key: cord-0908979-yd2wim3t authors: Jin, Lifu; Zheng, Bo; Ma, Jiahao; Zhang, Jiu; Xiong, Long; Jiang, Xiongfei; Li, Jiangcheng title: Empirical study and model simulation of global stock market dynamics during COVID-19 date: 2022-04-26 journal: Chaos Solitons Fractals DOI: 10.1016/j.chaos.2022.112138 sha: d93e109acd1b45ab1746ab70e720d45321022689 doc_id: 908979 cord_uid: yd2wim3t At the beginning of 2020, COVID-19 swept the world and changed various aspects of human society, such as economy and finance, life and health, migration and population. We first empirically study how the dynamic behaviors of stock markets are affected by COVID-19, and focus on the large volatility dynamics, variation-fluctuation correlation function and epidemic-fluctuation correlation function. Then we generalize the Heston model to simulate the global stock market dynamics, and an epidemic index computed from empirical data is directly taken as the external force in the modelling. In March 2020, the World Health Organization (WHO) declared that COVID-19 could be characterized as a pandemic. The outbreak of the epidemic has scientifically attracted the attention of scholars in various fields. Based on the epidemic model, government intervention policies and complex social networks have been introduced to investigate the spread of the epidemic and predict the trend of the epidemic [1] [2] [3] [4] [5] [6] . In fact, the epidemic has significantly changed people's lives in many aspects, such as health, transportation, catering service and economy etc [7] [8] [9] . Financial markets exhibit the fastest response at the state level [10] [11] [12] . After COVID-19 spread worldwide, the financial markets experienced strong fluctuations. For example, the U.S. stock markets collapse significantly, with the S&P 500 index dropping 20% in March 2020. The outbreak of COVID-19 has an impact on the oil price, exchange rate, and cryptocurrencies [13] [14] [15] [16] [17] [18] . The epidemic elevates the volatility of the oil markets and intensifies the correlation between the oil markets and the U.S. stock markets [13, 14] . The outbreak also affects the spillover of the RMB exchange rate, and enhances the relationship between the exchange rate of the Japanese Yen and the stock markets [15, 16] . The cryptocurrency markets reduce the self-similarity and the efficiency due to COVID-19 [17, 18] . Furthermore, the emergence of COVID-19 strengthens the economic policy uncertainty and the geopolitical risks [19] [20] [21] [22] . The financial markets exhibit heterogeneous behaviors towards socio-economic and political announcements on the epidemic, and a positive-negative asymmetry towards news about the epidemic [21, 22] . Moreover, the complex network structure of the global financial markets is analyzed [23] [24] [25] . There is a drastic reduction in connectivity among countries after the outbreak in the trade network, but not in the stock network. COVID-19 leads to a close J o u r n a l P r e -p r o o f Journal Pre-proof relation of the stock markets among countries [24, 25] . Besides, COVID-19 in 2020 has been compared with the global financial crisis in 2008 [26, 27] , and the European and U.S. markets are more influenced by COVID-19 than the Asian markets [26] . In these previous studies, the epidemic effect on the financial markets is explored from some specific aspects, such as the currencies, the economic policies, and the complex networks of the global markets. In this paper, we focus on the fundamental dynamic behavior of the stock markets, in particular, the specificity of the large-volatility dynamic in 2020, the impact of COVID-19 on the leverage effect, and the correlation between the epidemic and the stock market dynamics. Based on the empirical data, we investigate the large fluctuations induced by COVID-19 in 2020 and their dynamic effects, compared with those in the past 10 years. Due to different economic and medical levels, the epidemic effect on stock markets may vary from country to country. Therefore, it is very important to quantify the epidemic effect on stock markets through computing the correlation function between the epidemic index and the stock price. In addition to the empirical analysis, the model simulation is also an important approach to investigate the epidemic effect on the financial markets. The econometric models are used to study the impact of COVID-19 on stock market returns and volatilities [28] [29] [30] , and the deep learning models are applied to analyze the commodity prices [31] . Incorporating information about the epidemic improves the performance of forecasting the abnormal stock prices [32, 33] . In this paper, we generalize the well-known Heston model to simulate the stock market dynamics under the influence of COVID-19, and explain the empirical findings from the real market data. An The structure of the paper is as follows. Data and methods are described in Section 2. The empirical analysis is presented in Section 3. The generalized Heston model is simulated in Section 4. The conclusion comes in Section 5. The stock market data and epidemic data from 32 countries worldwide are collected, respectively from the websites https://cn.investing.com and https://github.com/owid/covid-19-data. The stock market indexes are listed in To study the dynamic relaxation after a large volatility, we introduce the remnant volatility, where ... c  represents the average over those t with specified large volatilities, and , and the threshold  is well above v , e.g., =3v  . For reducing the fluctuations, we introduce the cumulative function and () Vt  may approximately obey a power-law-like behavior up to a certain time period, since large shocks in volatilities are usually followed by a series of aftershocks [34] . Thus the cumulative function () Vt  could be written as The variation-fluctuation correlation function is defined as where ...  represents the average over time t , and the correlation between the past variation () Rt  and the future fluctuation | ( . The phenomenon of a negative () Lt is called the leverage effect. In Ref. [35] , it is shown that large volatilities dominate the variation-fluctuation correlation in the stock market dynamics. In other words, the leverage effect is more pronounced during the periods with large fluctuations. Therefore, the leverage effect after the outbreak of COVID-19 reflects the epidemic impact on the stock markets. We denote the daily number of new confirmed COVID-19 cases in each country with () Nt  . Occasionally, the government revised the number of the confirmed cases, resulting in a negative value. For simplicity, these negative data are set to zero. In Spain, the data of the new where () Nt   is the average number of the confirmed cases in the past  days, and = 14  is reasonably set to reflect the background epidemic [36] . In other words, the epidemic index () It  describes the temporal variation of the new confirmed cases compared to the background epidemic. In subsequent calculations, the non-trading days will be ignored, and t represents only the trading day. Then, the epidemic-fluctuation correlation function is defined as The impact of the epidemic on a stock market can be quantified through () Ct under a certain time window [36, 37] . The perspectives, one of which may be the shape of the Africa's population pyramid [38] . The public panic and mortality burden is mainly caused by the elder with underlying medical conditions, while Africa has the youngest population among the world. The epidemic did not caused a great panic in Africa, thus the correlation between COVID-19 and the stock dynamics is absent. From an economic intuition point of view, COVID-19 is a black-swan event that was new and unforeseeable, causing panic among people and strong fluctuations in financial markets. After the epidemic entered the global pandemic, the governments adopted city closures and travel bans etc, the epidemic was globally controlled to a certain extent. On the other hand, many countries have made great efforts to develop COVID-19 vaccines, which reduced the public fear [39] . In particular, China, the country with the earliest outbreak, basically returned to the normal life within four months. Therefore, the correlation between COVID-19 and the stock dynamics essentially diminished after June 2020. In 1993, Heston proposed a stochastic volatility model to price options [40] . The specific form of the model is as follows The coherent resonance phenomenon of the stock returns and volatilities can be investigated with the Heston model, and the herd behavior of the stock prices influenced by the time delay can also be explored by the delayed Heston model [41] [42] [43] . In addition, it is argued that the leverage effect could be explained in terms of a wide class of correlated stochastic volatility models, such as the Heston model [44] . In this work, we introduce a generalized Heston model to simulate the dynamic behaviors of the stock markets during COVID-19. Due to the sudden outbreak of COVID-19, the stock markets are exposed to exogenous System decided to lower the target range for the federal funds rate, which led to a bull market in the second half of 2020. Due to the government policy intervention, a zero risk-free rate  is not sufficient to capture the peculiarity in 2020. Therefore, we set a non-zero risk-free rate  for each country, which is about 0.6 -0.7. Moreover, as shown in Figure 4 ( To summarize, the characteristic dynamic behaviors induced by COVID-19 as displayed in Figure 4 can be fully simulated just through introducing the epidemic index computed from the empirical data as the external force in the generalized Heston model. This is a great success. COVID-19 has essentially influenced the dynamic behaviors of the stock markets after it Preliminary prediction of the basic reproduction number of the Wuhan novel coronavirus 2019-nCoV Maximum entropy method for estimating the reproduction number: An investigation for COVID-19 in China and the United States Self-isolation or borders closing: What prevents the spread of the epidemic better? Asymptotic estimates of SARS-CoV-2 infection counts and their sensitivity to stochastic perturbation Two-level modeling of quarantine Modeling the Spatiotemporal Epidemic Spreading of COVID-19 and the Impact of Mobility and Social Distancing Interventions COVID-19 and the march 2020 stock market crash. Evidence from SP500 Stay-at-Home Stocks Versus Go-Outside Stocks: The Impacts of COVID-19 on the Chinese Stock Market COVID-19: A pandemic with positive and negative outcomes on resource and waste flows and stocks The impact of covid-19 on emerging stock markets The Outbreak of COVID-19 and Stock Market Responses: An Event Study and Panel Data Analysis for G-20 Countries, Glob Stock markets and the covid-19 fractal contagion effects Revisiting oil-stock nexus during COVID-19 pandemic: Some preliminary results How has the relationship between oil and the US stock market changed after the Covid-19 crisis? Spillover effects of RMB exchange rate among the Belt and Road countries: Before and during COVID-19 event Japanese currency and stock market-What happened during the COVID-19 pandemic? Asymmetric efficiency of cryptocurrencies during COVID19 Changes to the extreme and erratic behaviour of cryptocurrencies during COVID-19 COVID-19 pandemic, oil prices, stock market, geopolitical risk and policy uncertainty nexus in the US economy: Fresh evidence from the wavelet-based approach COVID-19 lockdowns, stimulus packages, travel bans, and stock returns Financial earthquakes: SARS-CoV-2 news shock propagation in stock and sovereign bond markets COVID-19 and stock market volatility: An industry level analysis Implications of COVID-19 Pandemic on the Global Trade Networks A study of systemic risk of global stock markets under COVID-19 based on complex financial networks Analysis of global stock markets' connections with emphasis on the impact of COVID-19 COVID-19's disasters are perilous than Global Financial Crisis: A rumor or fact? Analysis of stock market efficiency during crisis periods in the US stock market: Differences between the global financial crisis and COVID-19 pandemic Exploring the Initial Impact of COVID-19 Sentiment on US Stock Market Using Big Data The role of Covid-19 for Chinese stock returns: evidence from a GARCHX model Investigating the Psychology of Financial Markets During COVID-19 Era: A Case Study of the US and European Markets Deep learning models for forecasting and analyzing the implications of COVID-19 spread on some commodities markets volatilities Impacts of COVID-19 local spread and Google search trend on the US stock market Methods for forecasting the effect of exogenous risks on stock markets Time-reversal asymmetry in financial systems On return-volatility correlation in financial dynamics Temporal correlation functions of dynamic systems in non-stationary states Simplified calculations of time correlation functions in non-stationary complex financial systems What could explain the lower covid-19 burden in africa despite considerable circulation of the sars-cov-2 virus? Covid-19: hotel industry response to the pandemic evolution and to the public sector economic measures A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options The time delay restraining the herd behavior with Bayesian approach Coherence resonance-like and efficiency of financial market Realized volatility: A review Random diffusion and leverage effect in financial markets Lifu Jin: Conceptualization, Software, Visualization, Writing -original draft Formal analysis, Supervision, Writing -review & editing, Funding acquisition Writing -review & editing, Funding acquisition