not the case then any continued strong linkages between the two markets
exist in all states. The latter is dubbed for by the authors as mere “interdependence” between the
two markets, instead of contagion.

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Financial crises
While each financial crisis is different in its’ very nature, crises often do reflect similarities
(Reinhart and Rogoff, 2008). Typical to almost every crisis is that generally market volatility
increases sharply and spills over between and across markets. During extremely bad events, read
crises, people often act irrational and tend to ignore economic fundamentals, resulting in excess
volatility (Bae et al., 2003). The key presumption made by Bae, Karolyi and Stulz is that small
shocks propagate fundamentally different from large-return shocks. The definite onset of a
financial crisis in terms of contagion effects, however, is heavily debated for over the last decades.
It can be argued that if trade is mainly regional so should the contagion be (Glick and Rose,
1999). Another reasoning yields that even though a crisis initially has local origins and
characteristics it can eventually have a substantial effect on global trade as a whole. Due to direct
or even indirect trade linkages to global markets, a local crisis can evolve into a global instability.
After the 1997 South East Asian crisis the OECD estimated that “a slowdown in trade with Asia
could result in a fall of nearly 1 percent in the level of GDP over two years in the OECD area as a
whole” (Caporale et al, 2006, p. 376). The origin of contagion however still remains hard to
identify as it might be caused by similarities in fundamentals between markets or can simple be a
result of spillovers across markets (Alba et al., 1998).
Interlinkages between the foreign exchange market and the stock market
In order to diversify a portfolio well knowledge about volatility transmissions between stock and
foreign exchange rates is essential. Some even argue that the “efficiency of the market can also be
known through the volatility spillover across the markets” (Panda & Deo, 2014, p. 70).
Generally, there exist two theories on the relationship between stock and foreign exchange
markets. Flow-oriented models (Dornbusch and Fischer, 1980) emphasize the relationship
between the behavior of the exchange rate and the current account. Underlying thought of these
models is that exchange rate movements work through within the ability for firms to generate
profits and are thereby affecting the overall firms’ competitiveness. When the domestic currency
is becoming cheaper compared to a foreign currency exports of the domestic firms should increase.
As an effect stock prices should increase due to these increased exports. Contrary, as an exchange
rate appreciates stock prices should decrease. These models therefore assume a positive correlation
between exchange rates and stock prices.

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The second theory is called ‘stock-oriented models’. These models imply that it is capital
mobilization, not trade flows, which drives exchange rate movements (Branson, 1983). Demand
and supply for domestic assets here determine the domestic exchange rate. The lead variable here
is the stock price and a negative relation with respect to exchange rates is assumed within these
models (Mozumder, 2015). Implying that an increase in stock prices, due to an increased demand
function for these domestic assets, should make the domestic currency more expensive. If stock
prices would deteriorate however the domestic exchange rate would depreciate also. The results
of empirical research, to what extent both theories match up to reality, are mixed.
Empirical methods
Several methodologies have been derived on how to measure volatility transmissions. This section
will briefly cover two of the most applied methods. The methodology of cross-market correlation
coefficients compares the correlation between markets prior to a shock and during the shock. As
during shocks volatility within the overall system increases substantially most studies find that
volatility spillovers increase across markets during a shock (e.g. Agenor et al., 2006). King and
Wadhwani (1990) test for an increase in stock market correlations between the United States, the
United Kingdom, and Japan after the United States market crash in 1987: contagion effects
between these markets are found. Another study by Lee and Kim (1993) confirms this finding and
states that that national stock markets became more interrelated after the crash. Not only did co-
movements among stock markets increased substantially, Lee and Kim also found that when
United States stock market volatility was high, overall correlations between markets intensified.
This finding testifies that volatility can, in part, be self-sustaining.
Another, probably most known, method for analyzing the transmission mechanism
between markets is the ARCH, and related GARCH, model. A more detailed explanation of what
these models entail can be found in Chapter 3, section 3.7. Hamao et al (1990) were among the
first to find out that daily close-to-open and open-to-close returns can be deployed in the GARCH
model and its’ extensions to measure volatility transmissions. Hamao et al (1990) compared three
major stock indices (London, Tokyo and United States) and found evidence of volatility spillovers
from London to Tokyo and New York to London over the years 1985 to 1988.
Two additional techniques, which might be applied by researchers to examine spillovers,
make use of co-integrating vectors and firm-level data (see Forbes and Rigobon, 2002; Dungey et

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al., 2005). For this research is chosen to make use of correlation analysis, the GARCH (1.1.) model
plus an extension of the standard GARCH model (the MGARCH-DCC model) to analyze volatility
spillovers between five global equity markets, see Chapter 3 for a detailed explanation.

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2. Hypotheses
Introduction
In this chapter the hypotheses will be outlined. All hypotheses are supported by recent theories or
earlier research conclusions from the field, besides most of the hypotheses build on further to
sections 1.2, 1.3 and 1.4 of Chapter 1. Each hypothesis matches one of the research questions. The
first hypothesis is related to the main research question of this study: Is volatility of a stock market
leading the volatility of other stock markets? The second hypothesis is linked to sub question 1,
the third hypothesis to sub question 2 and the fourth hypothesis to sub question 3.
Hypotheses
The Market Contagion Hypothesis of King and Wadhani (1990, p. 7) states that “individuals
cannot get the full information about the market and therefore they will get information from other
markets”. The Market Contagion Hypothesis, among several other theories, see section 1.3, form
the foundation for the first hypothesis of this thesis.
H1: Volatility of a stock market is leading the volatility of other stock markets.
The second hypothesis builds further onto the literature coverage and theories explained in section
1.4, Chapter 1. During a crisis, volatility generally increases sharply and spills over across markets.
Numerous papers have found evidence of increased contagion effects during crisis times (e.g.
Calvo and Reinhart, 1996; Baig and Goldfajn, 1999). More recently Hon et al. (2007) found that
the dot-com bubble in the United States NASDAQ led to a significant structural break in co-
movements within the technology, media and telecommunication industry. The second hypothesis
of this thesis therefore becomes:
H2: Volatility spillovers between stock indices increase during a financial crisis.
Theoretically, greater bilateral trade flows in goods and financial assets between countries lead to
a synchronization of business cycles. Erb et al. (1994) researched cross-equity correlations
between the G-7 countries for the years 1970 to 1993 and found that the degree of business cycle
synchronization has a significantly positive effect on stock market integration. Another source
stated that “the impact of financial integration on cycle synchronization, in turn, is not
unambiguous” (Imbs, 2004, p. 723). As the last decades have shown increased globalization, trade

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linkages and interrelated synchronization of financial markets, it can be hypothesized that volatility
spillovers between markets over time have intensified.
H3: Volatility spillovers between stock indices increase in the long-run.
Nowadays, where the ease and speed of gathering information is high, one should expect that time
differences become of less importance to stock markets’ co-movements. Besides improved
information access and availability, over the years, digitalization has clearly led to lower
transaction costs for all market participants. Improved information availability and decreasing
transaction costs hint at geographical distances becoming of less importance for stock markets.
In determining trade flows between countries however location still seems of key
importance. Many researchers have developed gravity models in order to explain trade of goods
between countries (e.g. Engel and Rogers, 1996; Brenton et al., 1999). Strong geographic equity
market linkages, among other things, therefore can be due to countries sharing a common border.
Secondly, it is known from “the international portfolio diversification literature that portfolios are
less internationally diversified than asset allocation models would predict” (Flavin et al., 2002,
p.3). As a third argument why location still might be of influence for co-movements one should
think of, and question, overlapping trading hours. Overlapping trading hours between markets
implicitly mean that market participants often focus on the same informational signals. The fourth
and final hypothesis of this thesis therefore yields:
H4: Geographical location is a source of influence on stock markets’ co-movements.

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3. Data & Methodology
Introduction
For this research five major stock indices, S&P 500 (United States), Toronto 300 Composite
(Canada), FTSE 100 (United Kingdom), DAX 30 (Germany) and Nikkei 225 (Japan) are compared
to each other. Section 3.2 covers the collection and criteria of the data. Section 3.3 and 3.4 outline
the importance of correlations and intraday volatility correlations. Section 3.5 explains the
difference between overnight and daytime rates of return of stock exchanges. The following
section, 3.6, outlines the descriptive statistics of the continuously compounded close-to-open and
open-to-close data series. For each index a GARCH (1,1) model is created. Section 3.6 starts off
with a main introduction on the ARCH family of statistical models. Section 3.7 derives the
GARCH (1.1) being tested in this research. The last section 3.8 covers an extension, multivariate
dynamic conditional correlation, of the GARCH (1.1) model.
Sample collection
This study employs daily open and close data of five stock indices, for the years 2002 to 2015,
chosen from the G-7 countries. The five stock markets used for this research are the S&P 500
(United States), Toronto 300 Composite (Canada), FTSE 100 (United Kingdom), DAX 30
(Germany) and Nikkei 225 (Japan). All data are collected from Thomson Reuters Datastream,
Yahoo Finance and Google Finance.
In order to make solid inferences about volatility spillovers, the dataset is sorted. In other
words, only if data on a specific day is available for all five indices this data is used. Approximately
this yields around 200 days, matching for all five indices, on an annual basis. Secondly, to test for
specification under different periods, the dataset is divided into three time periods. The first time
period entails the years prior to the subprime crisis (pre-crisis), the second period covers the crisis
period (crisis) and the third period covers the years after the subprime crisis (post-crisis). The total
period of study is from March 1, 2002 to October 1, 2015 with a total of 2303 observations. The
three periods range from:
1. Pre-crisis period – March 1, 2002 to January 10, 2008 (1024 observations).
2. Crisis period – January 11, 2008 to March 31, 2009 (236 observations).
3. Post-crisis period – April 1, 2009 to October 1, 2015 (1043 observations).

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According to Diebold and Yilmaz (2012, p. 13) one can see four “volatility waves” during
the recent, global financial, crisis: July to August 2007, January to March 2008, September to
December 2008 and in the first half of 2009. There is chosen for January 11, 2008 to March 31,
2009 for the crisis period as from the January to March 2008 episode the volatility index of all
markets surged most substantially. Panda & Deo (2014, p. 72), who investigated spillover effects
between the Indian and American stock market during the recent crisis, used the same crisis period
in their research.
Correlations
Correlation analyses depict how the five stock indices move together over time. Total return index
data is used here. This is rather important as not all indices do reinvest dividends, by using total
return index data, from Thomson Reuters, this problem is accounted for.
How correlations between the five indices move or change over time can be seen as a good
starting point for anyone who wants to know more about, possible, volatility spillovers between
markets. Although correlation and volatility spillovers often are interrelated to each other this does
not need to be the case, as there could be other reasons, apart from spillover effects, which causes
correlations between markets.
Intraday volatilities
The correlation analysis tells us how indices move together over time. In order to get a better view
if intraday volatilities of these five different markets show similarities as well, chosen is to look at
intraday volatilities also. By measuring the difference for each market between the intraday high
index prices and intraday low index prices one could figure out the correlations between intraday
indices movements.
𝑅𝑖,𝑡
𝐼𝑁𝑇𝑅𝐴
= ln(𝑝𝑖,𝑡
𝐻
) − ln(𝑝𝑖,𝑡
𝐿
) (3.1)
Where i represents the country’s stock exchange and 𝑝𝑖,𝑡
𝐻
the country’s index price, intraday high
and 𝑝𝑖,𝑡
𝐿
the country’s index price, intraday low. Subsequently, the correlations of intraday stock
price movements for all five countries’ (𝑅𝑖,𝑡
𝐼𝑁𝑇𝑅𝐴
) are compared.

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Overnight and daytime rate of return
There are two parts of the stock market’s return, the close-to-open and open-to-close returns. The
close-to-open return is often dubbed as the market’s overnight rate of return:
𝑅𝑖,𝑡
𝐶𝑂
= ln(𝑝𝑖,𝑡
𝑂
) − ln(𝑝𝑖,𝑡−1
𝐶
) (3.2)
The continuously compounded close-to-open return, 𝑅𝑖,𝑡
𝐶𝑂
, denotes the movement of the domestic
stock market after the market closes and opens the next day again. The continuously open-to-close
return or daytime rate of return captures the stock markets daily, difference between close and
open price of the market, movement:
𝑅𝑖,𝑡
𝑂𝐶
= ln(𝑝𝑖,𝑡
𝐶
) − ln(𝑝𝑖,𝑡
𝑂
) (3.3)
Descriptive statistics
The descriptive statistics of the open-to-close and close-to-open data for the five stock indices can
be found in Table 1, descriptive statistics. Overall the series are not normally distributed. The value
of kurtosis is positive in all three sub-periods. This indicates a leptokurtic character of returns. In
other words, the data is asymmetric in nature.
Interesting is that for all markets mean returns are higher during the pre-crisis overnight
market (close-to-open) than during the pre-crisis daytime part of the market (open-to-close). This
points out that, during the pre-crisis period, markets reacted more strongly to news coming out
during after-market hours than during opening hours. One explanation here can be that markets
are rather interrelated to each other. Another reason can be that important domestic news often is
published during the after-market hours (often the case with quarterly earnings calls of companies
for instance). During the crisis (see Table 1.2) however this changed as for most markets
movements during market hours (open-to-close) were greater than during after-market hours
(close-to-open). Post-crisis (see Table 1.3), average after-market moves are again of greater
magnitude than movements during opening hours.
Although skewness only tells us something about the period’s daily, overnight and
daytime, distribution of mean returns with respect to the median returns, several things can be
stated. During the crisis period, skewness, in general, widened. This is implying that during crisis
times, mean and median figures became more distorted from each other. The standard deviations
of the close-to-open and open-to-close returns of the five indices confirm this. During the crisis
period, for close-to-open and open-to-close returns, standard deviations increased significantly.

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Post-crisis we see that all markets are negatively skewed, the mean is less than the median here.
Data of the post-crisis period seems to be more asymmetric in nature than the pre-crisis period. It
can be stated that the distribution of returns therefore is less clustered than prior to the crisis.
Table 1.1, descriptive statistics close-to-open and open-to-close variables (pre-crisis period)
Pre-crisis variable mean median min. max st. dev. skewness kurtosis
S&P 500 𝑅 𝑆&𝑃,𝑡
𝐶𝑂
0.00024 -0.00002 -0.04495 0.06081 0.00650 0.483 20.627
𝑅 𝑆𝑃,𝑡
𝑂𝐶
0.0000028 0.00047 -0.03644 0.06025 0.00982 0.179 6.170
Toronto 300 𝑅 𝑇𝑆𝑋,𝑡
𝐶𝑂
0.00082 0.00086 -0.03243 0.03649 0.00640 -0.213 8.100
𝑅 𝑇𝑆𝑋,𝑡
𝑂𝐶
-0.00026 0.00003 -0.03136 0.05166 0.00708 0.041 5.923
FTSE 100 𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
-0.00012 0.00032 -0.05589 0.05904 0.01136 -0.234 7.613
DAX 30 𝑅 𝐷𝐴𝑋,𝑡
𝐶𝑂
0.00053 0.00036 -0.08899 0.10568 0.01116 0.084 21.992
𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
-0.00011 0.00055 -0.05411 0.07399 0.01414 0.113 7.437
NIKKEI 225 𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝐶𝑂
0.00044 0.00080 -0.06432 0.04152 0.01047 -0.624 7.633
𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
-0.00015 -0.00025 -0.04867 0.04535 0.00960 -0.175 4.218
Table 1.2, descriptive statistics close-to-open and open close variables (crisis period)
Crisis variable mean median min. max st. dev. skewness kurtosis
𝐶𝑂
-0.00153 -0.00044 -0.09142 0.11615 0.01632 0.398 22.267
𝑅 𝑆𝑃,𝑡
𝑂𝐶
-0.00092 0.00103 -0.09127 0.10246 0.02392 -0.121 5.579
𝐶𝑂
-0.00084 -0.00027 -0.08562 0.17261 0.02128 1.689 22.827
𝑂𝐶
-0.00105 0.00026 -0.07891 0.07154 0.02014 -0.389 5.680
𝑂𝐶
-0.00203 -0.00185 -0.09265 0.08469 0.02153 -0.076 5.901
𝐶𝑂
-0.00103 0.00015 -0.10405 0.12223 0.01951 0.159 16.455
𝑂𝐶
-0.00166 -0.00209 -0.06486 0.11141 0.02002 0.659 8.113
𝐶𝑂
-0.00084 -0.00025 -0.06841 0.05467 0.01640 -0.314 5.964
𝑂𝐶
-0.00159 -0.00160 -0.10563 0.11658 0.02344 -0.198 9.240
Table 1.3, descriptive statistics close-to-open and open close variables (post-crisis period)
Post-crisis variable mean median min. max st. dev. skewness kurtosis
𝐶𝑂
0.00018 0.00030 -0.06827 0.04682 0.00774 -0.652 15.782
𝑅 𝑆&𝑃,𝑡
𝑂𝐶
0.00071 0.00096 -0.04891 0.04563 0.01005 -0.298 5.975
𝐶𝑂
0.00022 0.00026 -0.05065 0.08428 0.00882 -0.064 15.008
𝑂𝐶
0.00018 0.00064 -0.03597 0.03346 0.00768 -0.214 4.920
𝑂𝐶
0.00029 0.00043 -0.04779 0.04193 0.01075 -0.108 4.531
𝐶𝑂
0.00064 0.00102 -0.06707 0.06352 0.01172 -0.429 7.784
𝑂𝐶
0.00017 0.00043 -0.07336 0.05879 0.01182 -0.194 5.781
𝐶𝑂
0.00086 0.00131 -0.08258 0.10326 0.01324 -0.067 9.693
𝑂𝐶
-0.00011 0.00002 -0.09277 0.05544 0.00999 -1.164 16.232

16
ARCH family of statistical models
In this research the standard GARCH (1.1) and an extension, the multivariate dynamic conditional
correlation model, are used. As there are many extensions to the ARCH and GARCH models, we
begin with a brief review of the ARCH family of statistical models. To capture the effect of
changing volatility in a time series, Engle (1982) developed the autoregressive conditionally
heteroscedastic (ARCH) model where the conditional variance 𝜎𝑡
2
is a linear function of past
squared errors. The simplest representation of this model is an ARCH (1) which has the form
𝑦𝑡 = 𝛽1 + ∑ 𝛽𝑖
𝑛
𝑖=2
𝑥𝑖𝑡 + 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
𝜎𝑡
2
= 𝛼0 + 𝛼1 ∈ 𝑡−1
2
where 𝑦𝑡 denotes the stock return in one market, and 𝑥𝑖𝑡 are the factors that could influence the
stock return. Although the ARCH framework forms the basis for many models it comes along with
some difficulties. First, it is not clear how to decide on the number of lags of squared residuals.
Second, the number of lags of squared errors might be very large if required to capture all
dependences in the conditional variance. Third, non-negativity constraints might be violated. “The
more parameters there are in the conditional variance equation, the more likely it is that one or
more of them will have negative estimated values” (Brooks, 2008, p. 391).
Four years later, in 1986, Bollerslev (1986) and Taylor (1986) independently developed
the GARCH model. The GARCH framework differs from the ARCH framework by the fact that
it allows the conditional variance to be dependent upon its’ previous own lags
𝜎𝑡
2
= 𝛼0 + 𝛼1 ∈ 𝑡−1
2
+ 𝛽𝜎𝑡−1
2
Over the years, several extensions have been made to GARCH models, resulting in more complex
hybrid models. Generally, as it is widely used among practitioners nowadays, it can be stated that
the ARCH model has been outdated by the GARCH model and its’ extensions.

17
Volatility spillover effects
In this research a GARCH (1.1) model is applied, where the domestic continuously compounded
close-to-open (equation 3.2) return is taken as a dependent variable and the continuously open-to-
close return (equation 3.3) of the foreign market is added as an independent variable. Due to time
differences, see Appendix Figure A. 1, lagged open-to-close returns are being used when
necessary.
S&P 500
The GARCH (1,1) model for the American market with respect to spillovers from the British
market therefore becomes:
𝑅𝑆&𝑃,𝑡
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
𝜎𝑡
2
= 𝛼0 + 𝛼1 ∈ 𝑡−1
2
+ 𝛽𝜎𝑡−1
2
As the S&P 500 and the Toronto 300 Composite index trade at the same hours, this effect is not
estimated. For sake of simplicity, for the other markets only the mean models are shown.
American market with respect to spillovers from the German market:
𝑅𝑆&𝑃,𝑡
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
American market with respect to spillovers from the Japanese market:
𝑅𝑆&𝑃,𝑡
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
Toronto 300 Composite index
The GARCH (1,1) model for the Canadian market with respect to spillovers from the British
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
Canadian market with respect to spillovers from the German market:
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
Canadian market with respect to spillovers from the Japanese market:
𝐶𝑂
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)

18
DAX 30
The GARCH (1,1) model for the German market with respect to spillovers from the American
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅𝑆&𝑃,𝑡−1
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
German market with respect to spillovers from the Canadian market:
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
German market with respect to spillovers from the British market:
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
German market with respect to spillovers from the Japanese market:
𝐶𝑂
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
NIKKEI 225
The GARCH (1,1) model for the Japanese market with respect to spillovers from the American
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅𝑆&𝑃,𝑡−1
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
Japanese market with respect to spillovers from the Canadian market:
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
Japanese market with respect to spillovers from the British market:
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
Japanese market with respect to spillovers from the German market:
𝐶𝑂
= 𝛽1 + 𝛽2 𝑅 𝐷𝐴𝑋,𝑡−1
𝑂𝐶
+ 𝜖 𝑡, ∈ 𝑡 ~ 𝑁 (0, 𝜎𝑡
2
)
Unfortunately, the FTSE 100 close-to-open return cannot be calculated as notational difficulties
make it impossible to extract the “real” opening prices from historical databases. Often the opening
price depicts the closing price of the former trading day. The New York Times even created a
special index to circumvent this problem, which states the opening price as of 08:03 (GMT). Long-
term daily data, for the years 2002 to 2015, from this index however could not be obtained.
Volatility spillovers from other markets to the FTSE 100 therefore are not calculated. As a result,
the open-to-close return of the FTSE 100 indeed captures the overnight return also, there is chosen
for this as it still provides us with valuable insights.

19
Multivariate Dynamic Conditional Correlation Model
An extensive literature (e.g. Bauwens et al., 2003) on alternative GARCH specifications exists,
here we will look deeper into a specific extension of the GARCH (1.1.) model, the multivariate
GARCH (MGARCH) models. The general MGARCH framework yields
𝑦𝑡 = 𝐶𝑥𝑡 + ∈ 𝑡
∈ 𝑡 = 𝐻𝑡
1/2
𝑣𝑡
where 𝑦𝑡 is a m-vector of dependent variables, C is a m x k parameter matrix, 𝑥𝑡 is a k-vector of
explanatory variables, 𝐻𝑡
1/2
is the Cholesky factor of the time-varying conditional covariance
matrix 𝐻𝑡, and 𝑣𝑡 is a m-vector of zero-mean, unit-variance independent and identically distributed
innovations (Baum, 2014).
Most applied multivariate volatility spillover models are the Constant Conditional
Correlation (CCC) model of Bollerslev (1990) and the Dynamic Conditional Correlation (DCC)
model of Engle (2002). Main criticism on the CCC model is that it does not account well for time-
varying correlations (see Tse, 2000; Savva & Osborn, 2004; Aielli, 2013). Another “desirable
practical feature of the DCC models, is that multivariate and univariate volatility forecasts are
consistent with each other. When new variables are added to the system, the volatility forecasts of
the original assets will be unchanged and correlations may even remain unchanged depending
upon how the model is revised.” (Engle, 2002, p. 29). For this reason, apart from the standard
GARCH (1.1) model, the DCC model is applied within this research. The DCC GARCH model
proposed by Engle (2002) can be written as
𝑦𝑡 = 𝐶𝑥𝑡 + ∈ 𝑡
∈ 𝑡 = 𝐻𝑡
1/2
𝑣𝑡
𝐻𝑡 = 𝐷𝑡
1/2
𝑅𝑡 𝐷𝑡
1/2
𝑅𝑡 = diag(𝑄𝑡)−1/2
𝑄𝑡diag(𝑄𝑡)−1/2
𝑄𝑡 = (1 − 𝜆1 − 𝜆2)𝑅 + 𝜆1 ∈̃ 𝑡−1∈̃́
𝑡−1+ 𝜆2 𝑄𝑡−1
where
𝑦𝑡 is an m x 1 vector of dependent variables;
𝐶 is an m x k matrix of parameters;
𝑥𝑡 is k x 1 vector of independent variables, which may contain lags of 𝑦𝑡;
𝐻𝑡
1/2
is the Cholesky factor of the time-varying conditional covariance matrix 𝐻𝑡;
𝑣𝑡 is an m x 1 vector of normal, independent, and identically distributed innovations;
and 𝐷𝑡 is a diagonal matrix of conditional variances.

20
For our analysis as a dependent is chosen for the domestic close-to-open returns and all,
three or four in our case, foreign market open-to-close returns are added to the mean part of the
model, see Results section 4.5.

21
4. Results
4.1 Introduction
The long-term success of a portfolio or wealth manager crucially depends upon investment
correlations. In order to reduce risks, and diversify a subset of investments accordingly, knowledge
about asset correlations is of key importance. Section 4.2 and 4.3 provide correlation and intraday
volatility correlation analyses of the five indices. Section 4.4 reflects on the results of the GARCH
(1.1) model. Section 4.5 depicts the results of the MGARCH-DCC model. The concluding section
4.6 sums up the results.
4.2 Correlations
Table 2 and 3 depict the correlations and intraday volatility correlations (see Chapter 3, sections
3.3 and 3.4) of the five indices. These correlations are calculated by use of the total return index,
which reinvests dividends, from Thomson Reuters Datastream. Graph 1 shows what would have
happened if you would have invested your money, not corrected for exchange rate effects, at the
beginning of 2002 in each of the five indices.
Graph 1, total return index, period January 2002 – October 2015
0
50
100
150
200
250
300
S&P 500 FTSE 100 DAX 30 TSX NIKKEI 225

22
It is interesting to see that, over the last 13 years, the DAX 30, FTSE 100 and the S&P500 basically
moved along the same pattern. Although the Toronto 300 Composite and Nikkei 225 depict strong
correlations to the DAX 30, FTSE 100 and S&P 500, periodically, movements of both indices
differ. Whereas the decline of Japanese stock markets clearly set off from beginning 2007, the
Toronto 300 Composite index showed its’ first signs of weakness just 1.5 years later, as of the
middle of 2008. The Canadian index also recovered most strongly from the crisis, whereas the
Japanese index struggled to recover. Table 2 shows how the five indices are correlated to each
other in the three different periods. The three periods range from:
1. Pre-crisis period – January 7, 2002 to January 10, 2008
2. Crisis period – January 11, 2008 to March 31, 2009
3. Post-crisis period – April 1, 2009 to October 1, 2015
Table 2, correlations, total return index
INDICES S&P TSX NIKKEI FTSE DAX
S&P (prior)
S&P (crisis)
S&P (after)
1
1
1
TSX (prior)
TSX (crisis)
TSX (after)
0.981***
0.969***
0.948***
1
1
1
NIKKEI (prior)
NIKKEI (crisis)
NIKKEI (after)
0.937***
0.978***
0.928***
0.960***
0.982***
0.854***
1
1
1
FTSE (prior)
FTSE (crisis)
FTSE (after)
0.976***
0.983***
0.970***
0.983***
0.955***
0.945***
0.965***
0.964***
0.862***
1
1
1
DAX (prior)
DAX (crisis)
DAX (after)
0.948***
0.991***
0.972***
0.939***
0.955***
0.946***
0.923***
0.975***
0.938***
0.970***
0.984***
0.956***
1
1
1
t statistics in parentheses
*
p < 0.05, **
p < 0.01, ***
p < 0.001
As expected, all correlations are significantly different from zero at a 0.001 significance level. All
correlations range from 0.854 (after crisis, Nikkei 225 versus Toronto 300 Composite) to 0.991
(crisis, DAX 30 versus S&P 500). This already depicts that markets are rather interrelated and
thereby can be seen as a first sign for supporting the first hypothesis (H1: Volatility of a stock
market is leading the volatility of other stock markets). During the crisis we see that correlations
between markets intensified. Except for correlations between the Toronto 300 Composite versus

23
FTSE 100 and Toronto 300 Composite versus S&P 500 all markets became more dependent on
each other. Once again this should be seen as a first sign that our second hypothesis holds (H2:
Volatility spillovers between stock indices increase during a financial crisis).
With respect to the third and fourth hypothesis, evidence is mixed. When comparing the
pre-crisis period versus the post-crisis period for some markets we see evidence correlations
between markets, over time, intensified, but not for all (e.g. FTSE 100 versus Nikkei 225). The
other analyses should clarify if volatility spillovers are indeed increasing over time (H3: Volatility
spillovers between stock indices increase in the long-run.). With respect to finding influences of
geography being a factor in determining co-movements (H4: Geographical location is a source of
influence on stock markets’ co-movements.) the results show a mixed picture. Correlations between
close geographical markets tend to be rather strong, e.g. DAX 30 versus FTSE 100 and S&P versus
Toronto 300 Composite, however so are correlations for separate geographical markets (e.g.
Nikkei versus S&P 500). Furthermore, correlations between close geographical markets are not
becoming stronger. So although correlations between close geographical markets remain strong,
and hereby clearly can be a source of influence, geography as a factor is not becoming more
important over time.
To see how these correlations moved in each of the different years (2002 to 2015) see Table
A. IV in the Appendix. The crisis year 2008 clearly shows the strongest correlations between all
markets. The years 2012, 2014 and 2015 (January to October) can be seen as special years in the
sense that overall correlations between markets decreased strongly. The Nikkei 225 is remarkable
by the fact that during the years 2004, 2007 and 2010 to 2012 the correlations with other markets
decreased significantly. Possible explanations for this can be that Japan’s business cycle is not
matching the business cycle of the other countries in those years, has a diverged monetary policy
or that other major internal events happened (e.g. a tsunami in 2011). With respect to a general
weakening of correlations over the years 2012, 2014 and 2015 there are several possible
explanations. Likely a worsening of the Euro crisis in 2012 and 2014, different central bank
policies, interventions in Ukraine in 2014 and the recently collapsed oil price are the main drivers
of this weakening of correlations during these three years.

24
4.3 Intraday volatilities
As correlations show how markets moved different over time it does not really tell us how markets
react to each other on a daily basis. Intraday volatility correlations (see Chapter 3, section 3.4)
already give us a better indication how daily volatility movements are related to each other. Table
3 shows the intraday volatility, daily difference between high and low prices, correlations.
Additionally, Figure A. III within the Appendix graphically depicts these intraday movements of
the five indices over the years 2002 to 2015.
Table 3, intraday volatility correlations, total return index
INDICES S&P TSX NIKKEI FTSE DAX
S&P (prior) 1
S&P (crisis) 1
S&P (after) 1
TSX (prior) 0.605***
1
TSX (crisis) 0.834***
1
TSX (after) 0.774***
1
NIKKEI (prior) 0.353***
0.1969***
1
NIKKEI (crisis) 0.608***
0.636***
1
NIKKEI (after) 0.211***
0.186***
1
FTSE (prior) 0.720***
0.491***
0.374***
1
FTSE (crisis) 0.709***
0.738***
0.631***
1
FTSE (after) 0.772***
0.681***
0.246***
1
DAX (prior) 0.760***
0.373***
0.385***
0.799***
1
DAX (crisis) 0.747***
0.692***
0.681***
0.820***
1
DAX (after) 0.709***
0.601***
0.173***
0.956***
1
t statistics in parentheses
*
p < 0.05, **
p < 0.01, ***
p < 0.001
Although intraday volatility correlations are less strong than general correlations all intraday
volatility correlations are significantly different from zero at a 0.001 significance level (H1).
During crisis times all intraday volatility correlations increased significantly (H2). Except for the
Japanese Nikkei 225 index, pre-crisis versus post-crisis, intraday volatility correlations increased
over time (H3). Furthermore, it is remarkable to note that intraday volatility movements between
geographic close areas are rather strong (Toronto 300 Composite versus S&P500 and the DAX 30
versus FTSE 100) but also intensified over the years. Geography thereby clearly seems of influence
(H4) with respect to intraday volatility movements.

25
4.4 Volatility spillover effects
Table A. V to A. XV within Appendix show the individual GARCH (1,1) models derived in
Chapter 3, section 3.8. As the output of all the models is rather extensive, for sake of simplicity,
only the betas of the open-to-close series are depicted in Table 4.
Table 4, betas of open-to-close series of GARCH (1.1) models.
𝐶𝑂
𝛽2 𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝛽2 𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝛽2
pre-crisis (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.0610*** (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.0472*** (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.0239***
crisis (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.340*** (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) -0.239*** (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.207***
post-crisis (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.0982*** (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.0399** (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.117***
TORONTO 𝑅 𝑇𝑆𝑋,𝑡
𝐶𝑂
𝛽2 𝑅 𝑇𝑆𝑋,𝑡
𝐶𝑂
𝛽2 𝑅 𝑇𝑆𝑋,𝑡
𝐶𝑂
𝛽2
pre-crisis (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.164*** (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.0961*** (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.102***
crisis (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.181*** (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.161*** (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.360***
post-crisis (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.295*** (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.198*** (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.170***
𝐶𝑂
𝛽2 𝑅 𝐷𝐴𝑋,𝑡
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝛽2
pre-crisis (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.235*** (𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
) 0.174*** (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) -0.0137 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.152***
crisis (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.156*** (𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
) 0.127*** (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) -0.0501 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.313***
post-crisis (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.140*** (𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
) 0.149*** (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) -0.0778** (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.330***
𝐶𝑂
𝛽2 𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝛽2
pre-crisis (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.483*** (𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
) 0.404*** (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) 0.315*** (𝑅 𝐷𝐴𝑋,𝑡−1
𝑂𝐶
) 0.311***
crisis (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.317*** (𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
) 0.251*** (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) 0.217*** (𝑅 𝐷𝐴𝑋,𝑡−1
𝑂𝐶
) 0.233***
post-crisis (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.616*** (𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
) 0.494*** (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) 0.431*** (𝑅 𝐷𝐴𝑋,𝑡−1
𝑂𝐶
) 0.448***
*** p<0.01, ** p<0.05, * p<0.1
As almost all betas are significantly positive: H1 is confirmed. Earlier we saw that indices and
intraday volatilities are strongly correlated to each other, now we see that foreign daytime (open-
to-close) movements are able to explain overnight (close-to-open) movements of stock indices.
Volatility spillovers therefore are real. During the crisis, spillovers increased significantly from
the FTSE 100, DAX 30 and Nikkei 225 (open-to-close) towards the S&P 500. The same is the
case for spillovers towards the Canadian Toronto 300 Composite index. For the DAX 30 (except
for spillovers from the Nikkei 225) and the Nikkei 225 spillovers during the crisis did not intensify.
The fact that America opens later than Tokyo, Berlin and London might explain why the
S&P 500 overnight’s return was so heavily influenced by other the markets’ daytime rate of return
during the crisis. Subsequently, overlapping trading hours of markets likely result in the fact that
most spillovers to the DAX 30 happen during opening hours. Japan’s different picture might be

26
explained by the fact that Japan is following a somewhat different route in terms of economic
sentiment, business cycle and domestic central bank policy. As a general conclusion to the second
hypothesis, during a crisis close-to-open returns are more affected to volatility spillovers from
foreign open-to-close returns, but not necessarily in all cases (H2).
Comparing the pre-crisis period to the post-crisis period we see that, generally, volatility
spillovers between markets over time intensified. This can be interpreted as that domestic markets
are becoming more sensitive to what happens on foreign exchange markets, which is pointing at
an increased globalization of financial markets (H3).

27
4.5 Multivariate Dynamic Conditional Correlation Model
In this section we cover the multivariate dynamic conditional correlation model. Table 5.1 depicts
the pre-crisis period, Table 5.2 the crisis period and Table 5.3 the post-crisis period.
Table 5.1, pre-crisis, multivariate dynamic conditional correlation model
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
VARIABLES VARIABLES VARIABLES VARIABLES
𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
0.156*** 𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
0.151*** 𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
0.228*** 𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
0.379***
(0.0283) (0.0247) (0.0377) (0.042)
𝑂𝐶
-0.0588** 𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
0.0025 𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
-0.0194 𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
-0.0199
(0.0245) (0.0194) (0.0451) (0.0489)
𝑂𝐶 -0.021 𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶 0.0717*** 𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶 0.130*** 𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
0.0861**
(0.0188) (0.0199) (0.0268) (0.0372)
𝑅 𝐷𝐴𝑋,𝑡−1
𝑂𝐶
0.102***
(0.0353)
MGARCH (1,1) MGARCH (1,1) MGARCH (1,1) MGARCH (1,1)
Constant 1.41e-07*** Constant 3.4e-05*** Constant 3.40e-07*** Constant 6.76e-07***
(5.04E-08) (3.91E-06) (1.24E-07) (2.48E-07)
α 0.0236*** α 0.119*** α 0.0286*** α 0.0192***
(0.00443) (0.0331) (0.00521) (0.00437)
β 0.973*** β -0.0108 β 0.968*** β 0.973***
(0.00437) (0.0951) (0.00511) (0.00598)
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
During the pre-crisis period the S&P 500 overnight return is most affected by the daytime rate of
return of the FTSE 100 (0.156), interestingly daytime movements of the Japanese Nikkei 225 are
not affecting the S&P 500 (-0.021). The Nikkei 225 (open-to-close) however is influencing the
Toronto 300 Composite close-to-open return (0.0717).
Not unsurprisingly the DAX 30 and Nikkei overnight’s return are most affected by the
S&P 500 daytime rate of return (0.228 and 0.379). The Nikkei’s overnight return is more
influenced by the DAX 30 daytime rate of return than by the FTSE 100 daytime rate of return
(0.102 versus 0.0861). One explanation for this can be time differences, as the DAX 30 compared
to Japan closes one hour later than the FTSE 100 index. Another, more likely, reason can be that
Germany is a more important trade partner to Japan than the United Kingdom. Supported by the
theoretical explanation that trade linkages, see section 1.3 in Chapter 1, might explain contagion
effects this would make sense. More research is needed however in order to proof this.

28
Table 5.2 depicts the crisis period. As this period is more volatile we expect greater
volatility spillovers between all markets and subsequently the signs to increase in magnitude.
Table 5.2, crisis, multivariate conditional correlation model
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝑂𝐶
0.284*** 𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
0.389*** 𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
-0.0745* 𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
0.375***
(0.0587) (0.117) (0.0404) (0.0527)
𝑂𝐶
-0.207*** 𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
-0.272** 𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
0.0277 𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
-0.0566
(0.0706) (0.12) (0.0405) (0.0526)
𝑂𝐶
0.141*** 𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
0.358*** 𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
0.481*** 𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
0.093
(0.0412) (0.0703) (0.038) (0.0587)
𝑂𝐶
-0.0253
(0.0762)
Constant 6.32E-07 Constant 2.66E-06 Constant 0.000109*** Constant 0.000504***
(5.52E-07) (2.3E-06) (2.14E-05) (4.31E-05)
α 0.129*** α 0.113*** α 1.614*** α -0.0238***
(0.0247) (0.0324) (0.472) (0.00222)
β 0.903*** β 0.892*** β -0.00118 β -0.993***
(0.0125) (0.0263) (0.00715) (0.00155)
With respect to the S&P 500 overnight’s return we see that all signs indeed increased in magnitude
during the crisis, FTSE 100 (pre-crisis 0.156 versus crisis 0.284), DAX 30 (pre-crisis -0.0588
versus crisis -0.207), Nikkei 225 (pre-crisis -0.021 versus 0.141). The same is the case for the
Toronto 300 Composite overnight’s return, FTSE 100 (pre-crisis 0.151 versus crisis 0.389), DAX
30 (pre-crisis 0.00225 versus crisis -0.272), Nikkei 225 (pre-crisis 0.0717 versus crisis 0.358).
The DAX 30 overnight’s return during the crisis significantly increased w.r.t. the Nikkei’s
daytime rate of return (pre-crisis 0.130 versus 0.481). Rationally this makes sense as the Nikkei,
of the five indices, is the market closest to the opening hours of the DAX 30, see Appendix, Graph
A. 1. Once again the Nikkei 225 behaves differently from the rest, as Nikkei’s overnight rate of
return is not per se more heavily influenced, by the foreign daytime rate of returns, during the
crisis. Overall H2 is confirmed, volatility spillovers do increase during crisis times.

29
Table 5.3 depicts the post-crisis period. As this period is less volatile than the crisis period we
expect smaller volatility spillovers between all markets, besides we are interested how this period
compares to the pre-crisis period (H3).
Table 5.3, post-crisis, multivariate conditional correlation model
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝑂𝐶
0.0986*** 𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
0.231*** 𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
0.121*** 𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
0.432***
(0.023) (0.0315) (0.0438) (0.0503)
𝑂𝐶 0.0876*** 𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
0.0521* 𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
0.0713 𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
0.0169
(0.0242) (0.0282) (0.0557) (0.0513)
𝑂𝐶 0.106*** 𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶 0.334*** 𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
0.0257
(0.0238) (0.03) (0.0422)
𝑂𝐶
0.208***
(0.0384)
Constant 0.000101*** Constant 1.5e-06*** Constant 3.04e-06*** Constant 3.53e-06***
(6.92E-06) (4.1E-07) (1.04E-06) (8.87E-07)
α -0.00997*** α 0.0662*** α 0.0450*** α 0.0497***
(0.00152) (0.0131) (0.00989) (0.0102)
β -0.799*** β 0.914*** β 0.929*** β 0.921***
(0.105) (0.0142) (0.0158) (0.0145)
Due to computational issues the statistical program (Stata) had with calculating the original DCC for the American market (close-to-open) DAX
returns (open-to-close) are not included within the model. Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
For the Toronto 300 Composite overnight’s return we observe that post-crisis volatility spillovers
are of greater magnitude than the prior-crisis volatility spillovers, FTSE 100 (pre-crisis 0.151
versus crisis 0.389 versus post-crisis 0.231), DAX 30 (pre-crisis 0.00225 versus crisis -0.272
versus post-crisis 0.0521), Nikkei 225 (pre-crisis 0.0717 versus crisis 0.358 versus post-crisis
0.106). Volatility spillovers to the Canadian market are increasing over time (H3).
For the DAX 30 index we find mixed evidence for H3, S&P 500 (pre-crisis 0.228 versus
crisis -0.0745 versus post-crisis 0.121), Nikkei 225 (pre-crisis 0.130 versus crisis 0.481 versus
post-crisis 0.334). Volatility spillovers from the Japanese market to the German market are
increasing over time but not from the American market to the German market. A possible
explanation for this is that most spillovers between the S&P 500 and the DAX 30 happen during
opening hours. For the Japanese market we find evidence for H3 for the spillovers from the S&P
500 (pre-crisis 0.379 versus crisis 0.375 versus post-crisis 0.432) and the DAX 30 (pre-crisis 0.102
versus crisis -0.0253 versus post-crisis 0.208).

30
For the American market, post-crisis spillover effects to the S&P 500 are smaller than pre-crisis
spillover effects, e.g. FTSE 100 (pre-crisis 0.156 versus crisis 0.284 versus post-crisis 0.0986).
Therefore, H3 cannot be confirmed for the American market. The fact that spillovers to America
are not increasing over time might be due to the relative size of the American equity market, see
Appendix Figure A. II.
4.6 Conclusion
In conclusion, this thesis tried to answer the main research question:
“Is volatility of a stock market leading the volatility of other stock markets?”
Basically all results depict this to be the case. Correlations and intraday volatility correlations
between all markets are rather strong (see Table 2 and 3). Besides, foreign open-to-close returns
significantly explain domestic close-to-open returns (see Table 4, 5.1, 5.2 and 5.3). Both GARCH
(1.1.) and MGARCH-DCC models confirm that volatility spillovers between the five indices do
exist: H1 is confirmed.
The first sub question and hypothesis 2 of this thesis are related to spillover effects during
a financial crisis. During crisis times, January 2008 to March 2009, overall correlations between
the five indices intensified. Intraday volatility correlations confirm this finding, a significant
increase during the crisis was found with respect to intraday volatility movements among the five
indices. Spillovers from foreign markets’ daytime rate of return on the S&P 500 and Toronto 300
Composite overnight’s rate of return did increase during the crisis. Germany’s DAX 30 overnight’s
rate of return, during the crisis, was not per se more affected by other markets’ daytime rate of
return. Spillovers from Japan (Nikkei 225) to Germany being an exception here. Most likely this
is explained by the fact that most volatility, from the S&P 500, Toronto 300 Composite and FTSE
100, towards the German market spills over during trading hours. Compared to all the markets
Japan shows a different picture from the rest, as volatility spillovers of foreign daytime movements
during the crisis did not intensify. Except for the Japanese market: H2 is confirmed.
The second sub question and hypothesis 3 of this thesis were aimed at spillovers and its’
relation to time. Depending upon which market linkage is being investigated, H3 for some linkages
holds (e.g. DAX 30 versus S&P 500) but for other linkages clearly does not (e.g. Toronto 300
Composite versus Nikkei 225). Both GARCH and MGARCH-DCC depict results hinting at an
increased integration of financial markets. Although, spillover effects to the S&P 500 for the post-

31
crisis period are smaller than during the pre-crisis period, spillovers on the other markets,
generally, increased. Not only does this hint at an increased integration of financial markets, it also
implies that the importance of the American market over time, 2002 to 2015, intensified. Except
for the American market: H3 is confirmed.
The last sub question and hypothesis of this study yielded that market linkages are related
to geographical closeness and overlapping trading hours. The correlation analysis depicts strong
linkages between close geographical markets. Other markets, geographically separated, however
reported equally strong linkages. Correlations between close geographical markets, however, did
not intensify over time. Geography thereby can still be a determinant factor, but does not seem to
become more important. Contrary, the intraday volatility correlations showed increased linkages
between close geographical markets over time. The results can be interpreted as that markets with
overlapping trading hours are becoming more dependent on each other, on a daily basis, but does
not necessarily have to explain long-term co-movements’ of both markets. The results for H4
thereby are mixed. More research is needed in order to determine and measure the exact impact
and importance of markets’ geographical closeness.

32
5 Discussion & Conclusion
5.1 Introduction
This final Chapter summarizes the results of this study. Section 5.2 discusses the results and
elaborates on future implications. Section 5.3 states the limitations of this research. Section 5.4
comes up with recommendations with respect to future research. Section 5.5 briefly concludes on
the most important findings of this study.
5.2 Discussion
During crisis times, January 2008 to March 2009, overall correlations between the five indices
intensified. Intraday volatility correlations and the GARCH analyses confirm this finding. This
study has shown that volatility spillovers across developed equity markets increased substantially.
As the last decades have shown an increased digitalization and globalization of financial
markets one should think of the implications. It can be argued that an interrelated system is most
efficient, it also can be proposed that it is more vulnerable. This research has shown that during
the great financial crisis markets became more dependent on each other, how this relates to other
periods of instability for now remains unclear. An open question therefore remains: Are spillovers
during a crisis becoming more severe, compared to other crises, due to an increased globalization
of financial markets?
Another observation of this study is that, generally, developed equity markets, over time,
are becoming more related to each other. This finding does not only question long-term
diversification strategies it also yields broader implications for global policy makers and
multinational enterprises. Due to increased digitalization and integration of financial markets
former ‘local’ actions might originate into ‘global’ instabilities. It stipulates that global leaders
should be more aware of what happens elsewhere in the world. Constructive interregional
communications and a critical, but open, decision-making process seem to benefit market
participants most. Remarkable is that the importance of the American market over time, 2002 to
2015, intensified. Is this a trend which will continue? Within the next decade it could be equally
likely that America’s dominance will be offset by an increased dominance of the Asian markets.

33
5.3 Limitations
This study yields several limitations. First of all, a limited period (2002 to 2015) is observed.
Observing a longer time period, and multiple crisis periods, might reveal more details about how
spillovers evolve over time.
Secondly, this research focused on determining volatility spillovers across equity indices
of developed markets, which is a limitation by itself. Analyzing more equity, developed and
developing, markets might bring up new valuable insights.
Thirdly, observing more than just equity market interactions, e.g. by adding foreign
exchange, bond or commodity markets to the equation, might bring up valuable explanations with
respect to the origin of volatility spillovers across global equity markets. This requires more
advanced and deeper research models. Future studies therefore might want to apply higher-order
models, capable of sketching a multidimensional view.
5.4 Future research
The importance of trade flows, exchange rates, regional and global business cycle differences,
geography being a factor and different monetary policies all seem plausible factors explaining the
origins of spillovers on financial markets. It can be stated that volatility spillovers probably are the
result of the interplay between all of these factors, more advanced models are needed however in
order to quantify the exact impact of these factors with respect to volatility spillovers. In order to
explain the total picture, higher-order interactions between factors such as trade flows, exchange
rates, regional and global business cycle differences, overlapping trading hours and different
monetary policies need to be tested accordingly. Future work should aim at coming up with more
narrowed definitions and models explaining the origin of volatility spillovers.
This study has also shown that the Japanese equity market behaves fundamentally different
from the other, United States, Canada, United Kingdom and Germany, OECD equity markets. A
possible explanation is that Japan’s internal policy, business cycle and domestic central bank
policy differ. Future research is needed here to confirm, or reject, these possible explanations.
Most importantly, future work should focus on the broader implications, discussed in section 5.2,
of the integration of financial markets. Whether globalization leads to greater instabilities and if
America’s dominance on financial markets will become stronger, from my point of view, are topics
which require most attention.

34
5.5 Conclusion
Improved knowledge about volatility spillovers not only benefits the average investor and portfolio
managers but also yields important implications for policy makers and multinational firms. For
national firms, a globalized functioning of financial markets might offer opportunities with respect
to economies of scale but also poses risks in terms of diversification, and hedging, the firm’s
investment portfolio. For politicians, globalization across financial markets stipulates that political
and global leaders should be well aware of what happens elsewhere in the world. As the
implications of spillover effects eventually do affect us all, research regarding volatility spillovers
is self-evident. By use of several analyses, this study has shown that volatility within one equity
market is often leading the volatility of other equity markets. The main research question of this
thesis thereby is answered. Most important findings of this study are:
- All analyses underline that, during the years 2002 to 2015, volatility spillovers across the
S&P500, Toronto 300 Composite, FTSE 100, DAX 30 and Nikkei 225 indices existed.
- During the great financial crisis, January 2008 to March 2009, overall correlations and
spillovers between the five indices intensified.
- Strong evidence is found that market linkages, and thereby volatility spillovers, over time
are increasing. As an effect the dominance of the American equity market on other markets
seems to be increasing over time, 2002 to 2015.
- On several aspects the Japanese equity market behaves differently. More in-depth research
is needed to explain the different behavior of the Japanese equity market.
The results of this study thereby have provided insights and answers to several questions, but also
raises new ones. Quantifying the origin of spillovers requires more narrowed definitions and more
advanced research frameworks. Additionally, a globalized functioning of financial markets raises
questions with respect to the impact of a new financial crisis. Future research should aim at finding
more concrete answers to these important questions.

35
Appendix
Figure A. I – Global world trading hours
Figure A. II – Free float equity market capitalization*
*Source: World Economic Forum and Business Insider. Article: “What the world would look like
if countries were the size of their stock markets.” Published Aug. 21, 2015.

36
Figure A. III – intraday volatility movements

39
Table A. VI - GARCH (1.1.) models S&P 500 during the crisis (January 11, 2008 to March 31, 2009)
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
VARIABLES (N = 236) VARIABLES (N = 236)
Constant -0.000519 Constant 6.03E-06
(0.000568) (0.000512)
𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.207*** 𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.340***
(0.032) (0.0568)
𝛽3 (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) -0.239***
(0.0901)
GARCH (1,1) GARCH (1,1)
Constant 9.61e-07** Constant 5.40E-07
(4.61E-07) (5.51E-07)
α 0.125*** α 0.137***
(0.0141) (0.0147)
β 0.906*** β 0.902***
(0.00671) (0.00623)
Table A. V – GARCH (1.1.) models S&P 500 prior to the crisis (March 1, 2002 to January 10, 2008)
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
VARIABLES VARIABLES VARIABLES
Constant 0.000156 Constant 0.000177* Constant -2.33e-06***
(0.0000994) (0.0000974) (0.000000179)
𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.0610*** 𝛽2 (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.0472*** 𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.0239***
(0.0057) (0.00408) (0.00765)
GARCH (1,1) GARCH (1,1) GARCH (1,1)
Constant -2.22e-06*** Constant -2.09e-06*** Constant 0.000133
(1.67E-07) (1.54E-07) (0.000106)
α -0.00282** α -0.00171 α -0.00283*
(0.00142) (0.0014) (0.0015)
β 0.708*** β 0.695*** β 0.718***
(0.0093) (0.00893) (0.00995)
Table A. VII - GARCH (1.1.) models S&P 500 after the crisis (April 1, 2009 to October 1, 2015)
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
𝑅 𝑆&𝑃,𝑡
𝐶𝑂
VARIABLES (N = 1042) VARIABLES (N = 1042) VARIABLES (N = 1042)
Constant 0.000126 Constant 0.000143 Constant 0.000158
(0.000239) (0.000237) (0.000237)
𝑂𝐶
) 0.117*** 𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡
𝑂𝐶
) 0.0982*** 𝛽2 (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.0399**
(0.0184) (0.019) (0.0171)
𝑂𝐶
) 0.0879*** 𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.112***
(0.0194) (0.0194)
Constant 0.000101*** Constant 0.000101*** Constant 3.07e-05***
(4.73E-06) (4.44E-06) (0.00000434)
α -0.0102*** α -0.0100*** α -0.0106***
(0.00321) (0.0034) (0.0034)
β -0.773*** β -0.796*** β -0.812***
(0.0748) (0.0726) (0.0616)

40
Table A. VIII - GARCH (1.1.) models Toronto 300 Composite index prior to the crisis (March 1, 2002 to January 10, 2008)
𝐶𝑂
𝐶𝑂
𝐶𝑂
VARIABLES VARIABLES VARIABLES
Constant 0.000865*** Constant 0.000848*** Constant 0.000872***
(0.000192) (0.000197) (0.000204)
𝑂𝐶
) 0.164*** 𝛽2 (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.0961*** 𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.102***
(0.015) (0.0115) (0.0181)
Constant 3.24e-05*** Constant 3.34e-05*** Constant 3.07e-05***
(0.00000246) (0.00000263) (0.00000434)
α 0.133*** α 0.141*** α 0.111***
(0.0202) (0.023) (0.0236)
β 0.00556 β 0.0105 β 0.117
(0.0634) (0.0652) (0.117)
Table A. VIII - GARCH (1.1.) models Toronto 300 Composite index during the crisis (January 11, 2008 to March 31, 2009)
𝐶𝑂
𝐶𝑂
𝐶𝑂
(0.000837) (0.000665) (0.000972)
𝑂𝐶
) 0.181*** 𝛽2 (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.161*** 𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.360***
(0.0288) (0.0547) (0.0559)
Constant 1.08e-05** Constant 1.73e-05*** Constant 4.02e-06*
(4.26E-06) (6.05E-06) (2.09E-06)
α 0.381*** α 0.562*** α 0.118***
(0.0571) (0.0989) (0.0267)
β 0.706*** β 0.598*** β 0.883***
(0.0332) (0.0456) (0.0249)
Table A. IX - GARCH (1.1.) models Toronto 300 Composite after the crisis (April 1, 2009 to October 1, 2015)
𝐶𝑂
𝐶𝑂
𝐶𝑂
(0.000213) (0.000219) (0.000239)
𝑂𝐶
) 0.295*** 𝛽2 (𝑅 𝐷𝐴𝑋,𝑡
𝑂𝐶
) 0.198*** 𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.170***
(0.0167) (0.0162) (0.0192)
Constant 1.54e-06*** Constant 1.65e-06*** Constant 1.67e-06***
(2.48E-07) (2.80E-07) (3.46E-07)
α 0.0731*** α 0.0730*** α 0.0583***
(0.0065) (0.00604) (0.00552)
β 0.908*** β 0.908*** β 0.919***
(0.00846) (0.00795) (0.00888)

41
Table A. XI- GARCH (1.1.) models DAX 30 during the crisis (January 11, 2008 to March 31, 2009)
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
VARIABLES (N= 235) VARIABLES (N = 235) VARIABLES (N = 235) VARIABLES (N = 236)
Constant -0.00129** Constant -0.00120** Constant -0.00138** Constant -0.000999
(0.000609) (0.000568) (0.000632) (0.000676)
𝛽2 (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.156*** 𝛽2(𝑅 𝑇𝑋,𝑡−1
𝑂𝐶
) 0.127*** 𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) -0.0501 𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.313***
(-0.0408) (-0.0487) (-0.0325) (-0.03)
GARCH (1,1) GARCH (1,1) GARCH (1,1) GARCH (1,1)
Constant 1.82e-06*** Constant 1.72e-06** Constant 1.36e-06** Constant 1.56e-06***
(0.000000611) (0.000000677) (0.000000661) (0.000000598)
𝛼1 0.121*** 𝛼1 0.125*** 𝛼1 0.126*** 𝛼1 0.0985***
(0.0132) (0.0143) (0.0139) (0.0116)
β 0.890*** β 0.888*** β 0.890*** β 0.907***
(0.0094) (0.00883) (0.00817) (0.00873)
Table A. XII- GARCH (1.1.) models DAX 30 after the crisis (April 1, 2009 to October 1, 2015)
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
VARIABLES (N = 1042) VARIABLES (N = 1042) VARIABLES (N = 1042) VARIABLES (N = 1043)
Constant 0.000608* Constant 0.000647** Constant 0.000714** Constant 0.000773**
(0.000323) (0.000322) (0.000326) (0.000308)
𝛽2 (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.140*** 𝛽2(𝑅 𝑇𝑋,𝑡−1
𝑂𝐶
) 0.149*** 𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) -0.0778** 𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.330***
(0.034) (0.0438) (0.0321) (0.0248)
Constant 4.00e-06*** Constant 4.72e-06*** Constant 4.65e-06*** Constant
3.88e-
06***
(9.57E-07) (1.08E-06) (1.06E-06) (9.49E-07)
𝛼1 0.0477*** 𝛼1 0.0546*** 𝛼1 0.0599*** 𝛼1 0.0558***
(0.00805) (0.00867) (0.00922) (0.00825)
β 0.922*** β 0.911*** β 0.907*** β 0.913***
(0.0137) (0.0149) (0.0149) (0.0142)
Table A. X - GARCH (1.1.) models DAX 30 prior to the crisis (March 1, 2002 to January 10, 2008)
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
Constant 0.000648*** Constant 0.000679*** Constant 0.000647** Constant 0.000632**
(0.000244) (0.000249) (0.000259) (0.000247)
𝛽2 (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.235*** 𝛽2(𝑅 𝑇𝑆𝑋,𝑡−1
𝑂𝐶
) 0.174*** 𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) -0.0137 𝛽2 (𝑅 𝑁𝐼𝐾𝐾𝐸𝐼,𝑡
𝑂𝐶
) 0.152***
(-0.0171) (-0.0278) (-0.0227) (-0.0258)
(0.0000000604) (0.0000000702) (0.0000000733) (0.0000000694)
𝛼1 0.133*** 𝛼1 0.0305*** 𝛼1 0.0301*** 𝛼1 0.0293***
(0.0202) (0.0023) (0.00225) (0.00217)
β 0.00556 β 0.967*** β 0.967*** β 0.968***
(0.0634) (0.00237) (0.00227) (0.00231)

42
Table A. XIII - GARCH (1.1.) model Nikkei 225 prior to the crisis (March 1, 2002 to January 10, 2008)
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
Constant 0.000394 Constant 0.000530* Constant 0.000448 Constant 0.000414
(0.000281) (0.0003) (0.0003) (0.000292)
𝛽2 (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.483*** 𝛽2(𝑅 𝑇𝑋,𝑡−1
𝑂𝐶
) 0.404*** 𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) 0.315*** 𝛽2 (𝑅 𝐷𝐴𝑋,𝑡−1
𝑂𝐶
) 0.311***
(0.021) (0.0395) (0.0205) (0.0187)
(0.000000153) (0.000000186) (0.000000174) (0.000000197)
α 0.0193*** α 0.0196*** α 0.0209*** α 0.0209***
(0.00316) (0.00367) (0.00362) (0.0036)
β 0.973*** β 0.973*** β 0.972*** β 0.971***
(0.00422) (0.00455) (0.0045) (0.00485)
Table A. XIV - GARCH (1.1.) models Nikkei 225 during the crisis (January 11, 2008 to March 31, 2009)
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
Constant -0.000787 Constant -0.000372 Constant -0.000373 Constant -0.000741
(0.000912) (0.00106) (0.00102) (0.000982)
𝛽2 (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.317*** 𝛽2 (𝑅 𝑇𝑋,𝑡−1
𝑂𝐶
) 0.251*** 𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) 0.217*** 𝛽2 (𝑅 𝐷𝐴𝑋,𝑡−1
𝑂𝐶
) 0.233***
(0.0514) (0.0354) (0.0434) (0.0513)
Constant 0.000377*** Constant 0.000463*** Constant 0.000478*** Constant 0.000453***
(2.42E-05) (2.91E-05) (3.60E-05) (3.13E-05)
α -0.0230** α -0.0218*** α -0.0408*** α -0.0329***
(0.0109) (0.00666) (0.0148) (0.0103)
β -0.897*** β -0.890*** β -0.870*** β -0.881***
(0.07) (0.0519) (0.0713) (0.0534)
Table A. XV - GARCH (1.1.) models Nikkei 225 after the crisis (April 1, 2009 to October 1, 2015)
𝐶𝑂
𝐶𝑂
𝐶𝑂
𝐶𝑂
Constant 0.000136 Constant 0.000587 Constant 0.000518 Constant 0.000489
(0.000342) (0.000376) (0.000357) (0.000342)
𝛽2 (𝑅 𝑆&𝑃,𝑡−1
𝑂𝐶
) 0.616*** 𝛽2 (𝑅 𝑇𝑋,𝑡−1
𝑂𝐶
) 0.494*** 𝛽2 (𝑅 𝐹𝑇𝑆𝐸,𝑡−1
𝑂𝐶
) 0.431*** 𝛽2 (𝑅 𝐷𝐴𝑋,𝑡−1
𝑂𝐶
) 0.448***
(0.0279) (0.0488) (0.0249) (0.028)
(7.51E-07) (9.55E-07) (7.85E-07) (7.02E-07)
α 0.0465*** α 0.0626*** α 0.0697*** α 0.0667***
(0.008) (0.00873) (0.0112) (0.00797)
β 0.923*** β 0.905*** β 0.903*** β 0.907***
(0.0135) (0.0135) (0.0145) (0.0113)

43
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