*Robustness Tests*

To test the robustness of our models first we focus on the three major economic areas, Asia, Europe, and North America to find out if our conclusions are in line with global conclusions presented in Table 2. The findings of these analysis are presented in Tables 3–7.


**Table 3.** COVID-19 death announcements and oil price volatility, European data.

Note: The table includes daily aggregated data of European countries. The number in parentheses represent t-statistics. \* and \*\*\* indicate 10%, and 1% level of significance, respectively. COV(f) is the logarithm of total deaths, COV(s) is the logarithm of (new daily COVID deaths divided by 7 days lagged total COVID deaths), MU is the US vix index, EU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1-6 is CBOE 30 days crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 months implied volatility index and the dependent variable in Model 8 is Brent 3 months implied volatility index.

> Table 3 presents the model's predictive ability in European data, while Table 4 presents the North American data under the specifications of the models presented in Table 2. They illustrate solid predictive power in terms of coefficients and adjusted R-square. In particular adjusted R-square ranges between 70% (Column 1, Tables 3 and 4) and 84% (Column 8, on both Tables 3 and 4).

**Table 4.** COVID-19 death announcements and oil price volatility, North American data.


Note: The table includes daily aggregated data of North American countries. The number in parentheses represent t-statistics. \*\* and \*\*\* indicate 5% and 1% level of significance, respectively. COV(f) is the logarithm of total deaths, COV(s) is the logarithm of (new daily COVID deaths divided by 7 days lagged total COVID deaths), MU is the US vix index, EU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1–6 is CBOE 30 days crude oil implied volatility index. The dependent variable in Model 7 is Crude oil 3 months implied volatility index. The dependent variable in Model 8 is Brent 3 months implied volatility index.

> On Table 5 we investigate whether by using the VSTOXX Index-EURO STOXX 50 Volatility index as a measure of Market Uncertainty for European data we can have significantly different results. In this case, the results we find are comparable.


**Table 5.** COVID-19 death announcements, European volatility, and oil price volatility, European data.

Note: The table includes daily aggregated data of European countries. The number in parentheses represent t-statistics. \*\* and \*\*\* indicate 5%, and 1% level of significance, respectively. COV(f) is the logarithm of total deaths, COV(s) is the logarithm of (new daily COVID deaths divided by 7 days lagged total COVID deaths), MU is the VSTOXX Index-EURO STOXX 50 Volatility index, EU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1–6 is CBOE 30 days crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 months implied volatility index and the dependent variable in Model 8 is Brent 3 months implied volatility index.

> We examine Asian data in Tables 6 and 7, using the Japanese stock market volatility (Table 6) and Chinese stock market volatility (Table 7) index to express market uncertainty.


Note: The table includes daily aggregated data of Asian countries. The number in parentheses represent t-statistics. \*\*\* indicate level of significance. COV(f) is the logarithm of total deaths, COV(s) is the logarithm of (new daily COVID deaths divided by 7 days lagged total COVID deaths), MU is the Nikkei Volatility index, EU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1–6 is CBOE 30 days crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 months implied volatility index, and the dependent variable in Model 8 is Brent 3 months implied volatility index.

> Tables 6 and 7 show the robustness of the significance data (COV(f)) but they do not confirm consistency for the significance of COVID-19 growth data (COV(s), columns 1, 6–8 of Table 6 and columns 7 and 8 of Table 7). This may be due to the slow growth of these indices in Asian markets, which probably does not reflect the importance of demand for oil consumption worldwide, as the main markets are the European and the North American markets.


**Table 7.** COVID-19 death announcements, Chinese volatility, and oil price volatility, Asian data.

Note: The table includes daily aggregated data of Asian countries. The number in parentheses represent t-statistics. \*\* and \*\*\* indicate 5%, and 1% level of significance, respectively. COV(f) is the logarithm of total deaths, COV(s) is the logarithm of (new daily COVID deaths divided by 7 days lagged total COVID deaths), MU is the Cboe China ETF Volatility index, EU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1–6 is CBOE 30 days crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 months implied volatility index, and the dependent variable in Model 8 is Brent 3 months implied volatility index.

> A second evidence for robustness is also provided in Table 8 which presents the results of our models using world aggregated data and shows that coefficients are positive and significant irrespectively of which model is applied while adjusted R-square is also sufficient.

**Table 8.** COVID-19 death announcements and oil price volatility, world aggregated data.


Note: The table includes world aggregated data. The number in parentheses represent t-statistics. \*\*\* indicate 1% level of significance. COV(f) is the logarithm of total deaths, COV(s) is the logarithm of (new daily COVID deaths divided by 7 days lagged total COVID deaths), MU is the US vix index, EU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1–6 is CBOE 30 days crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 months implied volatility index, and the dependent variable in Model 8 is Brent 3 months implied volatility index.

> Third, in Tables 9–11 we test the robustness of our models by replacing one of our variables using world panel data. In Table 9 we investigate the effect of COVID-19 infection speed instead of examining COVID-19 death speed. These models are significant, but they report a slightly lower adjusted R-square, indicating that markets are more worried about death growth rates and actual deaths than COVID-19 infection growth rates. This may be because they regard that economic effect of deaths is more certain and robust than reporting cases that can be manipulated or affected by the number of tests taken.


**Table 9.** COVID-19 death announcements, infection speed, and oil price volatility, world panel data.

Note: The table includes panel data of six geographical areas, namely North America, South America, Europe, Africa, Asia, and Oceania. The number in parentheses represent t-statistics. \*\*\* indicate 1% level of significance. COV(f) is the logarithm of total deaths, COV(s) is the logarithm of (new daily COVID infection case announcements divided by 7 days lagged total COVID deaths), MU is the US vix index, EU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1–6 is CBOE 30 days crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 months implied volatility index, and the dependent variable in Model 8 is Brent 3 months implied volatility index.

> Tables 10 and 11 present the results under different assumptions (2-week and 3-week respectively, instead of 7-day speed) about the COVID-19 death speed. These models are significant and report similar coefficients but convey slightly lower significance than our 7-day basic Model presented in Table 2.

**Table 10.** COVID-19 death announcements, 2-week speed, and oil price volatility, world panel data.


Note: The table includes panel data of six geographical areas, namely North America, South America, Europe, Africa, Asia, and Oceania. The number in parentheses represent t-statistics. \*\*\* indicate 1% level of significance. COV(f) is the logarithm of total deaths, COV(s)is the logarithm of (new daily COVID deaths divided by 14 days lagged total COVID deaths), MU is the US vix index, EU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1–6 is CBOE 30 days crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 months implied volatility index and the dependent variable in Model 8 is Brent 3 months implied volatility index.


**Table 11.** COVID-19 death announcements, 3-week speed, and oil price volatility, world panel data.

Note: The table includes panel data of six geographical areas, namely North America, South America, Europe, Africa, Asia, and Oceania. The number in parentheses represent t-statistics. \*\*\* indicate 1% level of significance. COV(f) is the logarithm of total deaths, COV(s)is the logarithm of (new daily COVID deaths divided by 21 days lagged total COVID deaths), EU is the US vix index, MU is the economic uncertainty index. R<sup>2</sup> adj is the R-square adjusted. The dependent variable in Model 1–6 is CBOE 30 days crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 months implied volatility index and the dependent variable in Model 8 is Brent 3 months implied volatility index.

> Table 12 compares the basic Model (Column 1, Table 12) with a model that takes account the weekly effect (Column 2, Table 12). The findings illustrate that there is no significant "day of the week" effect in the data examined, and the robustness of these data remains intact after we account for this factor.


**Table 12.** COVID-19 death announcement and oil price volatility, world panel data.

Note: The table includes panel data of six geographical areas, namely North America, South America, Europe, Africa, Asia, and Oceania in columns 1–2. The number in parentheses represent *t*-statistics. \*\*\* indicate 1% level of significance. COV(f) is the logarithm of total deaths, COV(s) is the logarithm of (new daily COVID deaths divided by 7 days lagged total COVID deaths), EU is the US vix index, MU is the economic uncertainty index, and week is a dummy variable taking the value one on Mondays, zero otherwise. The dependent variable is CBOE 30 days crude oil implied volatility index. R<sup>2</sup> adj is the R-square adjusted.

Our findings offer a valuable contribution to the existing literature as we provide evidence that COVID-19 death growth rates and deaths affect oil volatility significantly. The pandemic affects the volatility of the price of crude oil worldwide. This result is confirmed both by the new cases of infections and by the rate of infections. These conclusions are verified separately for each geographic area and the world as a whole. The contribution of this study is not limited to the indication that COVID-19 is a new factor of risk that affects oil prices on top of economic and market uncertainty but also provides new measures of risk factor like the speed rate of death.

## **6. Conclusions**

In this study we investigate the relationship between COVID-19 infection and death announcements with oil price volatility. We use the speed rate of deaths as a proposed measure for the COVID-19 risk and we apply panel data from six world geographical areas taking into consideration the existing economic uncertainty and stock market uncertainty in order to separate these effects from the effects resulting from the announcements of COVID-19 deaths and infection. The applied tests show that oil volatility is significantly affected by COVID-19 deaths which indicates that COVID-19 is a new factor of risk which one can argue has intensified the market risk.

The findings of our study underscore the importance of better understanding the effects of a pandemic shock on movements and the volatility of oil prices. In addition, it emphasizes the need for policy-makers and market stakeholders to explicitly consider changes in global health conditions when analyzing the causes and consequences, in order to plan an appropriate response to oil price shocks. In this regard, although lockdown policies of certain economic activities and restrictions in travelling had some positive effects in reducing the transmission of the health crisis, at the same time there were negative effects on the economy. In addition, the policies of governments around the world as well as Central Banks to support economies and individuals by offering them access to affordable financing have sent a clear message of calming the markets and addressing the crisis in many ways.

In particular, the EU has taken bold decisions by setting up a recovery fund for its Member States. Based on the results of our study, such measures are in the right direction and what is proposed at this stage is to create a framework with a permanent form. Such a framework should have two pillars, one institutional and one economic, in order to calm the markets from any concerns about similar cases in the future. The institutional framework will outline possible restrictive measures in countries with high rates of infection, but at the same time, these measures will be supplemented by financial support.

The conclusions of this study can be used as a guide for future decisions of managers, investors, and policy-makers regarding management, asset pricing, and market stability. Risk managers and asset pricing managers have already incorporated the pandemic in their short and medium-term decisions to prepare their business plans. Especially, for the energy companies that affected substantially by the restrictions in travelling and transportation, this study provides interesting considerations. Especially, oil and gas producers, it is crucial to have always a plan B to face similar phenomenon in the future while, individual investors must also take into consideration COVID-19 in their expectations.

In any way, we already know that although vaccines were available in the first semester of 2021 for the public worldwide, the Delta mutation of COVID-19 is spreading rapidly. Nonetheless, for future work, another important factor of this equation is the technological advances and especially the 5G infrastructure which provided significant solutions in business communication and education especially in the more developed countries.

**Author Contributions:** A.G.C., P.K., I.K. and K.V. contributed equally to all parts of the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** The APC was funded by MSc in Operations Management, University of West Attica and Technical University of Crete.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.


**Table A1.** Description of variables used in the study.
