**4. Methodology**

The current study investigates the relationship between COVID-19 infection and death announcements with oil price volatility. Our analysis considers existing economic uncertainty and stock market uncertainty in this relationship to disentangle the effects of these uncertainties from that of COVID-19 deaths and infection announcements.

$$\text{VOL(oil)} = \alpha + \beta \mathbf{1} \,\text{COV(f)} + \beta \mathbf{2} \,\text{COV(s)} + \beta \mathbf{3} \,\text{ELI} + \beta \mathbf{4} \,\text{MLI} + \beta \mathbf{5} \,\text{K} + \varepsilon \tag{1}$$

where:

> *VOL(oil)* refers to three different measures of oil price volatility,


The reason that our models apply more timeseries regarding the MU variable is due to the fact that the geographical areas are examined individually and each of them is combined with the corresponding stock index.

More details for the variables in our models can be found in the Appendix A.

Our models investigate how COVID-19 death or infection increase (speed) and actual deaths (fatal) affect oil volatility by using the following seven models

$$\text{VOL(oil)} = \mathfrak{a} + \beta \mathbf{1} \,\text{COV}(f) + \mathfrak{e} \tag{2}$$

$$\text{VOL(oil)} = \mathfrak{a} + \mathfrak{f}\mathfrak{2}\ \text{COV(s)} + \mathfrak{e} \tag{3}$$

$$\text{VOL(oil)} = \alpha + \beta 1 \,\text{COV(f)} + \beta 2 \,\text{COV(s)} + \varepsilon \tag{4}$$

$$\text{VOL(oil)} = \alpha + \beta \text{1 } \text{COV(f)} + \beta \text{2 } \text{COV(s)} + \beta \text{3 } \text{MLI} + \varepsilon \tag{5}$$

$$VOL(oil) = \alpha + \beta 1 \ COV(f) + \beta 2 \ COV(s) + \beta 3 \ EII + \varepsilon \tag{6}$$

$$\text{VOL(oil)} = \alpha + \beta \text{1 COV(f)} + \beta \text{2 COV(s)} + \beta \text{3 MLI} + \beta \text{4 ElI} + \varepsilon \tag{7}$$

$$\text{VOL(oil)} = \text{a} + \beta \text{1 } \text{COV(f)} + \beta \text{2 } \text{COV(s)} + \beta \text{3 } \text{MII} + \beta \text{4 } \text{EI} + \beta \text{5 } \text{K} + \varepsilon \tag{8}$$

In our analysis, we run fixed-effect panel models, and we interpret the fitness of estimated model and significance of coefficients as expressed by adjusted R2, t-statistics, and significance of t-statistics. Variance inflation factors (VIFs) of our models are between 1.6 and 1.85, significantly lower than 6. Then we investigate whether our models are robust in particular economic zones and under different model assumptions.

#### **5. Empirical Results**

In Table 1 we present the descriptive statistics from where we can observe two main results. First, there is an intensive oil price volatility, economic uncertainty, and market uncertainty and second, there is an accelerated growth rate of infections and deaths for the investigated period. The sharp increase in deaths and infection rates as a result of the pandemic COVID-19 and the consequent fear of an escalating crisis raised legitimate questions about the degree of impact of the pandemic in the price of crude oil in international markets as well as the volatility of its price.

**Table 1.** Descriptive statistics.


Note: VOL(oil) 1, 2 and 3 are respectively the CBOE 30 day crude oil implied volatility index, Crude oil 3 month implied volatility index, and Brent 3 month implied volatility index. Estimates of 3-month implied volatility. COV(s) 1,2,3 and 4 are respectively the logarithm of (new daily COVID-19 infection case announcements divided by seven days lagged total COVID deaths), the logarithm of (new daily COVID-19-related deaths divided by 7 days lagged total COVID deaths), the logarithm of (new daily COVID-19-related deaths divided by 14 days lagged total COVID deaths), and the logarithm of (new daily COVID-19-related deaths divided by 21 days lagged total COVID deaths). MU1,2,3 and 4 are respectively the VIX index, VSTOXX Index-EURO STOXX 50 Volatility, the NIKKEI Volatility Index, and the Cboe China ETF Volatility index.

Table 2 shows the results of the individual models presented above for the examined geographical areas of our study.

Our results in Table 2 are based on world panel data, and they indicate that COVID-19 deaths (COV(f)) and speed of death increase (COV(s)) can explain as stand-alone variables 11% and 39% of the oil-volatility (Columns 2 and 3 on Table 1 respectively).


**Table 2.** COVID-19 death announcements and oil price volatility, panel world 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. \*\*\* asterisks 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 day 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 day crude oil implied volatility index, the dependent variable in Model 7 is Crude oil 3 month implied volatility index, and the dependent variable in Model 8 is Brent 3 month implied volatility index.

> When market uncertainty (Column 5, Table 2) or economic uncertainty (Column 6, Table 2) is taken into account, the significance of the overall model (adjusted R-square) increases to 64% and 60% respectively. If both Market Uncertainty (MU, expressed by the American VIX index) and Economic Uncertainty (EU) alongside with COV(f) and COV(s) are considered in the model (Column1, Table 2) the adjusted R-square of the model increases to 69% if the dependent variable is the CBOE 30 day crude oil implied volatility index. In the models presented in that Table, COV(f) is the logarithm of total deaths, and COV(s) is the logarithm of new daily COVID-19 deaths divided by seven days lagged total COVID-19 deaths. The model illustrated in Column 7 uses as dependent variable the Crude oil three months implied volatility index, and the model presented in Column 8 uses as the dependent variable in Brent 3 month implied volatility index. The latter models report an even higher (77% and 82%) adjusted R-square. All the dependent variables in all these models are positive and significant at a 1% level, providing robust evidence of significance for world data.

> The above observations lead to comparable conclusions with other studies of the same period, which examine the effect of the pandemic on stock values or energy prices or on other products (Refs. [2,7,14]).

> From the above we conclude that the pandemic affected the volatility of the price of crude oil globally. This influence is confirmed both by the new cases of infections and by the rate of infections.
