Dependences and risk spillover effects between Bitcoin, crude oil and other traditional financial markets during the COVID-19 outbreak

Abstract

This study examines the relationship and risk spillover between Bitcoin, crude oil, and six traditional markets (the US stock, Chinese stock, gold, bond, currency, and real estate markets) from 2019 to 2020, during which the coronavirus disease 2019 (COVID-19) outbreak occurred as well. We first discuss the static relationship between Bitcoin and these markets using a quantile-on-quantile model and examine the dynamic relationship using a time-varying copula model. A conditional value-at-risk model is subsequently used to estimate the risk spillover between the markets studied. The empirical results reveal that the relationship between these markets is always time-varying, and the COVID-19 outbreak has revealed such changes in the relationship between Bitcoin and other traditional financial markets. The risk of all single markets has enhanced because of the pandemic. Further, the risk spillover of these markets has also changed dramatically since the COVID-19 outbreak during which the Bitcoin market has played an important role and exerted a significant impact on the crude oil market, and the four other markets (US stock, gold, Chinese stock, and real estate markets). Overall, our findings indicate that investors and policymakers need to be made aware of the risk spillover between Bitcoin, crude oil, and other traditional markets and that flexible hedge strategies and policies should be implemented in response to the challenges and economic recession observed following the COVID-19 outbreak.

Introduction

Following the coronavirus disease 2019 (COVID-19) outbreak worldwide, financial markets have suffered a huge shock and have been facing enormous risks. For example, the price of Bitcoin fell from over ten thousand dollars in January 2020 to less than six thousand dollars in March 2020—a drop of over 40%. More surprisingly, the price of Bitcoin exceeded fifty thousand dollars in January 2021, a price five times higher than that before the COVID-19 outbreak. Even more alarming is that the crude oil future of the West Texas Intermediate (WTI) crude oil price reported a negative price, revealing the seriousness of the crisis. At the same time, the stock markets in the USA suffered four shocking circuit breaks in March 2020, which received wide attention. The impact of the COVID-19 pandemic on stock markets may transcend the corresponding impact of all previous diseases, and more powerful policies should be implemented to respond to this unprecedented shock (Atkeson 2020). Owing to the unprecedented impact of the pandemic, the relationship among different financial markets has attracted extensive attention; the risk spillover effect on these markets requires further research and exploration.

Although younger than many other assets, the digital currency has attracted wide interest from investors, policymakers, and researchers since its emergence; among all kinds of digital currency, Bitcoin has become the focal point of research because of its high market value. Comprehensive studies have discussed the design and operation principles of Bitcoin, disclosing its current situation in the digital currency market, identifying its future uses, and uncovering its risks and interactions with traditional finance and the economy (Böhme et al. 2015). Moreover, in some studies, Bitcoin is considered an asset that can hedge the risk, which has been proven by using highly frequent data to discuss the relationship among six major currencies (Urquhart and Zhang 2019). The hedging strategy of Bitcoin is always compared with gold or other currencies. Bitcoin has a high average return and a low relationship with other financial markets; hence, it is capable of reducing portfolio risks involving other assets such as oil, gold, and equities (Guesmi et al. 2019). Some studies agree that Bitcoin can hedge the risk, similar to gold, expand portfolio returns, and reduce risk (Chkili et al. 2021; Dyhrberg 2016b; Selmi et al. 2018). In contrast, several other scholars regard the hedging efficiency of Bitcoin as being limited; it is doubtful whether Bitcoin can be considered virtual gold (Dutta et al. 2020; Klein et al. 2018; Shahzad et al. 2020).

Further, the relationship between Bitcoin and other traditional markets is also a concern. Several studies have focused on this relationship and the spillover effect in traditional markets. Considering the relationship between energy and Bitcoin, the empirical findings derived from using the asymmetric multivariate VAR-GARCH show that the long-run volatility of energy companies is affected by the volatility of Bitcoin (Symitsi and Chalvatzis 2018). Other studies also support the view that Bitcoin and traditional markets have a risk spillover effect on each other, and Bitcoin has a correlation with and a risk spillover effect on precious metals (Mensi et al. 2019) and Islamic indices (Rehman et al. 2020). However, the relationship between Bitcoin and other financial markets is controversial; investigators have found the relationship to be low in some hedging strategy studies (Qarni et al. 2019), while research focusing on the spillover effect has indicated that the relationship between Bitcoin and financial markets is rather significant (Bouri et al. 2018; Matkovskyy and Jalan 2019). As these controversial conclusions probably result from the linear time series analyses applied in these studies, neglecting the nonlinear and dynamic characteristics unexplored in the relationship between Bitcoin and other markets, we focus on the complexity of the relationship and combine both static and dynamic analyses to investigate the nonlinear relationship and measure the risk spillover effect on these markets.

Meanwhile, the existing literature lacks mention of the risk spillover effect of Bitcoin and other markets such as the crude oil market during COVID-19, even though a few studies have discussed COVID-19’s effect on the Bitcoin market. Most research in this area has focused on whether Bitcoin can replace gold or other traditional assets as a haven asset (Conlon and McGee 2020; Huang et al. 2021; Kristoufek 2020; Wen et al. 2022). However, it is more important to investigate the risk spillover effect observed between Bitcoin, crude oil, and other assets, particularly during the COVID-19 pandemic. Ever since Bitcoin was first introduced by Nakamoto (Nakamoto 2008), it has never encountered a serious shock such as that during the COVID-19 outbreak, which has generated devastating changes. Hence, it is significant that in this study we compare the relationship between and risk spillover effect on Bitcoin, crude oil, and several major assets observed before and after the outbreak.

Therefore, the study attempts to detect nonlinear and time-varying dependence between the Bitcoin, crude oil, and traditional markets by combining static and dynamic relationship analyses and then applying the model of conditional value at risk (CoVaR) to estimate the risk and observe the difference between the pre-crisis and post-crisis periods. Based on the above consideration, this study employs data on Bitcoin, crude oil, and seven major assets to discuss the relationship and risk spillover effect using different models. First, we examine the static nonlinear relationship between these assets pre-crisis and post-crisis using a quantile-on-quantile regression (QQR) model; it has been used to estimate the static relationship among different quantiles and has proven to have a better performance in nonlinear analysis (Haseeb et al. 2020; Shahzad et al. 2019; Sim 2016) than those using other models. Second, to discuss the dynamic change of the relationship and the spillover effect, the dependence between these assets is ascertained by applying four different models of the time-varying copula, which have been employed in some top-tier journal studies to capture the dynamic nonlinear dependence between markets, all revealing outstanding features to capture the dynamic change of the dependence (Avdulaj and Barunik 2015; Christoffersen et al. 2012; Oh and Patton 2018; Wang et al. 2015). Finally, we demonstrate the validity of the time-varying copula CoVaR model by accurately measuring extreme risk and describing the spillover effect (Ji et al. 2020; Karimalis and Nomikos 2018). We select the optimal time-varying copula to calculate the CoVaR and ΔCoVaR by employing the results of CoVaR and ΔCoVaR to assess extreme risk and discuss risk spillover during the pre-crisis and post-crisis periods.

The present study yields significant results. First, the static nonlinear analysis reveals that the relationship between Bitcoin and other traditional markets in different quantiles has evolved dramatically before and after the COVID-19 outbreak. Following the outbreak, some traditional markets, such as crude oil, US stock, gold, and Chinese stock markets, have begun to influence Bitcoin. Second, the dynamic relationship between Bitcoin and other traditional markets has changed dramatically over time, particularly since the outbreak. The dynamic relationship between Bitcoin and stocks, oil, and real estate has positively improved, but the dynamic relationship between Bitcoin and the US dollar exchange has negatively enhanced. Third, the risk spillover between most markets has shifted greatly since the outbreak, in which Bitcoin has played a significant role. Following the pandemic, the Bitcoin shock significantly increased the risk of some important assets, such as crude oil, US stock, gold, Chinese stock markets, and real estate markets.

This study has the following contributions. It presents the changes in the relationship and risk spillover between Bitcoin, crude oil, and traditional assets before and after the COVID-19 outbreak. First, we establish a static nonlinear and dynamic model to analyze the interdependence among these assets; compare post-crisis interdependence with pre-crisis interdependence; and discuss the effect of the pandemic on the dependence between Bitcoin, crude oil, and other markets, uncovering new evidence on the relationship between Bitcoin, crude oil, and these markets. Second, we consider the time-varying copula CoVaR model in the risk spillover analysis, focusing on the risk transmission between these markets and the risk variation trend following the COVID-19 outbreak, which has been previously ignored. Using the time-varying copula CoVaR model, we examine how the risk spillover effect on these markets has changed after the pandemic. Our empirical findings have important practical and theoretical implications for investors, policymakers, and researchers. On the one hand, from a practical standpoint, our study can assist investors in understanding the causes of interdependence and risk, as well as taking actions to hedge the risk and reduce the loss. On the other hand, from a theoretical standpoint, we enrich the research on the dependence and risk spillover between the Bitcoin market, crude oil market, and other traditional markets in the event of a major risk event. This study can provide policymakers with policy ideas such as monitoring the risk transmission between markets and enacting policies to reduce the harmful effects of risk events.

The remainder of this paper is organized as follows. Section 2 introduces the methods applied, including the QQR model, dynamic copula model, CoVaR, and ΔCoVaR. Section 3 presents the data and sample. Section 4 analyzes and discusses the study’s empirical results. Section 5 summarizes the main findings and presents the practical and theoretical implications of the study.

Methodology

We conduct the analysis in three steps. First, we utilize the QQR model to analyze the static and nonlinear relationship between Bitcoin and other financial markets at different quantiles and identify the changes in the static relationship between the pre-crisis and post-crisis periods. Second, we employ four time-varying copula models to estimate dynamic dependence, focusing on the dynamic dependence observed at different times, and discussing its resultant changes observed before and after the COVID-19 outbreak. Finally, to explore the risk spillover between the markets, we select an optimal copula model to estimate CoVaR and ΔCoVaR.

Quantile-on-quantile regression

We adopt the QQR model proposed in the existing literature (Sim and Zhou 2015). This model is regularly used for nonlinear regressions, and the relationship among the variables at each point in their distribution can be completely analyzed. This model can be expressed as follows:

$${\text{y}}_t={\beta }^{\theta }{x}_t+{\epsilon }_t^{\theta }$$ 1

where θ represents the quantile of the variable, and${\epsilon }_t^{\theta }$ is the residual; this equation shows the relationship between y and x at the θ quantile at time t. β^θ shows the relationship between x and y. To explain the linkage between the θ-quantile of y and the τ-quantile of x, the function β^θ(.) is represented by a first-order Taylor expansion, and its specific form is as follows:

$${\beta }^{\theta }{x}_t\approx {\beta }^{\theta }\left(x^{\tau }\right)+{\beta }^{\theta \text{'}}\left(x^{\tau }\right)\left(x_t,-,x^{\tau }\right)$$ 2

According to the study by Sim and Zhou (2015), β^θ(x^τ) and ${\mathrm{\beta }}^{{\theta }^{\prime }}\left(x^{\tau }\right)$ can be redefined by β₀(θ, τ) and β₁(θ, τ). Thus, Eq. (2) can be re-written as follows:

$${\beta }^{\theta }{x}_t\approx {\beta }_0\left(\theta ,,,\tau \right)+{\beta }_1\left(\theta ,,,\tau \right)\left(x_t,-,x^{\tau }\right)$$ 3

Then, Eq. (1) can be represented using Eq. (3) as follows:

$${\text{y}}_t={\beta }_0\left(\theta ,,,\tau \right)+{\beta }_1\left(\theta ,,,\tau \right)\left(x_t,-,x^{\tau }\right)+{\epsilon }_t^{\theta }$$ 4

In this equation, the static relationship between the θ-quantile of y and the τ-quantile of x can be estimated using β₁(θ, τ). We discuss the change in β₁(θ, τ) to identify the alteration in the observed relationship before and after the COVID-19 outbreak.

Time-varying copula model

Before modeling the time-varying copula, we estimate the marginal distributions of the markets to capture their typical characteristics. The data from the financial markets are always considered in terms of fat tails and high kurtosis, and a GARCH model can match these typical features (Jondeau and Rockinger 2006). The GARCH model we use in this study is AR(1)-GARCH(1, 1). The standardized residual follows a skewed generalized error distribution (sged). The marginal distribution model is as follows:

$$r_t={\mu }_t+\beta r_{t-1}+{\epsilon }_t$$ 5

$${\epsilon }_t={\delta }_t{z}_t$$ 6

$${\delta }_t={\alpha }_t+{\phi \epsilon }_{t-1}^2+{\theta \delta }_{t-1}^2$$ 7

$$z_t\sim sged\left({\eta }_t,+,{\lambda }_t\right)$$ 8

where r_t is the return of the asset; δ_t and ε_t represent the conditional volatility and residual, respectively. Similarly, z_t is the standardized residual and follows a skewed generalized error distribution. A skewed generalized error distribution significantly differs from a normal distribution and can capture the excess kurtosis and skewness using the shape parameter η_t and skewness parameter λ_t. The GARCH model in our study can compute marginal distributions to derive the data for the markets to be used in our time-varying copula model.

Copula models have been widely used in finance and economics to estimate the relationships between different financial markets. In Sklar’s theory (Sklar 1959), a copula model is used to calculate a joint distribution using copula and marginal distributions. This can be expressed as follows:

$$F\left(X_1,,,X_2\right)=C\left[f,\left(X_1\right),,,f,\left(X_2\right)\right]$$ 9

The time-varying copula reflects changes in the dependence relationship between markets over time. In this study, we select four time-varying copula models to analyze dynamic dependence: the Gaussian copula, Student’s t copula, Clayton copula, and symmetrized Joe-Clayton (SJC) copula.

Following one study (Patton 2006), we use the ARMA(1,10)-type process to estimate the dependence parameter. For the time-varying Gaussian copula, the following equation for dependence ρ_t is used:

$${\rho }_{\text{t}}=\mathrm{\Lambda }\left\{{\omega }_{\rho },+,{\beta }_{\rho },·,{\rho }_{\text{t}-1},+,{\alpha }_{\rho },·,\frac{1}{10},\sum _{i=1}^{10},{\varphi }^{-1},\left({\mu }_{t-i}\right),·,{\varphi }^{-1},\left(v_{t-i}\right)\right\}$$ 10

where ϕ⁻¹ represents the inverse of the cumulative distribution function, and Λ(x) ≡ (1 − e^−x)(1 + e^−x)⁻¹ is employed to obtain ρ_t in (-1,1). The formula u = F(X₁), ν = F(X₂) is employed.

The time-varying Student’s t-copula is similar to the time-varying Gaussian copula. The specific equation is as follows:

$${\rho }_{\text{t}}=\mathrm{\Lambda }\left\{{\omega }_{\rho },+,{\beta }_{\rho },·,{\rho }_{\text{t}-1},+,{\alpha }_{\rho },·,\frac{1}{10},\sum _{i=1}^{10},T^{-1},\left({\mu }_{t-i}\right),·,T^{-1},\left(v_{t-i}\right)\right\}$$ 11

Unlike the time-varying Gaussian and Student’s t copula, the time-varying Clayton copula to estimate the dependence between variables uses Kendall’s tau, which is expressed as follows:

$${\tau }_{\text{t}}=\mathrm{\Lambda }\left\{{\omega }_{\tau },+,{\beta }_{\tau },·,{\tau }_{\text{t}-1},+,{\alpha }_{\tau },·,\frac{1}{10},\sum _{i=1}^{10},\left|{\mu }_{t-i},-,v_{t-i}\right|\right\}$$ 12

The SJC copula estimates dependence by focusing on the lower and upper tail dependence; therefore, the dependence of the SJC copula has two equations.

$${\tau }_{\text{U},\text{t}}=\mathrm{\Lambda }\left\{{\omega }_U,+,{\beta }_U,·,{\tau }_{\text{U},\text{t}-1},+,{\alpha }_U,·,\frac{1}{10},\sum _{i=1}^{10},\left|{\mu }_{t-i},-,v_{t-i}\right|\right\}$$ 13

$${\tau }_{\text{L},\text{t}}=\mathrm{\Lambda }\left\{{\omega }_L,+,{\beta }_L,·,{\tau }_{\text{L},\text{t}-1},+,{\alpha }_L,·,\frac{1}{10},\sum _{i=1}^{10},\left|{\mu }_{t-i},-,v_{t-i}\right|\right\}$$ 14

In this study, we use the Akaike information criterion (AIC), Bayesian information criterion (BIC), and log-likelihood to select the best model for estimating the dependence of these assets.

CoVaR and ΔCoVaR

After analyzing the static and dynamic dependence, CoVaR and ΔCoVaR are used to explore risk transmission. After selecting the best time-varying copula, we use it to estimate CoVaR and ΔCoVaR.

The value at risk (VaR) is always used to measure the risk of financial assets. VaR represents the loss of an asset at a probability. It shows a small possibility that the loss is greater than VaR. The VaR at α percent is given as follows:

$$\text{P}\left(r_t,\le ,{\mathit{VaR}}_t^{\alpha }\right)=\alpha$$ 15

This equation indicates the possibility that the loss of return r_t,which is larger than${\mathit{VaR}}_t^{\alpha },$ is α. The VaR of each asset can be estimated using the GARCH model described in Section 2.1. The process of estimating VaR is expressed as Eq. (16):

$${\mathit{VaR}}_t^{\alpha }={\mu }_t+{\delta }_t·z_t^{-1}\left(\alpha \right)$$ 16

CoVaR has been used in some studies to estimate the risk spillover effect (Adrian and Brunnermeier 2016; Girardi and Ergün 2013). In our study, we focus on downside risk; hence, we follow Girardi and Ergün while using the downside G-E CoVaR. The downside of G-E CoVaR is defined as follows:

$$\text{P}\left(r_{1,t},\le ,{\mathit{CoVaR}}_{1\left|2,,,t\right)}^{\alpha \left|\beta \right)},\left|r_{2,t},\le ,{\mathit{CoVaR}}_{2,t}^{\beta }\right)\right)=\alpha$$ 17

where ${\mathit{CoVaR}}_{1\mid 2,t}^{\alpha \mid \beta }$ describes the downside risk of asset 1 when asset 2 takes place at the extreme downside risk.

For estimating ${\mathit{CoVaR}}_{1\mid 2,t}^{\alpha \mid \beta }$, we employ a copula model to solve the value; the process is explained in Eqs. (18) and (19):

$$\text{P}\left(r_{1,t},\le ,{\mathit{CoVaR}}_{1\mid 2,t}^{\alpha \mid \beta },|,r_{2,t},\le ,{\mathit{VaR}}_{2,t}^{\beta }\right)=\frac{C\left\{F_{1,t},\left({\mathit{CoVaR}}_{1\mid 2,t}^{\alpha \mid \beta }\right),,,F_{2,t},\left({\mathit{VaR}}_{2,t}^{\beta }\right)\right\}}{\beta }$$ 18

$$C\left\{F_{1,t},\left({\mathit{CoVaR}}_{1\left|2\right),t}^{\alpha \beta }\right),,,F_{2,t},\left({\mathit{VaR}}_{2,t}^{\beta }\right)\right\}=\alpha \beta$$ 19

In Eq. (19), the copula model $F_{2,t}\left({\mathit{VaR}}_{2,t}^{\beta }\right)=\alpha$, α, and β are given. In this study, α and β are equal to 0.05; thus, $F_{1,t}\left({\mathit{CoVaR}}_{1\mid 2,t}^{\alpha \mid \beta }\right)$ can be solved. We define$F_{1,t}\left({\mathit{CoVaR}}_{1\mid 2,t}^{\alpha \mid \beta }\right)=\gamma$, and ${\mathit{CoVaR}}_{1\mid 2,t}^{\alpha \mid \beta }$ can be estimated as follows:

$${\mathit{CoVaR}}_{1\left|2\right),t}^{\alpha \beta }={\mu }_t+{\delta }_t·z_t^{-1}\left(\gamma \right)$$ 20

When CoVaR is estimated, ΔCoVaR can be obtained as follows:

$$\Delta {\mathit{CoVaR}}_t=\frac{CoVa{R}_{1\left|2\right),t}^{\alpha \left|0\right).05}-{\mathit{CoVaR}}_{1\left|2\right),t}^{\alpha \left|0\right).5}}{CoVa{R}_{1\left|2\right),t}^{\alpha \left|0\right).5}}$$ 21

where ${\mathit{CoVaR}}_{1\mid 2,t}^{\alpha \mid 0.5}$ represents the loss of asset 1 when asset 2 is observed under a normal condition. ΔCoVaR reveals the difference in the loss in asset 1 when asset 2 is at extreme risk and under normal conditions, respectively.

Data and descriptive statistics

Data descriptions

We adopt the daily Bitcoin close price, crude oil, and six traditional financial market close prices, namely, the crude oil futures close price of the WTI crude oil market (Oil), the Dow Jones index (DJI), Shanghai Composite Index (SHCI), gold price of the New York Mercantile Exchange (Gold), 10-year US Treasury Yield rate (Treasury), US Dollar Index (USDX), and FTSE RAFI US 100 Real Estate (RE). These prices represent crude oil, the stock, metal, bond, currency, and real estate markets, respectively. The Bitcoin price data are obtained from Bitcoincharts (https://bitcoincharts.com/). The DJI, SHCI, Gold, Treasury, and USDX data are collected from the Wind database. Oil futures price data are selected from the US Energy Information Agency (https://www.eia.gov/), and data from the FTSE RAFI US 100 Real Estate are collected from the Investing database (https://www.investing.com/). Our dataset spans from January 1, 2019, to December 31, 2020; some observations on holidays and non-trading days are excluded. COVID-19 was first discovered in China in December 2019, and the Chinese government imposed strict control measures in January 2020. In this study, the period prior to the COVID-19 outbreak is defined as January 1, 2019, to December 31, 2019, and the period following the outbreak is defined as January 1, 2020, to December 31, 2020. In the post-pandemic time period, we will pay more attention to the results after March 2020, since COVID-19 was declared a global pandemic after March 2020.

Descriptive statistics

We use the log returns of our markets under study. Returns are calculated using the following equation:

$${\text{r}}_t=ln{p}_t-ln{p}_{t-1}$$ 22

where p_t is the price of the asset at time t. Table 1 reports the descriptive statistics of the returns. The mean value of all returns is close to zero, and the skewness and kurtosis values reveal that the returns in these markets have sharp peaks and fat tails. Therefore, we apply the GARCH (1, 1)-sged model.

Table 1.

Descriptive statistics

	Bitcoin	Oil	DJI	SHCI	Gold	Treasury	USDX	RE
Mean	0.0040	0.0013	0.0005	0.0007	0.0008	−0.0021	−0.0001	0.0001
Median	0.0025	0.0020	0.0012	0.0007	0.0010	0.0000	−0.0002	0.0013
Maximum	0.2081	0.3196	0.1076	0.0555	0.0513	0.3417	0.0188	0.0842
Minimum	−0.4940	−0.2822	−0.1384	−0.0804	−0.0526	−0.3151	−0.0191	−0.1970
Std. Dev.	0.0470	0.0437	0.0174	0.0123	0.0103	0.0505	0.0036	0.0220
Skewness	−2.0158	0.2440	−1.0594	−0.6909	−0.4606	0.1368	0.4070	−1.9314
Kurtosis	25.5201	19.4427	16.5958	6.5220	5.0365	13.1853	6.6818	18.8703

The table displays the summary statistics for eight markets. Std. Dev. represents the standard deviation

Empirical results and discussions

Static nonlinear correlation analysis using quantile-on-quantile regression

In this section, the QQR model is utilized to discuss the static nonlinear correlations between the markets under study. The QQR model, which uncovers the different reactions of other markets when Bitcoin is affected by the COVID-19 outbreak, shows the effect of Bitcoin at nine different quantiles on the other seven markets at the 10th quantile. The impact of seven traditional financial markets on Bitcoin is then demonstrated, which is used to analyze how traditional financial market shocks are induced in the Bitcoin market. This analysis focuses on the change in the static relationship between Bitcoin and other markets following the pandemic. In this part of the discussion, the null hypothesis of the coefficients in the table is that the coefficients are not significant in the QQR model. If the model rejects the null hypothesis at a certain confidence level, it indicates that the coefficient obtained by the model is significant.

Tables 2 and 3 illustrate the relationship between Bitcoin and the traditional financial markets under study prior to the COVID-19 outbreak. The results in Table 2 show that the returns of Bitcoin at the 10^th to 90^th quantiles affect the returns of the seven markets at the 10^th quantile. The 10^th quantile represents an extreme downside risk. The results of the QQR model show that Bitcoin has only significantly affected Oil, USDX, and RE in some quantiles before the outbreak. The return of Bitcoin at the 50^th quantile has an impact on the return of Oil at the 10^th quantile, and the coefficient β₁(θ, τ) is −0.2567. Similarly, the return of Bitcoin at the 10^th to 30^th and 90^th quantiles affects the return of Gold at the 10^th quantile. For RE, the return of Bitcoin at the 60^th and 70^th quantiles affects RE returns at the 10^th quantile. As shown in Table 3, the outcome of the analysis reports the return on the traditional markets, as well as the return on Bitcoin at some quantiles prior to the COVID-19 outbreak. According to this table, the effect of other five markets on Bitcoin is insignificant except Treasury and RE. According to Tables 2 and 3, the relationship between Bitcoin and the Oil and USDX has been asymmetric before the pandemic. Bitcoin affects the two markets, but the two markets have no impact on Bitcoin.

Table 2.

Shock from Bitcoin to seven financial markets before the COVID-19 outbreak

	To Oil	To DJI	To SHCI	To Gold	To Treasury	To USDX	To RE
0.1	0.0907	−0.0379	−0.0936	0.0553	0.1481	−0.0223***	−0.0795
0.2	0.1010	−0.0276	−0.0608	0.0384	0.1588	−0.0199***	0.0725
0.3	0.0322	0.0545	0.0368	0.0070	0.1520	−0.0179**	0.0737
0.4	−0.1297	0.0351	0.0165	0.0088	0.0839	−0.0105	−0.0048
0.5	−0.2567*	−0.0268	0.0134	0.0088	0.0442	−0.0075	−0.0484
0.6	−0.0086	−0.0418	−0.0454	0.0079	0.0219	0.0067	−0.0872***
0.7	0.0941	−0.0904	−0.0491	0.0128	−0.0205	0.0201*	−0.1204***
0.8	0.0794	−0.0988	−0.0179	0.0496	−0.0205	0.0201	−0.0159
0.9	0.0794	−0.1125	0.0435	0.1071	−0.0205	0.0498**	0.1228

The table displays the different quantiles of Bitcoin affecting the 10^th quantiles of the observed traditional financial markets before the COVID-19 outbreak. The values 0.1 to 0.9 represent the 10^th to 90^th quantiles of Bitcoin returns. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

Table 3.

Shock from seven financial markets to Bitcoin before the COVID-19 outbreak

	From Oil	From DJI	From SHCI	From Gold	From Treasury	From USDX	From RE
0.1	−0.0059	0.0470	0.5806	0.0211	−0.0546	−1.5894	1.1706
0.2	−0.0056	−0.0364	0.5806	0.0211	−0.0546	−1.5894	1.1706
0.3	0.0994	−0.0364	0.5806	0.0211	−0.1329	−1.5894	1.1706
0.4	0.1714	−0.0364	0.5806	0.0211	−0.2284	−1.5894	1.1706
0.5	0.0994	−0.0364	0.5757	0.0211	−0.4231 *	−1.5894	1.1706
0.6	0.0994	−0.2050	0.5632	0.0211	−0.4450 *	−1.5894	1.1706 *
0.7	0.0994	−0.2050	0.3718	0.0211	−0.4620 **	−1.5894	1.1706
0.8	0.2387	−0.2050	0.2890	0.0211	−0.4726 *	−1.5894	1.1706
0.9	0.2983	−0.2050	0.2686	0.0211	−0.4726 *	−1.5894	1.1706 *

This table reports the different quantiles of traditional financial markets affecting the 10^th quantile of Bitcoin before the COVID-19 outbreak. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

Tables 4 and 5 show the correlation between Bitcoin and the traditional markets following the pandemic. Table 4 shows that the return of Bitcoin affects the 10^th quantile return of all traditional markets, indicating that the pandemic has made the risk transmission of Bitcoin stronger than it was before. Moreover, unlike Tables 3, 5 shows that Oil, DJI, SHCI, and Gold have an effect on Bitcoin after the pandemic, but the effect of USDX on Bitcoin is still insignificant. Following the pandemic, the relationship between Bitcoin and the Oil, DJI, SHCI, Gold, Treasury, and RE is symmetric, whereas the correlation between Bitcoin and the USDX is asymmetric. In general, the correlation between Bitcoin and the DJI, SHCI, Gold, Treasury, and RE has shifted from asymmetric to symmetric after the pandemic.

Table 4.

Shock from Bitcoin to seven financial markets after the COVID-19 outbreak

	To Oil	To DJI	To SHCI	To Gold	To Treasury	To USDX	To RE
0.1	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
0.2	−0.6727 ***	0.0688 ***	−0.0433 ***	0.1278 ***	−1.0979 ***	−0.0418 ***	0.1124 ***
0.3	−0.6727 ***	0.0688 ***	−0.0433 **	0.1278 *	−1.0979 **	−0.0418 **	0.1124***
0.4	2.5959	−1.7922	−0.1281	−1.1152 **	1.9469	−0.1372 **	−3.4250
0.5	1.9332 **	1.1531 **	0.2308	0.3285	1.9469 *	−0.0600 *	1.6546 *
0.6	0.7179	0.6305 **	0.1415	0.2172	1.8023 ***	−0.0109	0.6424 *
0.7	0.4174 **	0.1992 ***	−0.0062	0.1448 ***	0.0848	−0.0156	0.2329 **
0.8	0.1696	0.0737	0.0124	0.0373	−0.2961	−0.0167 **	0.0632
0.9	0.2621	0.0431	−0.0228	−0.0864 *	0.1590	−0.0106	0.0384

This table displays the different quantiles of Bitcoin affecting the 10th quantiles of seven traditional financial markets after the COVID-19 outbreak. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

Table 5.

Shock from seven financial markets to Bitcoin after the COVID-19 outbreak

	From Oil	From DJI	From SHCI	From Gold	From Treasury	From USDX	From RE
0.1	0.6655	4.3120 ***	1.6706 *	1.6018	0.5136	−2.0465	−5.4679
0.2	0.3615	4.2177 ***	1.6706 **	1.5989 **	0.5136	−2.1189	3.7043 **
0.3	0.5885	1.3700	1.4093 **	1.3951 ***	0.2641	−2.1189	3.6481 ***
0.4	0.4349 **	0.7418 *	1.3889 ***	1.3557 ***	0.2186	−2.1189	1.2770
0.5	0.2280 **	0.5898 ***	1.3324 ***	1.1754 **	−0.1064	−2.1189	0.7637 **
0.6	0.1554	0.4872 ***	1.3324 ***	0.9781 *	−0.1570	−2.1189	0.4556 ***
0.7	−0.0058	0.5291 ***	1.2686 ***	0.9781 *	0.3889	−2.1189	0.2500 **
0.8	−0.0894	0.5387 ***	1.2686 ***	0.9393	0.0550	−2.1189	0.2260*
0.9	0.6181	0.7147 ***	1.2686 ***	0.6774	−8.7083 **	−2.1189	0.2206

This table reports the different quantiles of traditional financial markets affecting the 10th quantile of Bitcoin after the COVID-19 outbreak. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

The signs of some coefficients in the regressions change before and after the pandemic. For example, the return of Bitcoin at the 50th quantile has a negative impact on the return of Oil at the 10th quantile before the pandemic. While the effect turns positive after the pandemic. Compared before and after the pandemic, a similar situation also appears in the impact of bitcoin on RE.

Overall, for the static nonlinear dependence, as shown in Tables 2–5, the return of Bitcoin has had an effect on all markets after the pandemic, whereas, before the outbreak, only the Oil, USDX, and RE have been affected. While only Treasury and RE have an impact on Bitcoin prior to the outbreak. After the pandemic, there are more traditional markets affecting bitcoin. As the QQR model is a regression model, it may be unable to uncover dynamic changes in the relationship between these markets; therefore, a time-varying copula model is used in the following section to analyze their time-varying relationship.

Dynamic relationship analysis using the time-varying copula model

Before using the time-varying copula model, we must apply the AR(1)-GARCH (1,1)-sged model to fit the marginal distributions of the markets under study. The estimation results for the marginal distributions are shown in Table 6. From the results of the GARCH model, most of the parameters can be calculated significantly, and it is obvious that the GARCH model can perform well in fitting the marginal distributions. Each marginal distribution is estimated using the GARCH model; thus, the joint distribution can be calculated using the marginal distributions and the copula model.

Table 6.

Results of marginal distributions

	Oil	DJI	SHCI	Gold	Treasury	USDX	RE
μ	0.0007***	0.0007	0.0005***	0.0008***	−0.0018*	−0.0001	0.0005
β	−0.0450**	−0.1273**	−0.0197***	0.0104	−0.0769*	0.0386*	−0.0104
α	0.0000***	0.0000	0.0000***	0.0000	0.0000*	0.0000	0.0000
φ	0.1475***	0.1898***	0.0750***	0.1287***	0.2351***	0.0805	0.1884***
θ	0.8265***	0.7950***	0.8804***	0.8484***	0.7639***	0.9009***	0.8100***
η	0.8713***	0.8484***	0.9829***	0.9769***	0.9879***	1.0702***	0.7893***
λ	1.0570***	1.2546***	1.0270***	1.1136***	1.3717***	1.1687***	1.5091***

This table reports the marginal distributions of the markets under study. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

For the four time-varying copula models, we must choose the best model to compute the dynamic relationship between the markets. In this study, we choose the AIC, BIC, and log-likelihood (Logl) models to select the best time-varying copula model. The results are summarized in Table 7. This table shows the fitted effects of the four time-varying copulas for different markets. The values of the AIC and BIC are as small as better, and Logl is as large as better. In Table 7, although the time-varying Clayton, SJC, and Student’s t copula models exhibit better results in some markets, the Gaussian copula model is the best and steadiest in most situations; therefore, in this study, the time-varying Gaussian copula model is selected to examine the dynamic dependence between Bitcoin and other markets. The dynamic relationship between different assets and Bitcoin can be calculated through the time-varying copula model, and then the changes in the correlation between these assets before and after the COVID-19 pandemic can be found by analyzing the dynamic dependence relationship. Meanwhile, these dynamic dependence relationship also provides a basis for the analysis of risk spillover effect. This study computes dynamic dependence using a time-varying copula model, as shown in Figs. 1 and 2. These figures represent the dynamic change in the dependence relationship between Bitcoin and other markets from January 1, 2019, to December 31, 2020, which includes the COVID-19 pandemic period.

Table 7.

Tests for the time-varying copula models

	Clayton	SJC	Student-t	Gaussian
Oil-bitcoin
AIC	−1.6762	4.2977	−1.5008	−3.4907
BIC	11.0563	29.7627	11.2317	4.9976
Logl	3.8381	3.8512	3.7504	3.7454
DJI-bitcoin
AIC	−6.0824	4.7231	−9.9090	−7.2291
BIC	6.5913	30.0704	2.7647	1.2200
Logl	6.0412	3.6385	7.9545	5.6146
SHCI-bitcoin
AIC	2.5367	6.8895	−0.0781	−0.3778
BIC	15.0953	32.0068	12.4805	7.9946
Logl	1.7317	2.5552	3.0390	2.1889
Gold-bitcoin
AIC	−12.8951	−16.2782	−21.3782	−20.4136
BIC	−0.2215	9.0691	−8.7045	−11.9645
Logl	9.4476	14.1391	13.6891	12.2068
Treasury-bitcoin
AIC	2.3127	9.9400	4.3864	3.5754
BIC	14.9626	35.2397	17.0363	12.0086
Logl	1.8436	1.0300	0.8068	0.2123
USDX-bitcoin
AIC	4.7563	27.4296	−14.4663	−14.3609
BIC	17.4181	52.7532	−1.8046	−5.9197
Logl	0.6218	−7.7148	10.2332	9.1804
RE-bitcoin
AIC	−7.3891	1.6673	−4.9820	−4.9437
BIC	5.2846	27.0146	7.6917	3.5054
Logl	6.6945	5.1664	5.4910	4.4719

This table reports the test results of the time-varying copula models. Values in bold show the best estimation

Fig. 1.

Dependence of the DJI, SHCI, Oil, and RE with Bitcoin. This figure presents the dynamic dependence relationship between the DJI, SHCI, Oil, RE, and Bitcoin. The horizontal axis represents the dates, and the vertical axis represents the dynamic dependence relationship

Fig. 2.

Dependence between Gold, Treasury, the USDX, and Bitcoin. This figure presents the dynamic dependence relationship between Gold, Treasury, USDX, and Bitcoin. The horizontal axis represents the dates, and the vertical axis represents the dynamic dependence between the two markets

In Fig. 1, the dynamic relationship between crude oil and Bitcoin has a downward trend that has been observed to be negative after August 2019, and after January 2020, the relationship turns from negative to positive and has strengthened. In particular, the relationship between crude oil and Bitcoin remained at a high level after March 2020. The oil market suffers a huge shock after the pandemic, which may affect the dependence between these two markets. The dynamic dependence relationship between the DJI and Bitcoin is always observed to be in the interval (−0.2, 0.2) before the COVID-19 outbreak. Following the pandemic, there is an obvious increase in dependence and the dependence is always positive at most times after January 2020. The dependence reaches the maximum value around March 2020, which may be affected by the four circuit breaks in the US stock markets. Similar to the US stock market, the dynamic relationship between the SHCI and Bitcoin is always observed to be in the interval (−0.1, 0.2) before the COVID-19 outbreak. Following the pandemic, there is an obvious increase in dependence after March 2020. The dependence between the SHCI and Bitcoin has fluctuated from 0.1 to 0.2 in most cases after March 2020. When the pandemic was first reported in China, the Chinese government took strict control measures, and the Chinese stock market experienced significant volatility, so the dependence between these two markets increased. As indicated in Fig. 1, the time-varying relationship between RE and Bitcoin has exhibited volatility at (−0.1, 0.1) before the risk outbreak. However, this relationship shows a growth trend end of 2019. Especially around March 2020, the relationship between these two markets reaches its highest level, at about 0.3. This indicates that the COVID-19 outbreak has enhanced this relationship.

As shown in Fig. 2, the dependence between gold and Bitcoin is constantly changing and always positive, and their dependence is more volatile after the pandemic than before. Gold is known as a hedge asset, and Bitcoin is considered to have some features similar to that of gold and can hedge risk (Dyhrberg 2016a). While the dependence between these two markets remains volatile. The time-varying dependence relationship between Treasury and Bitcoin always maintains a stable and low level (not exceeding 0.05), as shown in Fig. 2. Although the pandemic has made the correlation stronger in some markets, the relationship between Treasury and Bitcoin has always been weak (Bouri et al. 2017); hence, this extreme result has no impact on their relationship. Figure 2 indicates that the dynamic relationship between USDX and Bitcoin has changed between 2019 and 2020. Before 2020, they maintained a negative relationship and the relationship is always observed to be in the interval (0, −0.2). While after the pandemic, a stronger negative relationship begins to emerge, especially after March 2020. The USDX is the only one of the seven markets that has maintained a negative relationship with the bitcoin market after the pandemic.

In summary, the dynamic relationship between Bitcoin and the DJI, SHCI, Oil, and RE is a positive enhancement after the COVID-19 outbreak. The relationship between Bitcoin and Gold and Treasury remains stable, but the relationship between Bitcoin and USDX is a negative enhancement. Combining the static nonlinear and dynamic analysis results, the Oil, DJI SHCI and RE markets have a stronger positive relationship with Bitcoin after the pandemic in both two analyses. The relationship between the USDX and Bitcoin is stronger negative in dynamic analysis, however, this is not apparent in the static analysis. In addition, for the comparison of the relationship between gold and Bitcoin before and after the pandemic, the dynamic analysis believes that there is also a relatively strong relationship between the two before the pandemic, but this cannot be proved in the static analysis. The relationship between Treasury and bitcoin is considered to be at a low level in the dynamic analysis, but it can be found that there is a certain relationship between the two in the static analysis. The reason for the partial difference between the dynamic analysis and the static analysis may be that the static analysis ignores the time variation and cannot reflect the time variation of the dependence relationship.

Risk spillover effect analysis using VaR, CoVaR, and ΔCoVaR

The above section estimates and discusses the relationship between the assets under study but ignores the extreme risk spillover effect. Therefore, in this section, CoVaR and ΔCoVaR are employed to analyze the extreme downside risk spillover effect. Tables 8–14 exhibit the extreme downside risk spillover effect between Bitcoin and the traditional financial markets. The Kolmogorov–Smirnov (KS) test is used to uncover the difference between VaR and CoVaR. The null hypothesis of the KS test is that the VaR is significantly equal to CoVaR, if the null hypothesis is rejected, it is assumed that there is risk spillover. As the tables show, the risk spillover effect in these markets has changed dramatically after the COVID-19 outbreak. The detailed outcomes are discussed below.

Table 8.

Estimation results of VaR, CoVaR, and ΔCoVaR for Oil and Bitcoin

Bitcoin|Oil	Before COVID-19				After COVID-19
	Mean	Std.	Max	Min	Mean	Std.	Max	Min
VaR	−6.25%	1.51%	−2.63%	−11.11%	−6.44%	2.60%	−3.88%	−20.98%
CoVaR	−7.05%	2.12%	−3.41%	−13.26%	−8.50%	3.94%	−4.68%	−29.60%
ΔCoVaR	−119.50%	3.49%	−107.81%	−128.27%	−122.76%	2.35%	−115.66%	−126.74%
Mean (CoVaR/VaR-1)			12.65%				32.09%
P (VaR= CoVaR)			0.00 ***				0.00 ***
Oil|Bitcoin
VaR	−3.90%	1.18%	−2.37%	−9.60%	−7.17%	6.30%	−2.28%	−28.70%
CoVaR	−4.26%	1.23%	−2.22%	−8.64%	−9.41%	8.84%	−2.27%	−40.51%
ΔCoVaR	−135.52%	5.37%	−125.46%	−148.80%	−140.86%	3.67%	−129.28%	−147.19%
Mean (CoVaR/VaR-1)			9.22%				31.10%
P (VaR= CoVaR)			0.00 ***				0.00 ***

This table presents the risk spillover effect between Oil and Bitcoin. P (VaR= CoVaR) is the result of the Kolmogorov–Smirnov (KS) test, and the null hypothesis shows that the value of VaR is equal to CoVaR. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

Table 14.

Estimation results of VaR, CoVaR, and ΔCoVaR for Treasury and Bitcoin

Bitcoin|Treasury	Before COVID-19				After COVID-19
	Mean	Std.	Max	Min	Mean	Std.	Max	Min
VaR	−6.48%	1.55%	−1.86%	−11.43%	−6.64%	2.66%	−4.34%	−24.26%
CoVaR	−6.81%	1.55%	−2.66%	−12.60%	−7.11%	2.84%	−5.29%	−27.23%
ΔCoVaR	−119.06%	0.91%	−106.12%	−120.62%	−119.59%	0.35%	−118.92%	−120.48%
Mean (CoVaR/VaR-1)			4.97%				7.09%
P (VaR= CoVaR)			0.02**				0.06**
Treasury|Bitcoin
VaR	−4.24%	1.37%	−2.51%	−9.41%	−9.47%	6.65%	−2.86%	−41.77%
CoVaR	−4.40%	1.39%	−2.68%	−9.87%	−10.00%	6.97%	−3.29%	−40.59%
ΔCoVaR	−137.28%	0.95%	−134.76%	−141.93%	−136.94%	0.57%	−135.92%	−138.36%
Mean (CoVaR/VaR-1)			3.73%				5.55%
P (VaR= CoVaR)			0.20				0.39

This table presents the risk spillover effect between Treasury and Bitcoin. P (VaR= CoVaR) is the result of the Kolmogorov–Smirnov (KS) test, and the null hypothesis shows that the value of VaR is equal to CoVaR. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

First, the VaR of all eight markets has increased following the pandemic, implying that the COVID-19 outbreak has exacerbated the loss of a single market. According to Tables 8–14, the mean VaR of all single markets is smaller, and the minimum VaR indicates that the extreme risk has clearly increased after the outbreak. This may indicate that COVID-19 has had a significant impact on the markets under study, and this impact should be taken seriously.

Second, the risk spillover between Bitcoin and Oil, Gold, and SHCI is bidirectional, as shown in Tables 8, 9, and 10, respectively, regardless of whether it occurred before or after the COVID-19 outbreak. The risk has been transmitted from Bitcoin to Oil, Gold, and SHCI, and vice versa. In Table 8, the VaR of Bitcoin (−6.25%) has been greater than that of CoVaR (Bitcoin|Oil, −7.05%) before the pandemic, indicating that risk spillover from the crude oil market to Bitcoin has increased the risk of the Bitcoin market by 12.65%. The risk spillover from Bitcoin to the crude oil markets has achieved a similar result. The risk spillover between Bitcoin and Oil always increases the risk of the markets whatever before and after the pandemic. This could be attributed to the positive relationship between Bitcoin and the crude oil market most time, and the risk spillover makes the risk of Bitcoin and the oil market increase by 32.09% and 31.10% after the pandemic, respectively.

Table 9.

Estimation results of VaR, CoVaR, and ΔCoVaR for Gold and Bitcoin

Bitcoin|Gold	Before COVID-19				After COVID-19
	Mean	Std.	Max	Min	Mean	Std.	Max	Min
VaR	−6.12%	1.80%	−2.77%	−11.85%	−6.33%	3.10%	−3.15%	−20.58%
CoVaR	−8.93%	2.53%	−4.94%	−16.22%	−9.59%	4.80%	−5.41%	−32.13%
ΔCoVaR	−124.20%	1.18%	−111.62%	−126.60%	−125.09%	1.29%	−122.32%	−128.21%
Mean (CoVaR/VaR-1)			45.97%				51.64%
P (VaR= CoVaR)			0.00***				0.00***
Gold|Bitcoin
VaR	−1.23%	0.31%	−0.80%	−2.52%	−1.85%	0.76%	−0.88%	−4.72%
CoVaR	−1.71%	0.43%	−1.11%	−3.28%	−2.64%	1.13%	−1.28%	−6.65%
ΔCoVaR	−137.31%	1.22%	−134.67%	−140.51%	−139.09%	1.95%	−134.67%	−143.40%
Mean (CoVaR/VaR-1)			38.87%				43.13%
P (VaR= CoVaR)			0.00***				0.00***

This table presents the risk spillover effect between Gold and Bitcoin. P (VaR= CoVaR) is the result of the Kolmogorov–Smirnov (KS) test, and the null hypothesis shows that the value of VaR is equal to CoVaR. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

Table 10.

Estimation results of VaR, CoVaR, and ΔCoVaR for the SHCI and Bitcoin

Bitcoin|SHCI	Before COVID-19				After COVID-19
	Mean	Std.	Max	Min	Mean	Std.	Max	Min
VaR	−6.26%	1.68%	−3.43%	−11.92%	−6.49%	2.92%	−3.45%	−21.52%
CoVaR	−7.25%	1.49%	−4.61%	−10.86%	−7.78%	4.04%	−4.68%	−29.42%
ΔCoVaR	−117.76%	1.98%	−112.88%	−126.81%	−117.92%	1.68%	−113.69%	−122.92%
Mean (CoVaR/VaR-1)			15.78%				19.78%
P (VaR= CoVaR)			0.00***				0.00***
SHCI|Bitcoin
VaR	−1.84%	0.46%	−1.20%	−3.52%	−1.97%	0.58%	−1.29%	−4.43%
CoVaR	−2.11%	0.54%	−1.45%	−3.54%	−2.29%	0.66%	−1.43%	−3.93%
ΔCoVaR	−129.91%	2.92%	−122.08%	−134.95%	−130.26%	2.30%	−124.44%	−136.14%
Mean (CoVaR/VaR-1)			14.65%				15.96%
P (VaR= CoVaR)			0.00***				0.00***

This table presents the risk spillover effect between the SHCI and Bitcoin. P (VaR= CoVaR) is the result of the Kolmogorov–Smirnov (KS) test, and the null hypothesis shows that the value of VaR is equal to CoVaR. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

A similar result can be found between the Gold and Bitcoin markets. Table 9 indicates the risk spillover between Bitcoin and Gold is bidirectional, and the risk spillover between these two markets increases the risk of Bitcoin and Gold by 51.64% and 43.13% after the pandemic. Table 10 shows that before and after the crisis, the risk spillover between Bitcoin and the Chinese stock market has been bidirectional, and the risk spillover between these two markets also increases the risk of Bitcoin and SHCI, while the risk increases to a lesser extent than for Gold and Oil. The risk of Bitcoin increases from 15.78 to 19.78%, and the risk of SHCI increases from 14.65 to 15.96%. This may be due to the policy of the Chinese government, which closed the transaction of Bitcoin in 2017, thereby weakening the relationship between Bitcoin and Chinese stock markets (Bouri et al. 2020); thus, the risk spillover effect is weakened.

Third, a difference exists in the direction of the risk spillover effect between some markets, observed before and after the pandemic. For example, there is no risk spillover effect between the DJI and Bitcoin before the pandemic. But after the pandemic, the risk spillover can be found between these two markets. In Table 11, the risk of DJI and Bitcoin is increased by 33.03% and 35.32%, respectively, due to risk spillover. That is a marked change from before the pandemic. After the pandemic, as Bitcoin faces downside risk, the CoVaR of DJI|Bitcoin (−3.92%) is less than the VaR of the US stock market (−2.94%), indicating that the risk from the Bitcoin market magnifies the loss of the US stock market. This is similar to the risk transmitted from US stocks to Bitcoin. The difference between VaR and CoVaR has increased after the pandemic, indicating that the pandemic has increased the risk of spillover between Bitcoin and US stock markets. The ΔCoVaR of these markets is lower after the pandemic, which indicates that the shock of extreme risk has increased to the normal shock after the pandemic.

Table 11.

Estimation results of VaR, CoVaR, and ΔCoVaR for the DJI and Bitcoin

Bitcoin|DJI	Before COVID-19				After COVID-19
	Mean	Std.	Max	Min	Mean	Std.	Max	Min
VaR	−6.28%	1.52%	−1.29%	−11.50%	−6.36%	2.69%	−3.89%	−25.95%
CoVaR	−6.09%	1.44%	−3.01%	−10.85%	−8.61%	5.03%	−3.70%	−39.94%
ΔCoVaR	−117.19%	3.88%	−106.85%	−123.86%	−122.88%	4.89%	−111.13%	−131.96%
Mean (CoVaR/VaR-1)		−3.00%					35.32%
P (VaR= CoVaR)		0.16					0.00***
DJI|Bitcoin
VaR	−1.40%	0.53%	−0.73%	−3.74%	−2.94%	2.50%	−0.88%	−14.79%
CoVaR	−1.35%	0.54%	−0.69%	−4.22%	−3.92%	3.85%	−0.68%	−22.28%
ΔCoVaR	−135.96%	6.81%	−118.56%	−146.47%	−146.30%	8.58%	−124.63%	−160.75%
Mean (CoVaR/VaR-1)			−3.07%				33.03%
P (VaR= CoVaR)			0.37				0.00***

This table presents the risk spillover effect between the DJI and Bitcoin. P (VaR= CoVaR) is the result of the Kolmogorov–Smirnov (KS) test, and the null hypothesis shows that the value of VaR is equal to CoVaR. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

Similar to DJI, the risk spillover between Bitcoin and RE has been insignificant before COVID-19, as shown in Table 12, the difference between VaR and CoVaR is not obvious. But after the pandemic, the risk spillover has become bidirectional. The extreme downside risk of Bitcoin can enhance the risk of RE, and vice versa. The ΔCoVaR of Bitcoin|RE, and RE|Bitcoin both exhibit a shock, and the extreme risk has become stronger after the pandemic than before. This result is attributable to their enhanced dynamic relationship after the pandemic, as shown in Section 4.2. Through the above analysis, it can be found that the risk spillover between Bitcoin and DJI as well as between Bitcoin and RE has been significantly enhanced, and the risk spillover has changed from insignificant to significant after the pandemic.

Table 12.

Estimation results of VaR, CoVaR, and ΔCoVaR for RE and Bitcoin

Bitcoin|RE	Before COVID-19				After COVID-19
	Mean	Std.	Max	Min	Mean	Std.	Max	Min
VaR	−6.28%	1.52%	−1.92%	−11.70%	−6.44%	2.71%	−4.19%	−22.97%
CoVaR	−6.39%	1.42%	−3.42%	−11.32%	−9.07%	4.66%	−5.65%	−37.01%
ΔCoVaR	−117.74%	1.63%	−107.78%	−122.21%	−124.22%	3.30%	−117.63%	−130.78%
Mean (CoVaR/VaR-1)			1.80%				40.81%
P (VaR= CoVaR)			0.39				0.00***
RE|Bitcoin
VaR	−1.40%	0.49%	−0.86%	−5.57%	−4.23%	3.35%	−1.08%	−18.74%
CoVaR	−1.43%	0.54%	−0.87%	−6.14%	−5.57%	4.94%	−1.10%	−28.10%
ΔCoVaR	−145.71%	4.26%	−137.31%	−193.17%	−158.66%	6.28%	−145.94%	−169.71%
Mean (CoVaR/VaR-1)			1.64%				31.80%
P (VaR= CoVaR)			0.62				0.00***

This table presents the risk spillover effect between RE and Bitcoin. P (VaR= CoVaR) is the result of the Kolmogorov–Smirnov (KS) test, and the null hypothesis shows that the value of VaR is equal to CoVaR. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

Fourth, Table 13 shows that the risk spillover between Bitcoin and USDX was bidirectional before and after the pandemic. However, different from the previous analysis, the risk spillover between these two markets reduces the respective risk, and with the onset of the pandemic, the risk reductions are deeper than before the pandemic, from −23.86 to −42.42% and from −20.24 to −35.22%, respectively. According to Section 4.2, the negative dynamic relationship between Bitcoin and USDX continues to strengthen since the outbreak. Owing to their negative relationship, they can hedge the risk when one of them has extreme downside risk. Table 13 shows that Bitcoin can reduce the risk of the USDX and vice versa, and the VaR has been less than CoVaR before and after the pandemic. The negative relationship between these two markets may play a key role in the risk spillover.

Table 13.

Estimation results of VaR, CoVaR, and ΔCoVaR for the USDX and Bitcoin

Bitcoin|USDX	Before COVID-19				After COVID-19
	Mean	Std.	Max	Min	Mean	Std.	Max	Min
VaR	−6.28%	1.64%	−3.98%	−12.59%	−6.29%	2.59%	−3.84%	−24.53%
CoVaR	−4.78%	1.34%	−1.26%	−9.52%	−3.62%	1.61%	−1.67%	−12.08%
ΔCoVaR	−113.23%	1.66%	−103.00%	−117.02%	−109.99%	2.82%	−105.38%	-116.45%
Mean (CoVaR/VaR-1)			−23.86%				−42.42%
P (VaR= CoVaR)			0.00***				0.00***
USDX|Bitcoin
VaR	−0.48%	0.26%	−0.27%	−1.98%	−0.55%	0.23%	−0.25%	−1.28%
CoVaR	−0.38%	0.19%	−0.23%	−1.77%	−0.36%	0.16%	−0.20%	−0.88%
ΔCoVaR	−123.25%	13.40%	−119.10%	−333.35%	−118.03%	3.78%	−111.61%	−126.60%
Mean (CoVaR/VaR-1)			-20.24%				-35.22%
P (VaR= CoVaR)			0.00***				0.00 ***

This table presents the risk spillover effect between USDX and Bitcoin. P (VaR= CoVaR) is the result of the Kolmogorov–Smirnov (KS) test, and the null hypothesis shows that the value of VaR is equal to CoVaR. ***, **, and * reflect the rejection of the null hypothesis at the 1%, 5%, and 10% levels of significance, respectively

Last, there has been a minor risk spillover between Bitcoin and Treasury, and the risk spillover is unidirectional both before and after the pandemic. In Table 14, the risk is only transmitted from Treasury to the Bitcoin market. While risk spillovers have increased after the pandemic, the increase has been small, with the risk in the Bitcoin market only increasing from 4.97 to 7.09%. As shown in the preceding analysis, the relationship between Bitcoin and Treasury is always weak, which explains why the risk spillover from Treasury to Bitcoin keeps a low level, and the risk spillover from Bitcoin to Treasury is insignificant before or after the COVID-19 outbreak. The pandemic has a small impact on the risk of spillover between these two assets.

Based on the above analysis, some recommendations can be made for investors and policymakers. First, the risk of a single market has increased following the pandemic; hence, attention must be paid to the impact of the pandemic on financial markets, and additional policies should be implemented to combat the economic depression. Second, the risk spillover between the markets changes over time; therefore, hedge strategies must adapt to changes in risk spillover. Specifically, the risk spillover between Bitcoin and the Oil, SHCI, Gold, DJI, and RE is enhanced after COVID-19; therefore, hedge strategies should be developed to the shock from these markets and reduce risks arising from risk spillovers between Bitcoin and these markets. Third, for the risk spillover between Bitcoin and the USDX, since the relationship between these two markets is negative, and the risk spillover between them can reduce the risk, such a relationship can be used to realize the risk hedging between assets. Last, Considering Bitcoin and Treasury, since both the relationship and the risk spillover between these two markets are weak, a specific hedging strategy may not be needed.

Conclusions

Our study examines the static and dynamic relationship between Bitcoin, crude oil, and six other financial markets from 2019 to 2020, during which the COVID-19 outbreak occurred, using QQR and a time-varying copula model. A CoVaR model is then utilized to discuss the downside risk spillover effect between these markets. We arrive at two conclusions. First, a static nonlinear and dynamic relationship analysis reveals that the relationship between some markets has changed significantly following the COVID-19 outbreak. The relationships between Bitcoin and other markets differ, and its relationships with cured oil, stock markets, gold, and RE should be given particular attention. Second, the risk of a single market has increased because of the pandemic, and COVID-19 has had a significant impact on these markets. The risk spillover observed between these markets before and after COVID-19 usually differs. COVID-19 has made the risk spillover between Bitcoin, crude oil, US stock, Chinese stock, gold, and real estate stronger; the risk spillover between Bitcoin and the USDX can reduce the single market risk, and the risk spillover between Bitcoin and Treasury is weak at all times. The available evidence suggests that the Bitcoin market has a significant impact on the risk spillover effect with traditional markets, including crude oil, and the pandemic has reinforced this effect.

We provide some suggestions to address the concerns and findings raised in this study. First, we argue that the shock of COVID-19 on these markets must be taken seriously and that investors and policymakers should change their hedge strategies and policies to face the associated challenges. Our study uncovers the relationship and risk spillover between Bitcoin, crude oil, and other markets, which can help investors reduce risk by using suitable strategies; policymakers could design more effective policies to prevent recessions. More importantly, the results of this study may offer an interesting approach to explaining why Bitcoin has become a people asset and why more investors are considering Bitcoin as part of their portfolios.

Author contributions

Rui Zha: Data curation, Investigation, Software R, Visualization, Validation, Writing-Original draft preparation. Lean Yu: Conceptualization, Methodology, Investigation, Writing – review & editing, and Supervision. Yi Su: Conceptualization, Methodology, Investigation, and Writing – review. Hang Yin: Conceptualization, Investigation, and Writing – review.

Funding

This work is partially supported by grants from the Key Program of the National Natural Science Foundation of China (NSFC No.71631005), the Fundamental Research Special Funds for the Central Universities-Research and Innovation Fund for Doctoral Students (No. 3072021GIP0903), and the Key Program of Research Center of Scientific Finance and Entrepreneurial Finance of Ministry of Education of Sichuan Province (No. KJJR2021-003).

Data availability

The data analyzed during the current study are available as follows.

The Bitcoin price data are obtained from Bitcoincharts (https://bitcoincharts.com/).

The DJI, SHCI, Gold, Treasury, and USDX data are collected from the Wind database.

Oil futures price data are selected from the US Energy Information Agency (https://www.eia.gov/).

FTSE RAFI US 100 Real Estate data are collected from the Investing database (https://www.investing.com/).

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.