Dynamic Connectedness among Vaccine Companies’ Stock Prices: Before and after Vaccines Released

: This study investigates the interconnectedness among the stocks of the publicly listed vaccine-producing companies before and after vaccine releases in 2020/21. In doing so, the study utilizes the daily frequency equity returns of the major vaccine producers, including Moderna, Pﬁzer, Johnson & Johnson, Sinopharm and AstraZeneca. First, the investigation applies the TVP-VAR Dynamic Connectedness approach to explore the time–frequency connectedness between the stocks of those vaccine producers. The empirical ﬁndings demonstrate that Moderna performs as the most prominent net volatility contributor, whereas Sinopharm is the highest net volatility receiver. Interestingly, the vaccine release signiﬁcantly increases the stock market connectedness among our sampled vaccine companies. Second, the cross-quantile dependency framework allows for the observation of the interconnectedness under the bearish and bullish stock market conditions by splitting any paired variables into 19 quantiles when considering short-, medium- and long-memories. The results also show that a high level of connectivity among the vaccine producers exists under bullish stock market conditions. Notably, Moderna transmits signiﬁcant volatility spillovers to Sinopharm, Johnson & Johnson and AstraZeneca under both the bearish and bullish conditions, though the volatility transmission from Moderna to Pﬁzer is less pronounced. The policy implication proposes that the vaccine release allows companies to increase their stock returns and induce substantial volatility spillovers from company to company.

Introduction
The spread of a novel coronavirus disease across the globe has considerably elevated the importance of the pharmaceutical industry, putting additional pressure on vaccineproducing companies to come forward with a protection, as vaccine inoculation appeared to be the most effective way to fight the pandemic. Therefore, the producing companies have strived to gain substantial knowledge of the virus's biological features and achieve technological sophistication to successfully develop vaccine treatments and also acquire a competitive advantage over other companies [1,2]. Moreover, due to the COVID-19 pandemic and the lockdowns, many businesses had to suspend their activities, whereas the activities of the pharmaceutical companies, especially the vaccine producers, turned out to be more prominent. In this paper, it is argued that the vaccine release provides positive sentiments to investors to consider their respective companies' stocks as safe and high yield investments. The news about vaccine releases against the COVID-19 disease is exceptional and expected to be a quality predictor since the impact of the COVID-19 pandemic is tremendous and global. Hence, the motivation of this study is to reveal whether the vaccine releases play a significant role in changing the pattern of total connectedness and the spillover effect among vaccine-producing companies.
Several studies [3][4][5][6][7][8] find strong evidence of increased market connectedness between the stocks of those vaccine companies due to the high level of uncertainty about infections and the promise of potential success during the pandemic. According to the findings of a few investigations [9][10][11][12][13][14][15], investors during crisis periods, including emergencies of uncertainty regarding infections, only consider risk seeking for safer assets, thus increasing the connectedness among relatively safer stocks. In particular, investors are likely to invest more in the vaccine-producing companies that are the most prosperous and safest during the pandemic. The companies used different vaccine processes and required different numbers of doses. Therefore, increased investments in the different vaccine companies could cause changes in the time-dynamic connectedness among them.
The literature primarily focuses on stock market connectedness under various external shocks. For example, the connectedness of major stock markets has increased after the global financial crisis in 2008 [16][17][18].
Stock market volatilities can be induced by such exogenous factors as critical political decisions, referendums, economic crises, stock and bond market uncertainty, high inflation, and crude oil and natural gas price fluctuations [19][20][21]. Developed stock markets transmit a spillover effect to emerging stock markets [22]. At the same time, emerging markets lack the power to transmit volatility to other markets. The interconnectedness between emerging and developed markets is also conditional on external shocks. For instance, during the global emerging market crisis, the U.S. stock market had less power to influence emerging African countries both in the short-run and long-run [23]. More recently, several studies have investigated the stock market connectedness in terms of the influence of the COVID-19 pandemic. The COVID-19 pandemic created a high level of uncertainty, leading to increased volatility and connectedness of various stock markets [24][25][26][27][28][29]. Moreover, the COVID-19 outbreak may change the direction of volatility spillovers from one stock market to another [30][31][32]. Interestingly, Chen [33] reveals that the stock market connectedness depends on markets' economic integration. However, these studies utilize stock indices instead of particular companies' equity returns in the same industry, as we do in this current study.
The literature suggests several channels for increasing stock market connectedness during crisis times. For example, Trevino [34] distinguishes between two informational channels of financial contagion: the fundamental and the social learning. The fundamental channel pertains to financial interaction among economic agents and economies. In contrast, the social learning channel means that economic agents make their decisions by observing the behaviour of other agents. Moreover, Trevino [34] documents that economic agents tend to underestimate the power of the fundamental channel and overvalue the social channel, thus weakening the fundamental correlation and enhancing the channel of social learning. Pritsker [35] describes several rational or fundamental channels of financial contagion, including financial market linkages, the real sector linkages, the interaction of financial institutions and markets, and financial institution linkages. When analyzing the financial contagion, US credit default swaps and TED spreads reduce the dynamic conditional correlation among the stock returns of emerging markets [17]. Baur [36] reveals that the main channels of financial contagion during the 2008 GFC include the contagion of aggregate stock market indices, the contagion of financial sector stocks across countries and the contagion of the real economy sectors. Notably, some sectors such as healthcare and technologies were least affected by the crisis. Horta et al. [37] argue that the behaviour of investors plays a crucial role in determining volatility transmission through wealth constraints [38,39] or portfolio rebalancing [40,41]. Portfolio rebalancing implies that investors reduce risks by switching to safer assets. Horta et al. [37] find that portfolio rebalancing was a more prominent factor during the GFC than wealth constraints.
Many studies emphasize that investors' behavior is crucially important in determining stock market co-movements. The influence of irrational behavior is transmitted through different perspectives. For example, sentiment-based factors significantly influence comovements, stock returns and volatility spillovers [11,[42][43][44]. Interestingly, during crisis periods, investors only consider risk-seeking for safer assets. Lee [45] documents that investors' expectations regarding future economic uncertainty intensify the stock and Treasury bond markets' co-movement in Europe. Moreover, COVID-19 cases and stock returns of the G7 countries demonstrate a strong co-movement [14]. Moreover, their study argues that during COVID-19, the pandemic investors are especially inclined to be risk averse. López-Cabarcos et al. [46] find that sentimental factors highly influence Bitcoin volatility. Pasquariello [47], by using a model of multi-asset trading, finds that financial contagion can still be an equilibrium result if speculators receive heterogeneous private information. Veldkamp [48] documents that stocks demonstrate a high price covariance due to the high cost of information.
In comparison with the existing literature, this study provides several contributions. First, the existing literature on market connectedness primarily utilizes stock indices instead of the equity returns of a particular industry, whereas this study analyzes the dynamics of vaccine-producing companies, and their high importance during the COVID-19 virus. Second, most other studies argue that stock market connectedness is induced by various exogenous shocks such as a financial crisis or the COVID-19 outbreak. However, this study suggests a more novel idea since we aim to examine if the vaccine release has induced the stock market connectedness of vaccine-producing companies. Third, the application of sophisticated econometric techniques allows us to overcome the high frequency and extreme volatility of the data. For instance, the TVP-VAR dynamic connectedness allows for measuring the volatility transmission from one vaccine producer to another, thereby identifying net volatility contributors and receivers. Moreover, the cross-quantilogram is not sensitive to an abnormal distribution, and the problems of high-frequency series in the presence of outliers enable splitting the relations of both dependent and independent variables into quantile coefficients. In addition, the cross-quantilogram approach provides a statistical significance level under each quantile, apart from the advantages above.
Fourth, the unique findings of this study approve the hypothesis that the vaccine release significantly increases the stock market connectedness among the major vaccineproducing companies. For example, the increase in the total connectedness index (TCI) from the second quarter of 2021 is induced by the vaccine release at the end of 2020-the beginning of 2021. Interestingly, Moderna appears as the most prominent net volatility transmitter, whereas Sinopharm is the highest net volatility receiver, transmitting no net volatility. The cross-quantilogram analysis consistently shows that Moderna transmits significant volatility spillovers to all companies, except Pfizer. Moreover, the results demonstrate a high level of connectivity under bullish market conditions. Moreover, all short and long terms are considered by taking 1-day, 5-day, 22-day and 66-day lags.
The structure of the remainder of the study is organized as follows. Section 2 explains the methods and data. Section 3 provides the results. Section 4 represents a discussion of the results. Section 5 concludes the study, highlighting policy implications.

TVP-VAR Dynamic Connectedness
To estimate the volatility spillover among the stock prices of Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca, this study applies the time-frequency connectedness namely the time-varying parameter vector autoregression (TVP-VAR) method proposed by Antonakakis and Gabauer [49]. The framework possesses a few advantages. First, it permits the variance to change over time horizon by using a stochastic volatility Kalman filter estimation as well as forgetting factors [50]. Therefore, this approach addresses the bias estimation problem by selecting the size of rolling window randomly. Second, the TVP-VAR dynamic connectedness is suitable for relatively less frequent series with small spans of time. The TVP-VAR method is determined as follows: where Y t represents an N × 1 conditional volatility vector, Y t−1 denotes the lagged conditional vector of Y t with a N p × 1 dimension. Further, β t signifies the time-varying parameters matrix with the N × N p order. Additionally, ∈ t represents the vector of errors with an N × 1 order along with the N × N time-varying covariance matrix S t . The vector of the parameter matrix, β t , depends on the respective coefficient of β t−1 following an N × N p error matrix along with an N p × N p variance-covariance matrix. The TVP-VAR dynamic connectedness estimates the generalized connectedness [51] and incorporating the timevarying parameters and the error covariance. The current method allows one to estimate the volatility spillovers by utilizing the generalized impulse response functions (GIRF) [52] and the generalized forecast error variance decompositions (GFEVD) [53]. Therefore, the transformation of the VAR to a vector moving average (VMA) provides a representation for GIRF and GFEVD estimation based on the Wold theorem as follows: A 0,t = I (5) where β t = β 1,t , β 2,t , . . . , β p,t and A t = A 1,t , A 2,t , . . . , A p,t , consequently, β i,t and A i,t are dimensional parameter matrices ordered as N × N. The GIRFs show the response of all respective variables to a shock in a variable, i. The approach implies testing the differences between a J − step − ahead forecast both when variable i is under and out of a shock as the model employed does not follow a structural modelling.
Equation (7) below shows the estimation of the difference to the shock in variable i.
where Ψ g j,t (J) is the forecast value of the time horizon J, and S − 1 2 jj,t A J,t S t j,t is a one standard error shock. In our study, we consider the stock returns of the major vaccine producing companies including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca in rotation as variables i and j. Note that δ j,t indicates the vector of selection and F t−1 characterizes the set of information until t − 1. After that, the GFEVD is calculated, namely by dividing one variable's variance share on the sum of other variables. Further, merging rows into one provides a normalization of the examined variances, and represents that the variable's forecast error is described by all variables. Consequently, the abovementioned estimation is defined as follows: where, φ g ij,t (J) is the summation of total variance share of all variables or total connectedness, Ψ (11) and (12) represent the calculation of the total connectedness index (TCI) considering GFEVD: First, the TVP-VAR measures the influence of a shock in a variable spillover on other variables. Equation (13) demonstrates how the shock variable i influences other variables j: Second, Equation (14) shows the calculation of the total directional connectedness from others, demonstrating a spillover effect received from other variables: Eventually, the total directional connectedness to others is subtracted from the total directional connectedness from others. Consequently, the net total directional connectedness is calculated, measuring the magnitude of the impact of variable i on the variables' network. Equation (15) demonstrates the estimation of the net total directional connectedness In the case when C g i,t (J) is positive, the magnitude of the impact of variable i is more pronounced than the impact of another variable on variable i, implying that variable i affects all other variables. On the contrary, if C g i,t (J) is negative, the impact of variable j on variable i is more pronounced than the impact of variable i on variable j or all the other variables.

Cross-Quantilogram
To estimate a bivariate co-movement between two time-series, this study applies the cross-quantilogram (CQ) method proposed by Han et al. [54]. CQ is applied due to a few distinct features of this approach. First, this approach is appropriate to measure the bivariate implied volatility between two series in the case of non-normal distribution and outliers [55]. Second, the CQ approach measures the strength of the volatility spillover shock transmitted from one market to another when considering various quantiles. Third, the CQ approach allows the assumption of moment conditions. Therefore, this approach is appropriate when considering distributions with fat tails. In addition, this technique permits the use of longer lags, allowing estimation of how strongly two variables are interconnected when considering duration and direction concurrently.
Equation (16), below, demonstrates the cross-quantilogram between two return series {(y t , x t ) : t ∈ Z} comprising y t = (y 1t , y 2t ) ∈ R 2 and x t = (x 1t , x 2t ) ∈ R d1 × R d2 , where is followed by the conditional distribution implying the stock return of a vaccine producer given the stock return of another vaccine producer, corresponding to q i,t (τ i ) = inf υ : F y i |x i (υ x it ) ≥ τ i for τ i ∈ (0, 1), f or i = 1, 2. This approach uses T in the form of a Cartesian product of two closed intervals within (0, 1), where, The CQ framework incorporates serial dependence between two shocks, {y 1t ≤ q 1 , t(τ 1 )} and y 2,t−k ≤ q 2 , t − k(τ 2 ) , for a particular pair of (τ 1 , τ 2 ) ∈ T when considering a lag order equal to k. Equation (16) shows the estimation of cross-quantilogram: where y i,t denotes the return series, i is represented as 1, 2, 3, 4 or 5 and demonstrates the stock returns of Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. Moreover, t indicates time (t = 1, 2, . . . , T), whereas the functions F i (·) and f i (·) consider the distribution and density functions of y it , i = 1, 2, accordingly. Besides, The estimation process of ρ τ (k) s variation with a lag length equal to k allows the identification of cross-quantile dependency's variation between the variables over time, thus calculating the dependence strength and duration. The length of the considered lags is as follows: k is equal to 1, 5, 22 and 66 indicating daily, weekly, monthly and quarterly lags, accordingly.
Subsequently, by employing the Ljung-Box type test the statistical significance of ρ τ (k) is considered, so that the test statistic is computed in accordance with Equation (17): whereρ τ (k) represents the cross-quantilogram calculated as follows: whereρ τ (k) represents the measured partial cross-quantilogram. Afterwards, stationary bootstrap allows approximation of the cross-quantilogram's null distribution, which is reflected in Equation (18) as well as the Q-statistics in Equation (17).
The approach further implies the calculation of the partial cross-quantilogram (PCQ) between the variables in order to consider the effect of uncertainties. Precisely, z t = [Ψ τ 3 (y 3t − q 3t (τ 3 )), . . . , Ψ τ l (y lt − q lt (τ l ))] is the following vector (l − 2) × 1 for l ≥ 3 of the control variables. Hence, Equation (19) represents the quantile-hit process, and its inverse matrix correlation matrix as follows: where h t (τ) = Ψ τ 1 (y 1t − q 1t (τ 1 )), . . . , Ψ τ l (y lt − q lt (τ l )) is the vector of the quantile hit process with matrix order l × 1. Besides, r τij and p τij represent the i-th element of R τ (which is the quantile-hit correlation matrix) and P τ (which denotes the coefficient considering each quantile) for i, j ∈ [1, . . . , l]. The cross-quantilogram is defined as r τ12 / √ r τ11 r τ22 . Then the partial crossquantilogram is represented as follows: (20) where ρ τ|z is the cross-quantilogram between two variables, y 1t and y 2t can be regarded as the cross-quantilogram between y 1t and y 2t dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data. DE t denotes the stock returns of one of the vaccine-producing companies' returns, whereas IE i signifies the stock price of another vaccine-producing company. DE t signifies the dependent variable, whereas IE i indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
where | is the cross-quantilogram between two variables, and can be garded as the cross-quantilogram between and dependent on the control var ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness ch of the results obtained from the TVP-VAR and CQ techniques. This framework has seve distinct features. Firstly, the QQ framework combines two approaches, namely, the stan ard quantile regression and the local linear regression which were proposed by Sim a Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by sp ting both variables into different quantiles [57,58]. Secondly, the framework overcom the issue of reverse causality by providing the quantiles' slope coefficients of the vario quantiles of independent variables on different quantiles of dependent variables. Mor ver, this method allows the abnormal distribution of the high-frequency data. notes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the pendent variable, whereas indicates the independent variable. We take the equity turns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of t different vaccine-producing companies is thus unknown. Additionally, Ԏ represe the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined transforming Equation (10), namely by considering the first-order Taylor expansion Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that b Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is rep sented as follows: Subsequently, the stock returns of the respective vaccine-producing companies substituted as dependent and independent variables in order to confirm the interconne edness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are cons ered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. T sample time frame ranges from 7 December 2018 to 20 September 2021 due to the ma mum data availability and by determining a common starting date for all considered co panies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the v able names, descriptions, units and respective sources.
where | is the cross-quantilogram between two variables, and garded as the cross-quantilogram between and dependent on the ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the rob of the results obtained from the TVP-VAR and CQ techniques. This framewo distinct features. Firstly, the QQ framework combines two approaches, nam ard quantile regression and the local linear regression which were propose Zhou [56]. The QQ technique considers the flaws of the aforementioned met ting both variables into different quantiles [57,58]. Secondly, the framewo the issue of reverse causality by providing the quantiles' slope coefficients quantiles of independent variables on different quantiles of dependent vari ver, this method allows the abnormal distribution of the high-frequency notes the stock returns of one of the vaccine-producing companies' returns signifies the stock price of another vaccine-producing company. sig pendent variable, whereas indicates the independent variable. We take turns of the different vaccine companies one by one as functions of each oth Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock r different vaccine-producing companies is thus unknown. Additionally, the error term when Ԏ is zero. Afterwards, the first order Taylor expansion transforming Equation (10), namely by considering the first-order Taylor Ԏ (. ), around : Subsequently, the stock returns of the respective vaccine-producing c substituted as dependent and independent variables in order to confirm the edness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing compani ered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and Astr sample time frame ranges from 7 December 2018 to 20 September 2021 du mum data availability and by determining a common starting date for all con panies. The data frequency is daily, precisely 5 days in a week. Table 1 prov able names, descriptions, units and respective sources.
The slope, β where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
(.), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, µ where | is the cross-quantilogram between two variab garded as the cross-quantilogram between and depe ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approa of the results obtained from the TVP-VAR and CQ techniques. distinct features. Firstly, the QQ framework combines two app ard quantile regression and the local linear regression which Zhou [56]. The QQ technique considers the flaws of the aforem ting both variables into different quantiles [57,58]. Secondly, the issue of reverse causality by providing the quantiles' slop quantiles of independent variables on different quantiles of d ver, this method allows the abnormal distribution of the hig notes the stock returns of one of the vaccine-producing comp signifies the stock price of another vaccine-producing comp pendent variable, whereas indicates the independent vari turns of the different vaccine companies one by one as functio Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship betwe different vaccine-producing companies is thus unknown. A the error term when Ԏ is zero. Afterwards, the first order Tay transforming Equation (10), namely by considering the first Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as sented as follows: Subsequently, the stock returns of the respective vaccine substituted as dependent and independent variables in order t edness among those companies.

Data and Sources
In this study the equity prices of several vaccine-produc ered, including Moderna, Pfizer, Johnson & Johnson, Sinoph sample time frame ranges from 7 December 2018 to 20 Septem mum data availability and by determining a common starting panies. The data frequency is daily, precisely 5 days in a week able names, descriptions, units and respective sources. where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of β where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
where | is the cross-quantilogram between two variables, and can garded as the cross-quantilogram between and dependent on the contro ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustnes of the results obtained from the TVP-VAR and CQ techniques. This framework has distinct features. Firstly, the QQ framework combines two approaches, namely, the ard quantile regression and the local linear regression which were proposed by S Zhou [56]. The QQ technique considers the flaws of the aforementioned methods b ting both variables into different quantiles [57,58]. Secondly, the framework ove the issue of reverse causality by providing the quantiles' slope coefficients of the v quantiles of independent variables on different quantiles of dependent variables. M ver, this method allows the abnormal distribution of the high-frequency data. notes the stock returns of one of the vaccine-producing companies' returns, wher signifies the stock price of another vaccine-producing company. signifies pendent variable, whereas indicates the independent variable. We take the eq turns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns different vaccine-producing companies is thus unknown. Additionally, Ԏ rep the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defi transforming Equation (10), namely by considering the first-order Taylor expan Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means tha Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is sented as follows: Substituting Equation (23) into the original QQ equation provides the following eq = (Ԏ, ) + Ԏ + (Ԏ, )( − ) + Ԏ Subsequently, the stock returns of the respective vaccine-producing compan substituted as dependent and independent variables in order to confirm the interco edness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are ered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZene sample time frame ranges from 7 December 2018 to 20 September 2021 due to the mum data availability and by determining a common starting date for all considere panies. The data frequency is daily, precisely 5 days in a week. Table 1 provides th able names, descriptions, units and respective sources.
The double indexing of β where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
where | is the cross-quantilogram between two variables, and garded as the cross-quantilogram between and dependent on the cont ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustn of the results obtained from the TVP-VAR and CQ techniques. This framework h distinct features. Firstly, the QQ framework combines two approaches, namely, t ard quantile regression and the local linear regression which were proposed by Zhou [56]. The QQ technique considers the flaws of the aforementioned method ting both variables into different quantiles [57,58]. Secondly, the framework o the issue of reverse causality by providing the quantiles' slope coefficients of th quantiles of independent variables on different quantiles of dependent variable ver, this method allows the abnormal distribution of the high-frequency data notes the stock returns of one of the vaccine-producing companies' returns, wh signifies the stock price of another vaccine-producing company. signifie pendent variable, whereas indicates the independent variable. We take the turns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock retur different vaccine-producing companies is thus unknown. Additionally, Ԏ r the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is d transforming Equation (10) Subsequently, the stock returns of the respective vaccine-producing comp substituted as dependent and independent variables in order to confirm the inte edness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies ar ered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZen sample time frame ranges from 7 December 2018 to 20 September 2021 due to mum data availability and by determining a common starting date for all conside panies. The data frequency is daily, precisely 5 days in a week. Table 1  where | is the cross-quantilogram between tw garded as the cross-quantilogram between and ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) of the results obtained from the TVP-VAR and CQ tech distinct features. Firstly, the QQ framework combines ard quantile regression and the local linear regression Zhou [56]. The QQ technique considers the flaws of th ting both variables into different quantiles [57,58]. S the issue of reverse causality by providing the quanti quantiles of independent variables on different quant ver, this method allows the abnormal distribution o notes the stock returns of one of the vaccine-producin signifies the stock price of another vaccine-produci pendent variable, whereas indicates the independ turns of the different vaccine companies one by one a Therefore, we introduce our empirical model as The slope, Ԏ (. ), which captures the relationshi different vaccine-producing companies is thus unkn the error term when Ԏ is zero. Afterwards, the first o transforming Equation (10)

Data and Sources
In this study the equity prices of several vaccin ered, including Moderna, Pfizer, Johnson & Johnson sample time frame ranges from 7 December 2018 to 2 mum data availability and by determining a common panies. The data frequency is daily, precisely 5 days i able names, descriptions, units and respective source where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other.
Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources. where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other. Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources. where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other. Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.
where | is the cross-quantilogram between two variables, and garded as the cross-quantilogram between and dependent on the cont ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustn of the results obtained from the TVP-VAR and CQ techniques. This framework h distinct features. Firstly, the QQ framework combines two approaches, namely, t ard quantile regression and the local linear regression which were proposed by Zhou [56]. The QQ technique considers the flaws of the aforementioned method ting both variables into different quantiles [57,58]. Secondly, the framework o the issue of reverse causality by providing the quantiles' slope coefficients of th quantiles of independent variables on different quantiles of dependent variable ver, this method allows the abnormal distribution of the high-frequency data notes the stock returns of one of the vaccine-producing companies' returns, wh signifies the stock price of another vaccine-producing company. signifie pendent variable, whereas indicates the independent variable. We take the turns of the different vaccine companies one by one as functions of each other. Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock retur different vaccine-producing companies is thus unknown. Additionally, Ԏ r the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is d transforming Equation (10), namely by considering the first-order Taylor exp Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22 Subsequently, the stock returns of the respective vaccine-producing comp substituted as dependent and independent variables in order to confirm the inte edness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies ar ered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZe sample time frame ranges from 7 December 2018 to 20 September 2021 due to mum data availability and by determining a common starting date for all conside panies. The data frequency is daily, precisely 5 days in a week. Table 1 provides able names, descriptions, units and respective sources.
Substituting Equation (23)  where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other. Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources. where | is the cross-quantilogram between two variables, and can be regarded as the cross-quantilogram between and dependent on the control variable z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness check of the results obtained from the TVP-VAR and CQ techniques. This framework has several distinct features. Firstly, the QQ framework combines two approaches, namely, the standard quantile regression and the local linear regression which were proposed by Sim and Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by splitting both variables into different quantiles [57,58]. Secondly, the framework overcomes the issue of reverse causality by providing the quantiles' slope coefficients of the various quantiles of independent variables on different quantiles of dependent variables. Moreover, this method allows the abnormal distribution of the high-frequency data.
denotes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the dependent variable, whereas indicates the independent variable. We take the equity returns of the different vaccine companies one by one as functions of each other. Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of two different vaccine-producing companies is thus unknown. Additionally, Ԏ represents the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is defined by transforming Equation (10), namely by considering the first-order Taylor expansion of Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that both Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is represented as follows: Substituting Equation (23) into the original QQ equation provides the following equation: Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources. REVIEW 7 where | is the cross-quantilogram between two variables, and can b garded as the cross-quantilogram between and dependent on the control v ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach for the robustness ch of the results obtained from the TVP-VAR and CQ techniques. This framework has sev distinct features. Firstly, the QQ framework combines two approaches, namely, the st ard quantile regression and the local linear regression which were proposed by Sim Zhou [56]. The QQ technique considers the flaws of the aforementioned methods by s ting both variables into different quantiles [57,58]. Secondly, the framework overco the issue of reverse causality by providing the quantiles' slope coefficients of the var quantiles of independent variables on different quantiles of dependent variables. Mo ver, this method allows the abnormal distribution of the high-frequency data. notes the stock returns of one of the vaccine-producing companies' returns, whereas signifies the stock price of another vaccine-producing company.
signifies the pendent variable, whereas indicates the independent variable. We take the equit turns of the different vaccine companies one by one as functions of each other. Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between the stock returns of different vaccine-producing companies is thus unknown. Additionally, Ԏ repres the error term when Ԏ is zero. Afterwards, the first order Taylor expansion is define transforming Equation (10), namely by considering the first-order Taylor expansio Ԏ (. ), around : The double indexing of Ԏ ( ) and Ԏ ( ) in Ԏ and means that Ԏ ( ) and Ԏ ( ) denote the functions of Ԏ as well as . Equation (22) is re sented as follows: Subsequently, the stock returns of the respective vaccine-producing companies substituted as dependent and independent variables in order to confirm the interconn edness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are con ered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. sample time frame ranges from 7 December 2018 to 20 September 2021 due to the m mum data availability and by determining a common starting date for all considered c panies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the v able names, descriptions, units and respective sources. where | is the cross-quantilogram between two variable garded as the cross-quantilogram between and depen ble z.

Quantile-on-Quantile
The study applies the quantile-on-quantile (QQ) approach of the results obtained from the TVP-VAR and CQ techniques. T distinct features. Firstly, the QQ framework combines two appro ard quantile regression and the local linear regression which w Zhou [56]. The QQ technique considers the flaws of the aforeme ting both variables into different quantiles [57,58]. Secondly, t the issue of reverse causality by providing the quantiles' slope quantiles of independent variables on different quantiles of dep ver, this method allows the abnormal distribution of the high notes the stock returns of one of the vaccine-producing compa signifies the stock price of another vaccine-producing compa pendent variable, whereas indicates the independent varia turns of the different vaccine companies one by one as function Therefore, we introduce our empirical model as follows: The slope, Ԏ (. ), which captures the relationship between different vaccine-producing companies is thus unknown. Ad the error term when Ԏ is zero. Afterwards, the first order Taylo transforming Equation (10) Subsequently, the stock returns of the respective vaccinesubstituted as dependent and independent variables in order to edness among those companies.

Data and Sources
In this study the equity prices of several vaccine-produci ered, including Moderna, Pfizer, Johnson & Johnson, Sinopha sample time frame ranges from 7 December 2018 to 20 Septem mum data availability and by determining a common starting da panies. The data frequency is daily, precisely 5 days in a week. able names, descriptions, units and respective sources. t (24) Subsequently, the stock returns of the respective vaccine-producing companies are substituted as dependent and independent variables in order to confirm the interconnectedness among those companies.

Data and Sources
In this study the equity prices of several vaccine-producing companies are considered, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. The sample time frame ranges from 7 December 2018 to 20 September 2021 due to the maximum data availability and by determining a common starting date for all considered companies. The data frequency is daily, precisely 5 days in a week. Table 1 provides the variable names, descriptions, units and respective sources.

Dynamic Connectedness among the Vaccine-Producing Companies
In order to measure the dynamic connectedness among the vaccine-producing companies, TVP-VAR dynamic connectedness was conducted in the R software. Table 2 represents the results of the TVP-VAR dynamic connectedness, which is the first step to analyze the frequency connectedness among the companies' stocks. The total connectivity index (TCI) demonstrates a relatively high degree of total market connectivity, in the magnitude of 47.32%. The rows of Table 2 stands for the volatility receivers, whereas the columns stand for the contributors. AstraZeneca receives 51.00% from the other markets. On the other hand, AstraZeneca overall transmits 51.53% to the other markets, specifically a 13.01% spillover to Sinopharm, 12.11% to Moderna, 7.75% to Pfizer and 18.66% to Johnson & Johnson. AstraZeneca is marginally a net volatility contributor in the magnitude of 0.53%. Besides, Johnson & Johnson receives a volatility spillover of 55.64%, whereas it contributes 60.56% to other companies. Therefore, Johnson & Johnson is a net volatility transmitter, overall contributing net 4.92% to other respective markets. in total volatility spillover. Moreover, Moderna appears as the highest net volatility contributor, contributing 27.25%. Pfizer's stock return receives 49.22%, whereas it contributes 35.11% of the volatility spillover to other respective markets, turning it into a net receiver of −14.11%. Finally, Sinopharm receives a volatility spillover of 39.07% from the other vaccine-producing companies. The second column indicates the magnitude of spillover from Sinopharm to the other respective companies.
Interestingly, the results represent Sinopharm as a weak spillover transmitter. Table 2 shows that Sinopharm is the least volatility contributor, at a total of 20.48% to the other markets. Therefore, Sinopharm turns into a net volatility receiver (−18.59%) from the stock returns of the other vaccine producers. Figure 1 is a volatility transmission diagram, representing our previous findings in an illustrative graph. For example, the graph affirms that Moderna is the most powerful transmitter. In particular, Moderna transmits the highest volatility spillover to Pfizer, a slightly lower volatility spillover to Sinopharm and has the smallest spillover to Johnson & Johnson. Interestingly, the only company that manages to transmit volatility spillover to Moderna is AstraZeneca. At the same time, AstraZeneca transmits a small volatility spillover to Sinopharm and receives volatility spillover from Pfizer and     Figure 2 represents the dynamic total connectivity index. The degree of connectivity was the highest during the fourth quarter of 2018 and the third quarter of 2019. Afterwards, a significant decline in total connectivity is observed. Nevertheless, the TCI rises in the second and third quarters of 2021 due to the COVID-19 pandemic. More particularly, the increased connectedness is likely to be induced by the vaccine release. For example, Pfizer and AstraZeneca released their vaccines in December 2020, whereas Johnson & Johnson, Moderna and Sinopharm achieved first authorization in the first quarter of 2021. This study argues that the stock market connectedness increased through the fundamental channel of foreign investment, for example, via foreign purchases of vaccines by other countries, which is also in line with Hwang et al. [17]. Moreover, investors' behaviour can induce an increase in the stock market connectedness. Due to the COVID-19 pandemic, the vaccine-producing companies are thriving. In addition, the pandemic has created a high level of uncertainty.  I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021 TCI TCI_adj  Notably, Moderna appears to be the most prominent net volatility contributor over time. Moderna receives a minor magnitude of spillover in the second quarter of 2020 and the second quarter of 2021. Conceivably, Moderna turns into a net volatility receiver due to the influence of AstraZeneca. Figure 3 shows that Astra-Zeneca is the only company that transmits volatility to Moderna.
Pfizer received a large spillover effect during the period from December 2018 to February 2020. Notably, in February 2021 Pfizer turns into a net volatility contributor, though the magnitude of spillover is minor. Moreover, AstraZeneca released the vaccine in February 2021; therefore, the transmission effect is likely to be conditional on the AstraZeneca vaccine authorization. Interestingly, Sinopharm is consistently a net volatility receiver over the sample period. Thus, Figure 3 affirms the previous findings that Sinopharm is the highest net volatility receiver, whereas Moderna is the most prominent net volatility transmitter.  Notably, Moderna appears to be the most prominent net volatility contributor over time. Moderna receives a minor magnitude of spillover in the second quarter of 2020 and the second quarter of 2021. Conceivably, Moderna turns into a net volatility receiver due to the influence of AstraZeneca. Figure 3 shows that AstraZeneca is the only company that transmits volatility to Moderna.
Pfizer received a large spillover effect during the period from December 2018 to February 2020. Notably, in February 2021 Pfizer turns into a net volatility contributor, though the magnitude of spillover is minor. Moreover, AstraZeneca released the vaccine in February 2021; therefore, the transmission effect is likely to be conditional on the AstraZeneca vaccine authorization. Interestingly, Sinopharm is consistently a net volatility receiver over the sample period. Thus, Figure 3 affirms the previous findings that Sinopharm is the highest net volatility receiver, whereas Moderna is the most prominent net volatility transmitter. Figure 3 demonstrates the volatility transmission from one company to another company. Figure 4 shows the bi-directional frequency connectedness between two stock returns. AstraZeneca appears as a net volatility transmitter to Sinopharm. Expectedly, most of the time Moderna significantly contributes to the volatility of AstraZeneca and Sinopharm. However, Moderna turns into a net volatility receiver from AstraZeneca in the period from the second quarter of 2020 to the second of quarter 2021. Notably, Pfizer is highly influenced by Moderna over the whole sample period. Additionally, Appendix A confirms these findings by demonstrating volatility spillovers transmission from and to every vaccineproducing company.  Figure 3 demonstrates the volatility transmission from one company to another company. Figure 4 shows the bi-directional frequency connectedness between two stock returns. AstraZeneca appears as a net volatility transmitter to Sinopharm. Expectedly, most of the time Moderna significantly contributes to the volatility of AstraZeneca and Sinopharm. However, Moderna turns into a net volatility receiver from AstraZeneca in the period from the second quarter of 2020 to the second of quarter 2021. Notably, Pfizer is highly influenced by Moderna over the whole sample period. Additionally, Appendix A confirms these findings by demonstrating volatility spillovers transmission from and to every vaccine-producing company.  I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021 astrazeneca-sy nopharm  I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021 Johnson&Johnson-astrazeneca  I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021   Johnson&Johnson-moderna   -20   -10   0   10   20   30   IV I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021 Johnson&Johnson-pf izer  I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021   Johnson&Johnson-sy nopharm   -10   0   10   20   30   IV I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021   moderna-astrazeneca   -10   0   10   20   30   40   IV I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021 moderna-sy nopharm  I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021 pf izer-astrazeneca  I  II  III IV  I  II  III IV  I  II  III   2019 I  II  III IV  I  II  III IV  I  II  III   2019  2020  2021 pf izer-sy nopharm

Cross-Quantile Dependence
This section represents the results of the cross-quantile dependence conducted in the Python software in the form of a heatmap matrix, considering the short and long term. Due to the long period of high-frequency and highly volatile observation, a 5% quantile is considered. The heatmap consists of white and black squares as shown in the crossdependence figures, where the white squares indicate lower or negative degrees, whereas

Cross-Quantile Dependence
This section represents the results of the cross-quantile dependence conducted in the Python software in the form of a heatmap matrix, considering the short and long term. Due to the long period of high-frequency and highly volatile observation, a 5% quantile is considered. The heatmap consists of white and black squares as shown in the crossdependence figures, where the white squares indicate lower or negative degrees, whereas the black squares signify the highest degrees of dependence or positive correlation. In addition, the star sign indicates a 10% significance level. Figure 5 demonstrates the cross-quantilogram dependence from AstraZeneca to Sinopharm. The lower quantiles are interpreted as bearish conditions and the higher quantiles as bullish conditions. As for the heatmap matrix with a 1-day lag, the results show a few significant squares under the higher quantiles of AstraZeneca and middle quantiles of Sinopharm. As per the heatmap matrix with a 5-day lag, more significant squares are observed compared with the one-day lag heatmap matrix. The volatility spillover from AstraZeneca to Sinopharm is pronounced under the bullish market conditions. AstraZeneca under the lower quantiles transmits a strong negative spillover to Sinopharm under the highest quantiles. In both the 1-day and 5-day lags, we observe a negative association, thus implying that AstraZeneca transmits a negative spillover to Sinopharm.  Figure 6 demonstrate the cross-quantile dependence from Sinopharm to Astra-Zeneca. The heatmap matrix demonstrates that Sinopharm under the middle and higher quantiles transmits a negative volatility spillover to AstraZeneca under the lower quantiles. It is also noteworthy that Sinopharm under the lowest and middle quantiles transmits a significant negative volatility spillover to AstraZeneca under the middle and higher quantiles. The impact turns out to be more pronounced when longer lags are considered.  Figure 6 demonstrate the cross-quantile dependence from Sinopharm to AstraZeneca. The heatmap matrix demonstrates that Sinopharm under the middle and higher quantiles transmits a negative volatility spillover to AstraZeneca under the lower quantiles. It is also noteworthy that Sinopharm under the lowest and middle quantiles transmits a significant negative volatility spillover to AstraZeneca under the middle and higher quantiles. The impact turns out to be more pronounced when longer lags are considered.  Figure 7 demonstrates the cross-quantile dependence from Johnson & Johnson to Pfizer. Mainly a positive correlation between these two companies is observed. The heatmap matrix with a 1-day lag has no significant squares, whereas the 5-day lag heatmap matrix shows one significant square under bullish market conditions and indicates a substantial positive spillover. Figure 7 shows a larger number of significant squares under the highest quantiles when considering the longer term.  Mainly a positive correlation between these two companies is observed. The heatmap matrix with a 1-day lag has no significant squares, whereas the 5-day lag heatmap matrix shows one significant square under bullish market conditions and indicates a substantial positive spillover. Figure 7 shows a larger number of significant squares under the highest quantiles when considering the longer term.    Figure 8 demonstrates the volatility spillover from Moderna to Pfizer. The volatility of this spillover is only significant under the highest quantiles of both variables, underscoring the significance during bullish market conditions. Moreover, the significant squares mostly indicate a strong positive correlation, thus implying that the magnitude of the positive spillover from Moderna to Pfizer is substantial. The number of significant squares increases when considering longer lags. Figure 9 shows the cross-quantile dependence from Moderna to AstraZeneca. This spillover becomes more profound when considering longer memories. In the short term (the 1-day and 5-day lags), Figure 9 demonstrates that Moderna under the middle and higher quantiles transmits volatility spillover to AstraZeneca under almost all quantiles. In the long term, a larger number of significant squares with a positive correlation is observed.  Figure 9 shows the cross-quantile dependence from Moderna to AstraZeneca. This spillover becomes more profound when considering longer memories. In the short term (the 1-day and 5-day lags), Figure 9 demonstrates that Moderna under the middle and higher quantiles transmits volatility spillover to AstraZeneca under almost all quantiles. In the long term, a larger number of significant squares with a positive correlation is observed.

Quantile-on-Quantile
This subsection describes the results of the quantile-on-quantile approach, which was conducted in the R and MatLab softwares. For example, Figure 14 demonstrates the influence of Moderna on the other respective markets, including Pfizer, Sinopharm, Astra-Zeneca and Johnson & Johnson. Our series are split into nine quantiles by a size of 10%. Yellow refers to a positive relationship, blue stands for negative and the green represents zero correlation between the markets. Moderna, under all quantiles, has a negative or almost a neutral impact on Pfizer under the lower and middle quantiles. Interestingly,

Quantile-on-Quantile
This subsection describes the results of the quantile-on-quantile approach, which was conducted in the R and MatLab softwares. For example, Figure 14 demonstrates the influence of Moderna on the other respective markets, including Pfizer, Sinopharm, AstraZeneca and Johnson & Johnson. Our series are split into nine quantiles by a size of 10%. Yellow refers to a positive relationship, blue stands for negative and the green represents zero correlation between the markets. Moderna, under all quantiles, has a negative or almost a neutral impact on Pfizer under the lower and middle quantiles. Interestingly, Moderna transmits a positive volatility spillover to Pfizer under the highest quantiles, which corresponds to bullish market conditions. Considering the influence of

Discussion
The findings of TVP-VAR represent that overall stock market connectedness among vaccine-producing companies has increased in the second and third quarters of 2021 due to the COVID-19 outbreak. More specifically, the vaccine release induced an increase in total stock market connectedness. This study argues that the stock market connectedness increased through the fundamental channel of foreign investment, for example, via foreign purchases of vaccines by other countries, which is also in line with Hwang et al. [17]. Moreover, investors' behavior can induce an increase in the stock market connectedness. Due to the COVID-19 pandemic, the vaccine-producing companies are thriving. In addition, the pandemic has created a high level of uncertainty.
Given that investors seek safer assets during crisis periods [9][10][11][12][13][14][15] this study argues that risk-averse agents invest more in vaccine-producing companies, thus increasing their stock returns and connectedness. This finding is in line with Trevino [34], who argues that apart from the fundamental factors, the social channel is crucially important in determining stock market dynamics. It is noteworthy that the increased fluctuations of TCI are conditional on the vaccine release dates. Therefore, the current study expands the findings of several studies [3,[5][6][7] who report that the stock market connectedness increased as a response to the COVID-19 pandemic.
The results of TVP-VAR also demonstrate that Moderna, Johnson & Johnson and AstraZeneca perform as net volatility spillover contributors, whereas Pfizer and Sinopharm are net volatility spillover receivers. Notably, Moderna is the most prominent

Discussion
The findings of TVP-VAR represent that overall stock market connectedness among vaccine-producing companies has increased in the second and third quarters of 2021 due to the COVID-19 outbreak. More specifically, the vaccine release induced an increase in total stock market connectedness. This study argues that the stock market connectedness increased through the fundamental channel of foreign investment, for example, via foreign purchases of vaccines by other countries, which is also in line with Hwang et al. [17]. Moreover, investors' behavior can induce an increase in the stock market connectedness. Due to the COVID-19 pandemic, the vaccine-producing companies are thriving. In addition, the pandemic has created a high level of uncertainty.
Given that investors seek safer assets during crisis periods [9][10][11][12][13][14][15] this study argues that risk-averse agents invest more in vaccine-producing companies, thus increasing their stock returns and connectedness. This finding is in line with Trevino [34], who argues that apart from the fundamental factors, the social channel is crucially important in determining stock market dynamics. It is noteworthy that the increased fluctuations of TCI are conditional on the vaccine release dates. Therefore, the current study expands the findings of several studies [3,[5][6][7] who report that the stock market connectedness increased as a response to the COVID-19 pandemic.
The results of TVP-VAR also demonstrate that Moderna, Johnson & Johnson and AstraZeneca perform as net volatility spillover contributors, whereas Pfizer and Sinopharm are net volatility spillover receivers. Notably, Moderna is the most prominent net volatility spillover contributor, whereas Sinopharm is the highest net volatility spillover receiver. In the second quarter of 2021, Moderna appears as a net volatility spillover receiver mainly from AstraZeneca and Pfizer. Such an effect is likely conditional on AstraZeneca and Pfizer vaccine developments and the first authorization in December 2020. However, after the release of the Moderna vaccine, this company turns into a strong net volatility transmitter.
The results of the cross-quantilogram are consistent with the previous findings that Moderna is the most prominent volatility transmitter. Moderna transmits significant volatility spillovers under both bearish and bullish conditions to Sinopharm, Johnson & Johnson and AstraZeneca, though the volatility transmission from Moderna to Pfizer is minor. Overall, the spillover effect is more pronounced in the long run than in the short run. In general, the interconnectedness is more substantial under the bullish market conditions. This finding is in line with several studies [16][17][18]33,44,59,60] who report that stock market connectedness increases during crisis times.

Conclusions
The vaccine-producing companies that developed vaccines have thrived during the pandemic period and this is reflected in their stock dynamics. The companies under consideration are: Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. This study investigates how the time-dynamic connectedness among the prominent vaccineproducing companies' stock returns changes due to the COVID-19 pandemic. Specifically, the study explores how vaccine releases change the pattern of total connectedness and the spillover effects among those companies. Moreover, this investigation explains the interconnectedness among those vaccine-producing companies under bearish and bullish market conditions. Given the high frequency of the time series with high fluctuations, several advanced econometric techniques are applied. Therefore, the significance of this article lies in several aspects: proposition of a novel idea, contribution to the existing literature by utilizing equity returns instead of stock indices, application of sophisticated econometric techniques and obtaining unique findings.
First, TVP-VAR dynamic connectedness is applied in order to determine the net volatility spillover receivers and contributors, considering the time dimension. Notably, the total connectivity among the markets is 47.32%. The TVP-VAR results demonstrate that Moderna performs as the most prominent net volatility contributor, whereas Sinopharm is the highest net volatility receiver. Interestingly, the volatility transmission diagram shows that AstraZeneca is the only company that transmits a spillover to Moderna. Exploring the net volatility transmission diagram, it is observed that Moderna turned into a net volatility receiver in the second quarter of 2021, whereas AstraZeneca and Pfizer were net volatility transmitters. Such an effect is likely conditional on AstraZeneca and Pfizer vaccine developments and the first authorization in December 2020. However, after the release of the Moderna vaccine, this company turns into a strong net volatility transmitter.
Moreover, this study reveals that the total connectedness index rises in the second and third quarters of 2021 after the vaccine release. The study argues that the stock market connectedness has increased through the fundamental channel of foreign investment, for example, via foreign purchases of vaccine by other countries. Moreover, risk aversive agents invest more in vaccine-producing companies, thus increasing their stock returns and connectedness. Second, a cross-quantile dependency is applied to reveal the interconnectedness among different markets under bullish and bearish market conditions and consider short memory (the 1-day and 5-day lags) and long memory (the 22-day and 66-days lags). The spillover effect is more pronounced in the long run than in the short run. Consistent with the previous findings, Moderna transmits significant volatility spillovers under both bearish and bullish conditions to Sinopharm, Johnson & Johnson and AstraZeneca. However, the volatility transmission from Moderna to Pfizer is less pronounced. We generally observe a higher interconnectedness under the bullish market conditions that correspond to the COVID-19 pandemic circumstances.
The empirical findings of this study provide several policy implications from the investors' point of view since the findings show that the vaccine-producing companies under consideration are successful in terms of achieving higher stock returns. The total connectivity among the stock returns of the respective companies is found to be considerably high, reaching 80% in 2019 and implying that the stock return of each company can be a good hedge against the stock returns of another company. Moreover, Moderna turns out to be the most prominent net volatility spillover transmitter, providing an opportunity for a rational investment. Moderna and Johnson & Johnson can predict the stock returns of other vaccine producers' stock returns in quarterly lags at the extreme quantiles, indicating their directional prediction follows long memory. Therefore, the findings of this study are useful for portfolio managers in terms of improving their revenues by portfolio diversification. Finally, it is important to highlight a policy implication for the medications and vaccine-producing companies. The empirical finding shows that vaccine development and release allows companies to enhance their stock returns but induced substantial volatility spillovers from company to company. For instance, after the vaccine release, Moderna and Pfizer enjoyed higher stock prices and a better prediction of the stock returns of the respective companies.
One of the limitations of the current study is that it considers only a few vaccineproducing companies, while state-owned vaccine producers are excluded (e.g., Sputnik V). Moreover, vaccine release may spur the stock market overall, which has been overlooked. Thus, future study may incorporate those issues to fill up the literature loophole.  IV I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021   FROM astrazeneca   30   40   50   60   70   80   IV I  II  III  IV  I  II  III  IV  I  II  III   2019 I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021   FROM moderna   20   30   40   50   60   70   80   90   IV I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021   FROM pfizer   0   20   40   60   80   100   IV I  II  III  IV  I  II  III  IV  I  II  III   2019 I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021   TO astrazeneca   0   20   40   60   80   100   120   IV I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021   TO Johnson&Johnson   0   40   80   120   160   IV I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021   TO moderna   10   20   30   40   50   60   70   IV I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021   TO pfizer   0   10   20   30   40   50   60   IV I  II  III  IV  I  II  III  IV  I  II  III   2019  2020  2021 TO synopharm Figure A2. Volatility transmission to AstraZeneca, Johnson & Johnson, Moderna, Pfizer and Sinopharm.