Dynamic Cross-Market Volatility Spillover Based on MSVModel: Evidence from Bitcoin, Gold, Crude Oil, and Stock Markets

.is paper examines the spillover effect between bitcoin, gold, crude oil, and major stock markets by using the MSV model with dynamic correlation and Granger causality. .e empirical results of the DC-GC-MSVmodel are logically correct and convergent. .e DIC test result has proved that the DC-GC-MSV model is better and more accurate. Bitcoin has no significant Granger causality spillover effect than other assets. As a safe haven product for stock assets, gold price has one-way spillover effect from stock market volatility. Moreover, crude oil has the highest correlation with the stock market. In the recent COVID-19 epidemic and the sluggish economic environment, investors need to consider a balanced asset allocation among low-correlation assets, medium-correlation assets, and high-correlation assets to reduce risks.


Introduction
Bitcoin has been around for a short time, but its influence is increasing day by day. It is generally believed that there is a certain degree of connection between the commodity market and the stock market. After 10 years of development, bitcoin has gradually been regarded as an investment product similar to gold. Its ability to maintain value and diversify risks has received increasing attention. Early research believes that the volatility of bitcoin is highly endogenous and speculative, just like chaos [1]. Some research studies [2,3] have show that the volatility of seven electronic cryptocurrencies is highly random, highly chaotic, and highly risky, so they cannot be considered suitable for hedging purposes. Although the academic research on bitcoin theory and models has just begun, and bitcoin has become a practical financial product. Especially after the Chicago Board of Trade (CME Group) launched bitcoin futures products, bitcoin can be legally traded and the transaction data was standardized. It provides a foundation for the further research on volatility spillover of bitcoin. e uncertainty of global economy provides the possibility that the bitcoin becomes a new basket for diversified investment [4]. Some researchers [5][6][7] have studied the asymmetry, thick tail, long-term, and short-term features of bitcoin price volatility. e cryptocurrencies usually have thick tails, autocorrelation, and asymmetry [8]. It brings the cryptocurrency closer to the general financial product such as oil future or gold [9].
Gold has long been considered as a safe haven for hedging stocks. But more and more studies have put forward different views. Wen and Cheng [10] believe that gold can be used as a safe asset in emerging markets such as ailand. In contrast, the US dollar has better risk reduction capabilities. Choudhry et al. [11] have used a multivariate nonlinear dynamic test to prove that gold has a close relationship with stock market volatility and cannot be used to lower the risk in stock market. Hussain Shahzad et al. [12] have found that compared with the bond market, the gold market cannot be used as a hedging tool for the stock market. Gold needs some qualifications related to market conditions before it can be used as a tool to hedge the risk of other assets [12,13]. For example, only when stocks and gold are in extremely low volatility or high volatility periods, gold can be used as a hedging tool for diversified investment [14]. Spillover effect often occurs between different assets in developing and developed market [15]. Many studies show that diversification of different assets with lower correlation is an important way of hedging [16][17][18]. Cryptocurrencies also have spillover effect [19]. In 2020, COVID-19 has hit the oil price and caused the stock market panic. e investors and researchers try to find a new basket to diversify risks [20].
GARCH [21] and SV models [22] are often used to detect the volatility of price.
e MSV model has been proved efficient and accurate in many situations [23]. e NP problem of multivariate stochastic volatility model can be solved by the Markov Monte Carlo method [24,25]. Many SV models have been established to solve different problems, such as nonlinear [26], mean [27], leverage [28], T-distribution [29], and two-factor [30]. is paper has established a multivariate stochastic volatility model with dynamic correlation and Granger causality test between each series. We have simulated the volatility spillover between each asset through the Markov Monte Carlo method, and we provide advice on diversified investment in bitcoin, gold, crude oil, and stock assets.

Multivariate Stochastic Volatility Model
(1) In equation (1), y t is the yield sequence. ϕ 11 and ϕ 22 are unobserved. y t represents the yield at time t. ε t represents the volatility of yield sequence. ξ t represents the independent disturbance of yield sequence volatility. σ represents the standard error. ϕ 11 and ϕ 22 are the continuous parameters of yield sequence.

GC-MSV Model.
In equation (2), Yu [31] has added one-way Granger cause test in the MSV model for the first time. Equation (2) has an improved two-way Granger cause test in the MSV model. When ϕ 12 and ϕ 21 are nonzero, a Granger causality in volatility between the two sequence is obvious. ϕ 12 represents the Granger cause of sequence 1 from sequence 2. It suggests that the volatility in sequence 2 Granger causes the volatility in sequence 1. ϕ 12 represents the opposite. ϕ 11 and ϕ 22 represent the autocorrelation of sequence 1 and sequence 2.

Complexity
In equation (3), ρ t reflects the time-varying dynamic correlation, ranging from −1 to 1. Yu [31] has achieved the constraint by using the Fisher transformation, following the suggestion of Tsay [32] in the MARCH model.

DC-GC-MSV Model.
In equation (4), we have used the DC-MSV and GC-MSV model to improve the multivariate stochastic volatility model. e DC-GC-MSV model has the timevarying dynamic correlation and the Granger causality test. When ϕ 12 and ϕ 21 are nonzero, the Granger causality in volatility between the two sequence is obvious. ϕ 12 represents the Granger cause of sequence 1 from sequence 2. It suggests that the volatility in sequence 2 Granger causes the volatility in sequence 1. ϕ 12 represents the opposite. ϕ 11 and ϕ 22 represent the autocorrelation of sequence 1 and sequence 2. ρ t reflects the time varying dynamic correlation, ranging from −1 to 1.

Markov Monte Carlo Method and Gibbs Sampling.
e Markov Monte Carlo method assumes that X t , t ∈ T is a random process with a discrete set I � x 1 , x 2 , . . . as follows: erefore, we determine the transition probability by its one-step probability: en, using Gibbs sampling as follows: follows a multivariate normal distribution: When t ⟶ ∞, the distribution of (x (t) 1 , x (t) 2 ) will converge.

Data and Preprocessing.
In this section, we choose the most important assets of cybercurrency, gold, oil future, and Complexity stock index, including CME Group bitcoin futures (BC), international gold price (GD), Brent crude oil future price (BO), and 7 major stock indexes. e Chicago Mercantile Exchanges Bitcoin futures is the worlds largest bitcoin futures product, which has an important influence on the cybercurrency market in terms of market size and brand effect. S&P, Dow Jones, and Nasdaq are the major U.S. stock indexes. e Shanghai Composite Index is a major stock index in China. e Nikkei 225 is a major stock index in Japan. e DAX and the FTSE Index are important stock indexes in Europe. British Brent crude oil futures are the most important crude oil futures products and have an important influence on crude oil market prices. All asset data come from the open market data. Table 1 is the descriptive statistics result of 10 asset prices.

Parameter Estimation.
In this paper, we have used the WinBUGs software to do the MCMC simulation. Taking bitcoin (BC) and Dow Jones index (DQ) as example, we burn-in the first 10,000 iterations. In Table 2, we simulate the last 100,000 iterations as follows.
In Table 2, ϕ dq bt reflects the volatility of bitcoin has the Granger cause of Dow Jones stock market. ϕ dq bt and ϕ bt dq are nearly zero, which means the spillover effect is not obvious. μ bt shows the volatility of bitcoin is 2.497, and μ dq shows the volatility of Dow Jones index is −0.2231. Bitcoin volatility is obviously greater than stock market. erefore, the cybercurrency has greater risk than stock. ϕ dq bt of bitcoin is 0.6768, and ϕ bt dq is 0.9614. is means Dow Jones index has more volatility persistence than bitcoin. In Figure 1, the Gelman Rubin test results are good. e result of each parameter is lower than 1.1 and convergent. e simulation results of this paper are also convergent. e deviance information criterion (DIC) is a popular method to test the MCMC simulation result. In Table 3, the DIC test results prove the DC-GC-MSV model is better than other models.
If ϕ12 and ϕ12 are significantly nonzero, it means there is a Granger causality of spillover effects between two assets [31]. We have defined ϕ12 and ϕ21 2.5% quantile is greater than zero as positive significant. If only 5% quantile is greater than zero, it can be defined as subsignificant. Table 4 shows the spillover relation between bitcoin, gold, and oil. ϕ bog d of oil price is positive which means one-way spillover to the gold price. Table 5 shows the spillover relation between bitcoin and stock index.
ere is no significant spillover. Table 6 shows the spillover relation between gold and stock. ϕ spg d , ϕ dq g d , ϕ nqg d , ϕ jpg d , ϕ geg d , and ϕ eng d are positive. e result reflects a significant one-way spillover from stock to gold. Table 7 shows the spillover relation between oil and stock index. e index of S&P, Dow Jones, NASDAQ, and FTSE have two-way spillover to oil price. e Brent oil future price causes the one-way spillover to ϕ bojp because Japan is highly dependent on crude oil. As an emerging stock market, the Chinese stock market did not reflect a significant spillover to bitcoin, gold, and oil.

Conclusion
e empirical results of DC-GC-MSV model are logically correct and convergent. e DIC test result has proved that the DC-GC-MSV model is better and more accurate. (1) Bitcoin has a high degree of independence and is affected neither by the volatility in the major stock markets nor by the volatility in the gold and crude oil market. e volatility of bitcoin futures trading shows more speculation and high risk. Bitcoin can be used as a component of high-risk asset allocation. But Bitcoin still cannot be regarded as a general financial product. (2) Gold is subject to one-way   spillover from the stock market, showing that gold is widely recognized as a safe haven product for stock assets. As a financial product, gold has a hedging function in asset allocation. (3) Crude oil has the highest correlation with the stock market. As a highly correlated asset, it is necessary to reduce the proportion of asset decentralized allocation. Investors need to consider a balanced asset allocation among low-correlation assets, mediumcorrelation assets, and high-correlation assets to reduce risk.
Our further research will try to use the MSV model to hedge between different assets.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare there are no conflicts of interest regarding the publication of this paper.