The effect of COVID‐19 pandemic on global stock markets: Return, volatility, and bad state probability dynamics (2024)

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Data Availability Statement

Abstract

This study investigates the impact of COVID‐19 pandemic on stock returns, conditional volatility, conditional skewness and bad state probability. This study utilizes an asymmetric exponential generalized autoregressive conditional heteroscedasticity model to capture the asymmetric effect of positive and negative shocks (news) on conditional volatility. Using a sample consisting of international stock market indices in Brazil, China, Italy, India, Germany, Russia, Spain, United Kingdom, and United States, over the period from January 1, 2013 to December 31, 2020, we find unprecedented increases in conditional volatilities and bad state probabilities across all the markets. However, this impact is not symmetric across markets. Furthermore, we find that the negative affect of deaths is more pronounced, compared to the positive impact of recovered cases.

Keywords: bad state probability, COVID‐19, pandemic, stock market, volatility

1. INTRODUCTION

In late 2019, a new virus called “COVID 19” had started to spread, causing “severe pneumonia.” Thus, this virus led to an extraordinary rate of death between the elderly and the most vulnerable in society, leading to an international social distancing and home isolation of more than 2 billion people worldwide, with tremendous social, political and economic consequences (Goodell,2020; Sharif et al.,2020). Moreover, one of the commercial effects of this virus was an unexpected disruptions in the flow of goods and services, commodity prices and financial conditions, creating an economic disasters across many countries because of its impact on the production and supply chains in China, the United States, Europe, and Japan, as well as the most important economies in the world (IMF,2020).

Significant changes in the financial structures of countries was caused by the “domino effect” created by retrenched investors in many countries (Kenourgios et al.,2011). This contagion effect in the global market led to unprecedented disturbing effects in different economies that were only comparable to the depression of 1920 (Corbet et al.,2020). Moreover, all the countries face a great health crisis, severe external demand shock, dramatic shrinking in global financial conditions, and a plunge in the commodity prices that will have a severe effect on economic activity in commodity exporters (IMF,2020). In addition, the outbreak of COVID‐19 has been declared as a global pandemic on June, 2020 by the World Health Organization (WHO), which shaken the global financial markets. As of June 16, 2020, there are 9,653,048 confirmed cases and 491,128 deaths across the world for 216 Countries, areas or territories with cases, including emerging and developed countries (WHO,2020).

The objective of this research is to analyze the influence of COVID‐19 on the stock price behavior of equity market indices of selected nine countries. We selected the countries that had the largest confirmed cases of COVID‐19 at the end of March and June 2020. Accordingly, the final sample included United States, Italy, Spain, United Kingdom, Germany, China, Brazil, Russia, and India. We also compare how the stock price behavior differs across the periods pre‐ and during the COVID‐19 (to examine the initial effect of the shock of COVID‐19 on the markets) and then between the first and second quarters during the COVID‐19 period (to explore whether the markets are rebounded after the shock is being assessed and absorbed). Our analysis of stock market behavior is based on examining stock returns, conditional volatility, conditional skewness, and bad state probability, measured using a widely applied econometric model, an asymmetric exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model.

The advantage of this model is to allow for capturing the well‐documented asymmetric effect of positive and negative shocks on conditional volatility as positive shocks may have less impact on volatility than the negative shocks (Alberg et al.,2008; Hentschel,1995; Nelson,1991). It is commonly known fact that volatility clustering produces heavier tails, as documented by Engle's(1982) seminal paper on autoregressive conditional heteroscedasticity (ARCH) model and its generalization by Bollerslev's(1986) paper on generalized autoregressive conditional heteroscedasticity (GARCH) model, and others (e.g., Tsay,2010). However, since normal GARCH model links directly the kurtosis to the variance, it is unable to well capture the excess kurtosis that exists in financial returns and produces low probability of extreme realizations (extreme returns) than observed in the data. In addition, inclusion of conditional skewness in the model captures the asymmetry, and also impacts the persistence in conditional variance as highlighted by Harvey and Siddique(1999). To overcome these drawbacks when using the normal GARCH model, our EGARCH model adds two extra parameters in the distribution of returns, namely the skewness and kurtosis. Moreover, this model is augmented to capture the impact of the number of death and recovered cases to distingue between the effects of negative information (deaths) verses positive information (recovered cases). Moreover, as any other major crisis, the COVID‐19 pandemic was associated with an adverse impact on the financial markets, caused by panic, uncertainty, negative sentiment and investor pessimism during the pandemic. Hence, it was crucial for us to estimate bad state probabilities (i.e., the probability that stock market returns might fall below the expected returns) to quantify the likelihood of bad events, and assess the probability of markets downturns in bad times of high uncertainty.

Therefore, this paper contributes to the literature in several ways. First, this study extends the evolving literature on the impact of COVID‐19 on stock market behavior. Although several studies have investigated how financial markets have been affected during COVID‐19 period (Baker et al.,2020; Corbet et al.,2020), to the best of our knowledge, none have examined the impact of COVID‐19 on global stock markets, using an asymmetric exponential EGARCH model with an emphasis on conditional volatility, conditional skewness and bad state probability. This allows for not only capturing the dynamic behavior of conditional variance but also taking into account the asymmetric impact of negative versus positive return innovations. Second, this study aims to estimate the impact of COVID‐19 recovered cases and deaths on the conditional mean, conditional volatility and conditional skewness of the returns of equity market indices. By doing that, we distinguish between the impact of positive and negative information on stock market behavior to examine the asymmetric characteristics of stock market behavior. Third, we demonstrate how the COVID‐19 pandemic can amplify bad state probability, which is important in a period when financial markets experience extreme uncertainty and investors' behavior is driven by their fear and panic. Therefore, this study adds not only to the literature on COVID‐19's effect on stock markets but also to the overall literature on financial market crashes and crises. Fourth, our long analysis period (January 1, 2013 to December 31, 2020) enables us to compare the stock price behavior across not only the periods pre‐ and during the COVID‐19 pandemic but also the first and second quarters during the COVID‐19 period. This allows for better understanding of how stock markets have initially reacted to the shock of COVID‐19, compared to how they are rebounded after the shock is being absorbed. Moreover, our findings provide important implications for investors, practitioners and policy makers. For traders and investors seeking to invest in international stock markets, the results indicate which markets are most correlated and risky, which have strong consequences for portfolio optimization and implementation of profitable trading strategies. For practitioners, the findings allow to get insights into the dynamic behavior of stock markets in the countries that are heavily affected by the pandemic in order to examine the best investment options. For policy makers, the findings confirm the critical role that the political leadership and governments can play, via mitigating the spread of pessimistic views and negative feelings amid citizens, in conveying positive signals to the investors and thereby decreasing market uncertainty.

2. LITERATURE REVIEW

Following such a huge worldwide crisis, the literature on the economic effects of COVID‐19 has emerged quickly in recent months. For example, Ramelli and Wagner(2020) and Zaremba et al.(2020), among other, have investigated the adverse impact of COVID 19 on stock returns and volatility. Other studies have examined how the outbreak of COVID‐19 affected the financial contagion in financial markets. For example, Akhtaruzzaman et al.(2020) examine how the COVID‐19 period has affected the financial contagion between China and G7 countries and show that stocks listed across China and G7 countries have been associated with a significant increase in conditional correlations between their stock returns. Consistently, Just and Echaust(2020) show close dependence between S&P 500 index returns and both implied volatility and implied correlation during the COVID‐19 period.

Other studies focus on exploring how COVID‐19 has affected commodity markets. Gharib et al.(2021) examine the economic impact of COVID‐19 on the causal relationship between crude oil and gold prices and find a bilateral contagion effect of bubbles in oil and gold markets during the recent COVID‐19 outbreak. Sharif et al.(2020) analyze the connectedness between COVID‐19, oil price volatility shock, the stock market, geopolitical risk and economic policy uncertainty in the United States. Their finding show that the effect of the COVID‐19 on the geopolitical risk substantially higher than on the US economic uncertainty. In related context, Conlon and McGee (2020) examine the price behavior of Bitcoin during the COVID‐19 bear market and provide empirical evidence casting doubt on the ability of Bitcoin to act as a safe‐haven asset. While other studies focus on assessing the role of governmental policies in mitigating the negative impact of the pandemic on financial markets. For instance, Narayan et al.(2020) examine the effect of government responses of G7 countries to the coronavirus pandemic (COVID‐19) on stock market returns, showing that lockdowns, travel bans, and economic stimulus packages have exerted a positive effect on the G7 stock markets. Ma et al.(2020) reveal that countries with more aggressive government fiscal policy exhibit a superior ability to decrease the adverse impact of the pandemic on GDP growth, while emerging market are most likely to experience superior negative influences from COVID‐19. Table1 outlines a summary of related literature to provide more insights into the research approaches adopted by the studies depicted in Table1. In‐depth analysis has been conducted to categorize these studies in Table1.

The first category considers mainly samples from developed countries. These studies adopt different methodology and statistical models using time‐series regression model (e.g., Narayan et al.,2020); Two‐regime Markov switching model (e.g., Baek et al.,2020; Just & Echaust,2020); ordinary least square (OLS) (e.g., Albulescu,2020; Mazur et al.,2020); GARCH (1,1) model (e.g., Baig et al.,2021; Yousef,2020); Wavelet coherence analysis (e.g., Choi,2020); nonlinear smooth transition regime switching model (e.g., Lyocsa & Molnár,2020) and the wavelet coherence and the wavelet‐based Granger causality tests (e.g., Sharif et al.,2020). On the other hand, the second category focus on samples from developing countries. The approaches used in these studies include: the average adjusted return rate model (e.g., He, Sun, et al.,2020); the market index adjusted return rate model and the market model (e.g., Jelilov et al.,2020); GARCH model (e.g., Waheed et al.,2020) and auto regressive integrated moving average and exponential smoothing.

While, in the third category, other studies provides empirical evidence based on both developed and developing markets. Those studies adopted various models, such as bivariate fractionally integrated vector autoregressive model (e.g., Bissoondoyal‐Bheenick et al.,2020); unit root test, the ARCH effect test, and the GARCH (1,1) model (e.g., Chaudhary et al.,2020); conventional t tests and nonparametric Mann–Whitney tests (e.g., He, Liu, et al.,2020); market model, and the OLS (e.g., Liu et al.,2020); pairwise correlations (e.g., Zhang et al.,2020); CAAR model (Kotishwar,2020); and capital asset pricing model (CAPM), three‐factor model (FF), and four‐factor model (e.g., Zaremba et al.,2020).

3. METHODOLOGY

4. EMPIRICAL RESULTS

Table2 the daily stock returns for the nine countries during the period of pre‐COVID‐19 that starts from January 1, 2013 to December 31, 2019 and the COVID‐19 period that starts from January 1, 2020 to December 31, 2020. The descriptive statistics show that the mean of stock returns for the period of pre‐COVID‐19 are positive for all countries in the sample except India that has a negative return as shown in Panel (A). The mean of United States refers to the highest positive stock return while Spain and United Kingdom returns experienced the lowest positive mean. On the other hand, during the period of COVID‐19, Panel (B) demonstrates that the United Kingdom, Brazil, Russia and Spain have, on average, negative returns, while the United States, Italy, Germany, China, and India have positive returns. As it can be also shown in Figure1, the markets initially exhibit a sharp decline in 2020 before being rebounded for the remainder of the year.

Next, we seek examine how the markets initially reacted and got rebounded after the shock is being absorbed. Therefore, we focus our analysis on the first 6 months that have been divided into two quarters to compare and examine the effect of COVID‐19 over time where quarter 1 covers the period (January 1, 2020 to March 31, 2020) and quarter 2 covers the period (April 1, 2020 to June 30, 2020). Table3 depicts the returns during the period of COVID‐19 for the first two quarters of the year 2020. The mean of stock returns for all nine countries are negative for the quarter 1 (starts from January 1, 2020 to march 31, 2020) which indicates that all countries had shock in their stock markets resulted from the pandemic COVID‐19. Brazil, India, Russia and Spain are the highest countries that have been affected dramatically by the decrease in their stock returns. Finally, Panel (B) shows that all countries have been shifted their means of returns to be positive in the second quarter of the pandemic which indicates that these countries have taken actions and adopted some strategies to deal with the COVID‐19.

Table4 reveals that all countries are positively correlated and pairwise correlations are strongly significant. Therefore, there is no possible risk diversification for investors via buying all countries' indices. However, the investors can invest in US market and Chinese market as the market give positive average returns even during COVID‐19 period as demonstrated in Table2. This fact is supported by the results in Table3 since the average returns during the first quarter of COVID‐19 are −02817 for United States and −0.1689 for China exhibiting lower losses after the shock.

As demonstrated in Tables2 and ​and3,3, all indices' returns exhibit skewed distribution with fat tails. That is, the returns have negative skewness, meaning that the probability of losing an amount of money buying a country index is higher than the probability of gaining the same amount. Also, fatter tails of the distribution of returns reveal that there is high probability to get extreme returns than the normal, that is, either extreme gains or extreme losses. In the other side, Figure1 shows that there is a volatility clustering and volatility persistence, as there are periods of high volatility followed by periods of high volatility and periods of low volatility followed by periods of low volatility. Accordingly, the conditional volatility is computed using an asymmetric EGARCH (1, 1) of Nelson(1991) to capture these stylized facts of returns. That is, the model (skewed t‐distribution of Hansen) comprises two key parameters capturing the dynamics of the asymmetry and fat tailedness of the distribution. In one side, the parameter ηt controls the shape of the distribution and hence capture the degree asymmetry and hence governs the probability of bad state of the market. In the other side, the parameter υ captures the likelihood of extreme returns. Model speciation is presented in Section3.

Figure2 displays the dynamics of the estimated conditional volatility across the selected countries. As mentioned, we compute the conditional volatility, using an asymmetric EGARCH (1, 1) of Nelson(1991). Stock price crashes unfolded extreme volatility during the COVID‐19 pandemic, which led to unprecedented rise in conditional volatilities across all the markets, as it can be apparent in the graph. Unsurprisingly, the highest levels of volatility are observed in the United States and the United Kingdom while countries, like China and Germany, exhibit less conditional volatility. The surge in new cases and deaths despite the government's efforts to mitigate the spread of COVID‐19 in the United States and the United Kingdom were associated with the spread of pessimistic views and negative feelings amid both the political leadership and citizens, which has adversely affected market uncertainty. In contrast, the stock markets in China and Germany appear to have suffered less and the prompt intervention of their governments to control the spread of the virus appeared to convey positive signals to the investors and mitigate the prevailing market uncertainty. As it can be also shown, the excessive increase in conditional volatility appears not to be persistent during the COVID‐19 period as for all the markets the figure exhibits a significant fall in the conditional volatility once the shock has been absorbed.

As any other major crisis, the initial market reaction to the COVID‐19 pandemic is associated with panic, uncertainty, negative sentiment and investor pessimism, which exerted an adverse impact on the financial markets. To get more insights into this impact, we estimate the bad state probabilities to compare how the likelihood of bad events differs across the periods pre‐ and during the COVID‐19 (to examine the initial effect of the shock of COVID‐19 on the markets) and between the first and second quarters during the COVID‐19 period (to examine whether the markets get rebounded after the shock is being assessed and absorbed). As demonstrated in Table5 and Figure3, the impact of the COVID‐19 was visible worldwide on the major equity markets, which generally experienced noticeable increase in bad state probabilities, indicating that market participants perceived the event as a global shock and so it has reflected on their adverse expectation with respect to the market behavior. In comparison with the time period before COVID‐19, we observe—on average‐ an increase in bad state probabilities across the United Kingdom, Germany, Brazil and India. In contrast, the United States, Russia, China, Italy, and Spain exhibit a decrease in bad state probabilities.

Again, these findings should not be surprising due to the pessimistic views and negative feelings which were prevailing amid both the political leadership and citizens in markets, such as the United Kingdom and Germany, after the COVID‐19 pandemic; in contrast other markets (e.g., Russia and China) were associated with relatively lower market uncertainty not only due to their economic/political strength but also to their prompt response to markets' fears and investors' worries. It is also worth mentioning that bad state probability exhibited larger SD and maximum values in all the markets, which indicates that the probability of stock market declines becomes more volatile and is expected to move up to larger highest values compared the period pre‐COVID‐19 pandemic.

A closer examination of the behavior of bad state probability during the first two quarters in the COVID‐19 period, as displayed in Table6, reveals that bad state probability differs during the second quarter in the COVID‐19 period (April 1, 2020 to June 30, 2020) as compared to that of the first quarter period (January 1, 2020 to March 31, 2020). This difference between the two quarters varies across countries. For example, except for Germany, China and Spain, bad state probability becomes—on average—higher during the second quarter. As expected, Italy exhibits the highest increase in bad state probability (by ~35% from 0.5642 to 0.7638) during the second quarter in the COVID‐19 period caused by soaring levels of uncertainty and investors' pessimism due to the surge in new cases and deaths despite the government's efforts (e.g., lockdowns, stimulus packages and travel bans) to mitigate the spread of COVID‐19. Again, among the markets that experienced higher bad state probability during the second quarter, Russia has the lowest increase (by 0.73% from 0.5361 to 0.5400), which can be attributed to Russia's policies that helped subdue panic and so mitigated the adverse effects of the pandemic on the stock markets, in addition to the impact of the positive news associated with Russia's experimental COVID‐19 vaccines. On the other hand, China, Germany and Spain experienced lower bad state probability during the second quarter in the COVID‐19 period, which might reflect that investors' confidence has been resorted, and so stock markets in these counties have recovered quicker than the other markets. The prompt intervention of the government in China and Germany to control the spread of the virus managed to maintain business and confidence and conveyed positive signals to the stock markets, whereas in Spain the noticeable decline in daily new cases and deaths starting from April might have positively influenced the financial markets and so reflected on the fall in bad state probability in the second quarter during the COVID‐19 period. Taken together, these findings suggest that for risk‐averse investors, Chinese market is more attractive since the average of bad state probability is the lowest among all countries and is less than 50% during the second quarter of COVID‐19 period as shown in Tables5 and ​and66.

After gaining insights into how the risk–return behavior of stock markets differed across the periods pre‐ and during the COVID‐19 and between the first and second quarters during the COVID‐19 period, we further investigate the impact of COVID‐19 (proxied by the number of deaths and recovery cases) on stock returns, conditional volatility and conditional skewness. Table7 reports the results. Our dependent variable is mean return that represents the daily percentage changes in the selected markets' stock indices in Panel A, while it is conditional volatility modeled using an asymmetric EGARCH (1,1) of Nelson(1991) in Panel B, and it is conditional skewness estimated using an asymmetric EGARCH (1,1) of Nelson(1991) in Panel C. In general, our results are in line with the findings on the adverse impact of financial crises in general (e.g., Novotny,2010; Sarkar & Patel,1998) and the COVID‐19 pandemic in specific (e.g., Baek et al.,2020; Chaudhary et al.,2020; Zhang et al.,2020). Particularly, for our independent variable “mean return,” we observe a consistently negative relationship between coronavirus death cases and stock return only in the Italy, whereas the coefficients are insignificant in the other markets. As for the impact of recovery, the coefficient is only consistently positive and statistically significant in the United Kingdom, Italy and Brazil while it remains insignificant in other markets. In economic terms, an increase in death cases by 1000—in Italy, for example,—is associated with about 0.014% decrease in average stock returns while an increase in recovered cases by 1000 is associated with about 0.0044% increase in average stock returns.

With respect to our dependent variable “conditional volatility,” the number of coronavirus death cases is found to be significantly positively associated with conditional volatility in the United Kingdom, the United States, Italy, Germany, and Spain. For example, an increase in the number of death cases in the United Kingdom by 1000 is associated with about a 0.018% increase in conditional volatility. In contrast, the findings across the other markets exhibit generally insignificantly positive coefficients (Russia, and India) or inconsistently negative coefficients (Brazil and China). The findings on the impact of recovered cases reveal a consistently negative and significant association only in Italy. For our dependent variable “conditional skewness,” we find a significant impact of the number of deaths on conditional skewness in the United Kingdom, Italy, and Brazil. We observe mixed results on the relationship with number of recovered cases and conditional skewness across the markets.

5. ROBUSTNESS TESTS

To further explore the robustness of our analysis, diagnoses tests will be performed as follows:

The CDF skewed t distribution of Hansen is given by

Let εt+1=rt+1−μt be the error term, then the distribution of εt+1 is

If the model is well specified, then ut+1=Fεt+1 will follow the uniform distribution on (0, 1). In addition, the standardized residual Zt+1=Φ−1ut+1 will follow the normal distribution with mean zero and SD one, where Φ. is the cumulative distribution function of the standard normal distribution and Φ−1. is its quantile, that is, Φ−1. is the inverse of Φ.. To assess the quality of the model (robustness check) and test the specification of the models, we estimated residual u^t+1=Fε^t+1 which under a correct specification should be independent and uniformly distributed. Following Vlaar and Palm(1993) and Berkowitz(2001), if the model is well specified, the estimated residual Z^t+1=Φ−1u^t+1 follows the standard normal distribution with mean zero and SD one. Using the normalized run four classical tests: Cramervon Mises, Anderson–Darling, Watson empirical distribution, and Jarque–Bera tests. Table8 summarized the results of the four tests. We notice from the table that the null hypothesis that the model is well specified is not rejected at least at 1% confidence level for all the four test and hence the model does capture all the stylized facts highlighted in the literature concerning returns.

As mentioned before, since normal GARCH model link directly the kurtosis to the variance, it is unable to well capture the excess kurtosis that exists present in financial returns, resulting in having low probability of extreme realizations (extreme returns) than observed in the data. Therefore, we also conduct a Lagrange multiplier (LM) test for the presence of GARCH effect, as Table9 illustrates, the null hypothesis is strongly rejected for all countries, testifying for the existence of the effect of GRACH on extreme returns.

In addition, Table10 provides the descriptive statistics of the GARCH conditional volatility and conditional variance of the proposed model. While in the normal GARCH they are equal, in our model the conditional variance is higher that the GARCH volatility. This testifies that the estimated risk implied by the proposed model is higher than in the normal case, with the case of Brazil exhibiting the highest level. Furthermore, in the normal GARCH model the distribution is symmetric (skewness=0) meaning that there is equal probability of losing or gaining the same amount of money investing in the financial market, the results of our model produces in average negative skewness (η<0) as Table11 (second row) shows. These results signify that the distribution is left asymmetric which translate in higher probability of losing an amount of money than gaining the same amount except for the case of China where η>0 and hence the likelihood of gain is higher than the likelihood of loss.

The model also captures also the likelihood of extreme events (extreme returns) since the kurtosis parameter ν is small than 30³ (infinite for the normal distribution) as Table11 (third row) shows. It is even smaller for the case of China, Brazil, Russia, and India compared with other countries, attesting that the likelihood of extreme returns is higher in the emerging countries than the developing ones. We mention that the case of China is the most extreme.

6. CONCLUSION

This study attempts to explain how COVID‐19 pandemic has affected the stock market behavior of international equity indices in nine markets. Unlike other studies we focus on several dimensions of a stock market, that is, stock returns, conditional volatility, conditional skewness, and bad state probability, measured using an asymmetric exponential GARCH model. Furthermore, we have examined the influence of COVID‐19‐related death cases and recovered cases on these indicators. Unsurprisingly, our findings show that COVID‐19 has exerted adverse impact on major equity markets, which led to unprecedented rise in conditional volatilities and bad state probabilities across all the markets. However, this impact is not symmetric across all the markets. For example, China and Germany exhibit less conditional volatility; in contrast, Italy, the United States and the United Kingdom experience excessive volatility and bad state probability. Furthermore, we also find that the excessive increase in conditional volatility appears not to be persistent during the COVID‐19 period as for all the markets the conditional volatility exhibits a significant fall once the shock has been absorbed. With respect to the impact of COVID‐19‐related deaths and recovered cases on stock price behavior, the overall findings reveal that the negative affect of deaths is more pronounced, compared to the positive impact of recovered cases. These findings confirm prior empirical findings on the adverse impact triggered by financial crises (Novotny,2010; Sarkar & Patel,1998) and the COVID‐19 pandemic (Baek et al.,2020; Chaudhary et al.,2020; Zhang et al.,2020). Moreover, our findings provide important implications for investors, practitioners and policy makers. For traders and investors seeking to invest in international stock markets, the results indicate which markets are most correlated and risky, which have strong consequences for portfolio optimization and implementation of profitable trading strategies. For practitioners, the findings allow to get insights into the dynamic behavior of stock markets in the countries that are heavily affected by the pandemic in order to examine the best investment options. For policy makers, the findings confirm the critical role that the political leadership and governments can play, via mitigating the spread of pessimistic views and negative feelings amid citizens, in conveying positive signals to the investors and thereby decreasing market uncertainty.

AUTHOR CONTRIBUTIONS

Mohamed A. K. Basuony developed the idea, collected all the required data, and drafted and revised the manuscript, in addition to supervising the work. Mohammed Bouaddi performed the model and empirical analysis (tables and figures), in addition to writing the methodology. He also revised the manuscript. Heba Ali wrote and interpreted the empirical results, introduction and conclusion, in addition to revising the final manuscript. Rehab EmadEldeen wrote the literature section and provided a summary table of all the papers, in addition to revising the final manuscript. All authors read and approved the final manuscript.

Biographies

APPENDIX A. 

In the following proof, we derive the probability of bad state. The probability πt at time t of the market to be in bad state at time t +1 is given by

Let zt=btrt+1−μt+atσt1−ηtσt, then

The last equality follows from the fact that Τχν is the CDF of the standard Student t distribution of χ (with degree of freedom ν) evaluated at zero.

Notes

Basuony, M. A. K., Bouaddi, M., Ali, H., & EmadEldeen, R. (2021). The effect of COVID‐19 pandemic on global stock markets: Return, volatility, and bad state probability dynamics. Journal of Public Affairs, e2761. 10.1002/pa.2761 [PMC free article] [PubMed] [CrossRef]

Footnotes

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

REFERENCES