COVID19 Outbreak Impact on International Stock Markets Volatility Contagion

We analyze volatility contagion between the U.S. and Chinese stock markets and international capital markets. The volatility is modeled using: GARCH, TARCH, EGARCH, APARCH, IGARCH, FIGARCH, ACGARCH and GAS models under Gaussian, GED and t-Student distributions. 21,000 intraday observations of thirteen markets from January/1st to June/25th 2020 are employed. Once volatility is modeled, the incidence of Chinese and American markets on the rest of the bourses is tested employing Vector Autoregressive Markov Switching Models. Evidence confirms incidence of the Chinese and American capital markets volatility in other markets volatility; common breakpoints and Intermarket incidence in high volatility periods stand out.


Introduction
Since its inception, the ongoing pandemic situation had an enormous social, economic, and financial impact all over the world. The COVID 19 crisis has had a local and international impacts: sharp unemployment increments, large contraction of industrial activity, tourism practically paralyzed, and international trade and investment weakened; all these economic effects contracted sharply global demand, affecting enterprises' productivity and output, as well as financial corporations returns.
Bad news, increasing uncertainty, negative expectations, and lower corporate profits generated widespread stock market crashing, in Paris and Frankfurt about 12% and London FTSE 11%, outstripping the depth of the Eurozone debt crisis. In March 2020, the Dow Jones had its worst day since 1987 (12.9%) and S&P 500 dropped 20% from a prior high (Lynch et al., 2020). The price of a barrel of oil collapsed by more than $30 in the worst trading day since 1930 (Sheppar, Raval & Lockett, 2020).
In other financial markets, investors bought government bonds from UK, US and Germany considered as safe havens with low to negative interest rates. Currency markets suffered important depreciations, above all in emerging markets (The FRED® Blog, 2020), Brazil's and Mexico's exchange rates spiked, and their currencies depreciated 46% and 30%, respectively from January to May 2020. In the derivatives market, futures were in a contango situation.
Economic and monetary authorities and multilateral organisms have developed strategies intervening in financial markets, stimulating economies, and thus creating some certainty, reducing fear and nervousness among investors. The International Monetary Fund (IMF) has provided assistance since late March for $250 billion, a quarter of its $1 trillion lending capacity (IMF, 2020). It estimated that the global fiscal support neared $9 trillion at the end of May 2020, the direct budget support was around $4.4 trillion, and additional public sector loans, and equity injections, guarantees, and other quasi-fiscal operations amounted other $4.6 trillion (Battersby, Lam & Ture, 2020).
Closely related with our study, Baker et al. (2020) find that government restrictions due to the COVID-19 pandemic generated a bigger effect, in the US stock market, than previous pandemics 1918-19, 1957-1958and 1968. Al-Awadhi et al. (2020 evidence that the number of deaths and confirmed cases of COVID-19 had a negative impact on Chinese stock returns. Topcu and Gulal (2020) determines that Asian and European stock markets had the highest impact among emerging stock markets. Phan and Narayan (2020) argue that stock markets overreacted to unexpected news, when the information expanded and markets calmed down, the market corrected itself. Akhtaruzzaman, Boubaker and Sensoy (2020) found that financial firms were more contagious than nonfinancial firms and China and Japan transmitted more spillovers than they received during the COVID-19 crisis period.
Follow Bai et al. (2022), Bai et al. (2021), Goodell (2020), Liang et al. (2021, and Akhtaruzzaman et al. (2021), this study contributes expanding knowledge about the COVID19 financial effects transmission, using stock markets intraday data for thirteen economies, including developed and developing countries. The empirical approach includes volatility estimation employing GARCH and GAS models under three distributional assumptions. Once volatility is modeled, it is used to test whether Chinese and US market volatilities influenced the rest of the markets or vice versa, through two regimes: high and low volatility; to test the two ways influence, MS-VAR model is used. Finally, MS-VAR probability results are analyzed to find common breaks and contagion periods.
The rest of the paper is structured as follows. Section 2 describes the data and methodology, section three deals with the models results and their analysis. Finally, section shows the conclusions.

Data and Methodology
Our data consist of 21,000 intraday observations (one-minute frequency data is employed, on average 300 prices per day) of thirteen stock market indexes over the period January 1st, 2020 to June 25th, 2020. According to Barclay and Litzenberg (1988), intraday data permit more efficient estimation of the effects of new information on stock prices. Dionne, Duchesne & Pacurar (2009) emphasize that using intraday data also allows that the risk measure has a higher informational content.
The period selection was based on immediate COVID19 financial effects. Data were collected from Bloomberg. We define the intraday log-returns = log � −1 � � and estimate the following GARCH models.
where ℎ 2 is the conditional variance of , and is a permanent component of ℎ 2 . All the GARCH specifications are considered with innovations distributed as follows: Normal (Gauss), t-Student, and Generalized Error Distribution (GED).
GAS models are based on the score function of the predictive conditional density of the stock index returns at time t. Two particular advantages of GAS models are: 1) these models allow for GARCH or Auto-regressive Conditional Duration (ACD) specifications advanced by Engle and Russell (1998), and 2) time-varying parameters re-estimation avoids the problem of using an inadequate forcing variable when the correct specification is not evident (Troster et al., 2019).
The optimal model is chosen according to Akaike (AIC) and Hannan-Quinn Information Criteria. The selected model is the one with the minimum criteria and, the higher Log-likelihood value, ensuring statistical significance (*) and positive parameters (+) (Appendix, Table A.1).

GAS Model
Let −1 be the past information set of up to t-1. Let ( ; ) be the conditional distribution of the returns, | −1~( ; ), and let ∈ Θ ⊆ be a vector of time-varying parameters that completely identifies (⋅). GAS model is described as follows: where , , and are coefficient matrices, is vector of scaled-score steps, and ( ) is a positive-definite scaling matrix that adjusts the shaper of the score, for instance: GAS approach is estimated under the same three distributions than GARCH models: Gauss, GED y t-Student.
Once, GARCH and GAS models are applied, variance series are used to model the twoways impact of the US and China markets on the rest of the countries.

Markov Switching Vector Autoregressive
The MS-VAR developed by Krolzig (1997) is a multivariate generalization of the univariate Markov switching autoregressive model. The general concept behind this model is that the parameters of a VAR process are not static as linear approaches assume; specifically, parameters could be time-invariant whether a particular regime is maintained. However, the parameters change, if the regime does it (Pontines & Siregar, 2009).
The regime-generating process determining which regime prevails at any point in time, is assumed to follow an ergodic Markov chain with a constant transition probability of the form The procedure was applied to examine whether transmissions of shocks across countries intensified during the COVID19 immediate effects. Thus, we analyze the dynamic relationship between the Chinese and the US equity markets and other 13 stock markets. The MS-VAR model can be expressed as follows: where ℎ and represent the stock market volatility of the Chinese and American market, respectively, is the volatility of the rest of the stock markets; is the innovation process with a ( ) variance which depends on regime, which follows an ergodic Markov process with two regimes, defined by probability transition between those regimes.
The use of MS-VAR evades the arbitrary selection of the crisis episodes to one that endogenizes the process splitting up crisis from calm periods. Therefore, the discussion about the sample selection bias is evaded which other analyses of contagion are subjected to (Pontines & Siregar, 2009).
Finally, once the smooth probability of being in a high volatility period is obtained, a multiple structural breaks test is applied to identify the exact moment of regime change.

Results
Appendix A.1 presents descriptive statistics of the series; mean intraday returns are negative, skewed, leptokurtic, thus, non-normally distributed. Appendix A.2 shows ADF results, the null hypothesis is: series have unit root. In all the cases, the series are stationary.
GARCH model results are presented in Appendix A.3, APARCH model with t-Student innovations is the most suitable to model to capture the indexes behavior (seven of the thirteen series). APARCH model introduced by Ding et al. (1993) allows measuring asymmetric effects and non-normality, both are important characteristics of financial series.
To begin with the MS-VAR estimation, it is necessary to determine the lag length. Based on Likelihood Ratio (LR) tests of alternative lengths, a lag length of 1 was chosen to estimate the model. Secondly, the LR and AIC tests are applied to demonstrate that regime-switching behavior exists in the linkages of stock and exchange rate markets, the results are presented in Appendix A.4.
The evidence proves that LR tests reject the null hypothesis of no regime switching in the relationship between the stock market and exchange rate returns in all cases; it means that the alternative MS-VAR is the more-suitable model. The Akaike Information Criterion (AIC) also favors the MS-VAR model in all cases. Hence, MS-VAR is estimated, the results are in Tables 1  and 2.

Table 1. MS-VAR Results The US vs The Rest of the Countries.
Source: Own elaboration with estimation results. Reported values are statistical significance levels of * 1%, ** 5% and 10% ***. Standard deviations are reported in parentheses.

Table 2. MS-VAR Results China vs Rest of the Countries.
Source: Own elaboration with estimation results. Reported values are statistical significance levels of * 1%, ** 5% and 10% ***. Standard deviations are reported in parentheses. Table 1 shows results for the US market. The standard deviation of the stock markets is lower in regime one (low volatility regime) than in regime two (high volatility regime), for all the markets. It indicates the presence of two different volatility regimes. Average duration results evidence that the high volatility periods lasts less than low volatility periods, which is consistent with the expected result; crisis periods are shorter than calm episodes.
The estimated coefficients capturing the impact of the international stock markets volatility on the US stock market volatility ( 31 and 32 ) are statistically significant, for almost all the market's volatility except for the Spanish, Korean, Argentinian and British economies, in other words, there is a significant effect of the international markets' volatility on the US market.
On the other hand, the coefficients ( 31 and 32 ) capture the effects of the US stock market volatility on the rest of the volatility stock markets. They are not statistically significant in the cases of Peru, Korea, Argentina, Canada and the UK; this means the US volatility market does not have a significant impact on these markets' volatility. Table 2 presents the results for the Chinese market. The estimated coefficients capturing the impact of the international stock markets volatility on Chinese stock market volatility ( 31 and 32 ) are statistically significant, for almost all the relations except for the French, Brazilian, Mexican and Canadian markets; in other words, there is a significant effect of the international markets on the Chinese market. These findings confirm that, despite the fact that China has had an increasing role in the economy and financial markets, the US market still influence more markets, in relation to the Chinese market. Figure 1 shows the graphic analysis from the smooth probability of being in high volatility for each relation US vs the rest of the markets. It is observed alike behavior among the different markets. For all the economies the probability of being in high volatility level increased after January 29 th when the number of Covid19 cases augmented and flights to China were suspended.
In Figure 2 it is observed the smooth probability of being in high volatility for each linkage between Chinese market volatility and the rest of the indices volatility. European, American, and Canadian markets display similar behavior, but the rest of the markets have different performance. It seems that developed countries´ markets have a similar reaction to Chinese market volatility, and developing ones react differently according to their own characteristics and local situations.  Source: Own elaboration with estimation results.
Once the graphic analysis is elaborated, the multiple structural break test is applied on smooth probabilities series to confirm whether all markets present coincident dates. In other words, we test when series exhibit changes to confirm common structural break dates. Table 3 shows the results of structural breaks. Findings sign the existence of four structural breaks in the models, both in the sequential, as well as in the repartition structural detection. For all the relationships dates coincide, showing as key days: January 29th, March 9th, April 1st, and April 28th. These dates match with the following events: January 29th the number of infected increased and flights to China were suspended (Regan et al., 2020 and Reuters, January 30, 2020); March 9th economy and financial markets crashed, Italy closed its borders, a prices war started between Saudi Arabia and Russia, that day was called Black Monday (Li, 2019;Bayly, 2020 andBBC, 2020). April 1st the US bonds yield diminished (Smith, 2020) and the oil price fell (Reuters, April 1st, 2020) and, April 28th the US had more than 1 million of confirmed cases and Trump began to blame China for the virus generation and propagation (Davidson &Rourke, 2020, andBloomberg, 2020).
The results reveal the presence of four structural breaks in the model, in both strategies: sequential and repartition. Source: Own elaboration with estimation results. Table 4 shows the multiple structural breaks test results in the dynamic relationships between the S&P 500 and other indexes. For almost all the markets, except the Spanish market, four structural breaks are statistically significant for sequential and repartition strategies. As in the Chinese case, four dates were coincident for all the markets: February 20 th , April 16 th , May 19 th , and March 19 th .

Table 4. Multiple Structural Break Test Results -American Market vs The Rest.
Source: Own elaboration with estimation results.
February 20 th was declared the beginning of the 2020 stock market crash which ended on April 7 (ZACKS, April 7, 2020). At February 20 th stock markets suffered important losses (Huang, February 20, 2020), oil prices fell by 1% (Verma, 2020) and yields of 10 year and 30-year U. S. Treasury securities fell to 1.51% and 1.96% respectively (Hyerczyk, 2020). On March 19 th Asia-Pacific equity markets closed with losses (Huang, March 19, 2020) while European ones closed winning 3% (Ellyatt & Smith, 2020), oil prices rose by 23% and the yields on 10-year and 30-year U. S Treasury securities fell to 1.06% and 1.68% respectively. The FED announced foreign exchange swap lines for $450 billion in Australia, Brazil, South Korea, Mexico, Singapore, Sweden, Denmark, Norway and New Zealand Central Banks (60 billion for each) (Schneider & Dunsmuir, 2020). The FED also opened an additional lending facility alike to CPFF for money market mutual funds (Neuman, 2020). The Bank of England, the Denmark's National Bank (Reuters, March 19a, 2020), the South African Reserve Bank, Bank of Indonesia and the Central bank of the Republic of China (Loo & Lee, 2020) announced changes in their rates (Meredith, 2020). Chile (Reuters, March 19b, 2020) and the U.S (Hirsch and Pramuk, 2020) also announced a fiscal stimulus package.
On April 16 th , benchmarks closed with losses after disappointing corporate earnings reports and weak economic data because of damage by the COVID19 outbreak. The DJI fell 1.9%, S&P500 2.2%, Nasdaq 1.4%. The fear-gauge CBOE Volatility Index (VIX) increased 7.5% (ZACKS, April 16, 2020). May 19th Wall street recovered on Monday after the disappointing results of potential coronavirus vaccine. Fed Chairman promised more stimulus to lift the pandemic-affected, this improves investors´ sentiments. DJI, S&P500 and Nasdaq closed up (ZACKS, May 19, 2020).

Conclusion
This paper modeled intraday volatility for 13 markets and analyzed the incidence of Chinese and American markets volatility in the rest of the stock markets´ volatility, pointing out the breakpoints, structural changes on the probability of being in high volatility regime; and contagion episodes.
To achieve this purpose, we estimated the stock index returns volatility employing GARCH extensions and GAS model. Volatility measure results indicated the APARCH model is the most suitable for a major part of the equity indexes. Once volatility was modeled, conditional variance was employed to test the incidence of the Chinese and the U.S. stock market volatility on the rest of the markets; MS-VAR was proposed to analyze two-ways volatility incidence.
MS-VAR models evidence, for almost all the stock markets, a significant two-ways incidence, which evolves according to two regimes: high volatility regime, and low volatility regime. Finally, MS-VAR smooth probabilities of being in high volatility regime series are used to detect structural changes, i.e., to find the exact dates when the high volatility period started. Those dates could also be identified as moments when contagion periods started.
The findings confirm that, even though China has had an increasing role in the economy and in the financial markets, the US market still maintains greater influence on more markets than the Chinese market does.
Multiple break test reveals which dates were relevant for each market: Chinese and American. Results also allowed to observe in which days mutual incidence of the stock markets was took place, provoking high volatility periods The empirical evidence is of outmost importance in terms of widening the knowledge about the volatility contagion effect between the American and the Chinese stock markets, as well as the rest of the stock markets analyzed, during the COVID19 immediate effects.
Future studies agenda could include research about the contagion effect on other financial markets, the period of study might be extended or the application of other methodologies could be incorporated.