Complexity

Complexity / 2021 / Article

Research Article | Open Access

Volume 2021 |Article ID 9912418 | https://doi.org/10.1155/2021/9912418

Jing Zhang, Qi-zhi He, "Dynamic Cross-Market Volatility Spillover Based on MSV Model: Evidence from Bitcoin, Gold, Crude Oil, and Stock Markets", Complexity, vol. 2021, Article ID 9912418, 8 pages, 2021. https://doi.org/10.1155/2021/9912418

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

Academic Editor: M. Irfan Uddin
Received10 Mar 2021
Revised24 Mar 2021
Accepted03 Apr 2021
Published13 Apr 2021

Abstract

This 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. The empirical results of the DC-GC-MSV model are logically correct and convergent. The 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.

1. 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. The uncertainty of global economy provides the possibility that the bitcoin becomes a new basket for diversified investment [4]. Some researchers [57] have studied the asymmetry, thick tail, long-term, and short-term features of bitcoin price volatility. The 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 Thailand. 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 [1618]. Cryptocurrencies also have spillover effect [19]. In 2020, COVID-19 has hit the oil price and caused the stock market panic. The 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. The MSV model has been proved efficient and accurate in many situations [23]. The 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]. This 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.

2. Multivariate Stochastic Volatility Model

2.1. Stochastic Volatility Model
2.1.1. Basic MSV Model

In equation (1), is the yield sequence. and are unobserved. represents the yield at time t. represents the volatility of yield sequence. represents the independent disturbance of yield sequence volatility. represents the standard error. and are the continuous parameters of yield sequence.

2.1.2. 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 and are nonzero, a Granger causality in volatility between the two sequence is obvious. 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. represents the opposite. and represent the autocorrelation of sequence 1 and sequence 2.

2.1.3. DC-MSV Model

In equation (3), 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.

2.1.4. DC-GC-MSV Model

In equation (4), we have used the DC-MSV and GC-MSV model to improve the multivariate stochastic volatility model. The DC-GC-MSV model has the time-varying dynamic correlation and the Granger causality test. When and are nonzero, the Granger causality in volatility between the two sequence is obvious. 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. represents the opposite. and represent the autocorrelation of sequence 1 and sequence 2. reflects the time varying dynamic correlation, ranging from −1 to 1.

2.2. Markov Monte Carlo Method and Gibbs Sampling

The Markov Monte Carlo method assumes that is a random process with a discrete set as follows:

Therefore, we determine the transition probability by its one-step probability:

Then, using Gibbs sampling as follows:(1)Sampling from (2)Sampling from (i)Sampling from .(n) Sampling from

follows a multivariate normal distribution:

When , the distribution of will converge.

3. Empirical Analysis

3.1. Data and Preprocessing

In this section, we choose the most important assets of cybercurrency, gold, oil future, and stock index, including CME Group bitcoin futures (BC), international gold price (GD), Brent crude oil future price (BO), and 7 major stock indexes. The 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. The Shanghai Composite Index is a major stock index in China. The Nikkei 225 is a major stock index in Japan. The 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.


BCGDBOSPDQNQSHJPGEEN

Mean0.0706050.05471‒0.0450920.0479510.0290110.09324‒0.0001580.0190850.004953−0.026783
Median0.0670470.0589460.1678390.1497650.1248520.1940130.030620.0558010.0804940.059978
Maximum23.630484.68600419.078588.96831610.764338.9346957.5481267.73137510.414298.666807
Minimum‒32.14742‒6.261981‒30.98756‒12.76521‒13.84181‒13.14915‒6.712451‒6.273569‒13.05486−11.51243
Std. dev.5.1105930.9875173.3550181.5587241.6492971.707691.3216421.3394941.5601031.3618
Skewness‒0.307979‒0.580902‒1.820156‒1.187611‒1.18846‒1.096672‒0.1665180.038317‒0.754934−1.087716
Kurtosis8.0861779.42669627.5138418.4651519.9700413.691377.0288238.19165716.7724116.43635
Jarque–Bera692.30681124.95216199.016456.9347744.5433141.686431.0288711.04835062.9184886.44

3.2. 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.


NodeMeanSDMC error2.50%5.00%10.00%Median97.50%StartSample

2.4970.16740.0029052.172.2262.2882.4962.8310000100001
−0.22310.37390.007361−1.028−0.8612−0.6923−0.20490.477210000100001
0.67680.087060.0030410.48440.51950.55970.68570.822210000100001
0.027310.04390.000828−0.05429−0.04121−0.026480.025410.119910000100001
0.96140.015040.0004250.92820.93440.94140.96270.98710000100001
0.018940.019350.000468−0.01839−0.0122−0.0053430.018750.0581210000100001
0.97080.13930.005290.70990.7490.79260.96791.2510000100001
0.32750.049260.0021380.24120.2530.26720.32360.431910000100001

In Table 2, reflects the volatility of bitcoin has the Granger cause of Dow Jones stock market. and are nearly zero, which means the spillover effect is not obvious. shows the volatility of bitcoin is 2.497, and shows the volatility of Dow Jones index is −0.2231. Bitcoin volatility is obviously greater than stock market. Therefore, the cybercurrency has greater risk than stock. of bitcoin is 0.6768, and is 0.9614. This means Dow Jones index has more volatility persistence than bitcoin. In Figure 1, the Gelman Rubin test results are good. The result of each parameter is lower than 1.1 and convergent. The simulation results of this paper are also convergent. The 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.


DbarDhatpDDIC

CC-MSV5122.684898.25224.4295347.11
GC-MSV5125.54902.97222.5285348.02
DC-MSV5098.344871.57226.7655325.1
DC-GC-MSV5089.594857.83231.7615321.35

If and are significantly nonzero, it means there is a Granger causality of spillover effects between two assets [31]. We have defined and 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. 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. There is no significant spillover. Table 6 shows the spillover relation between gold and stock. , , , , , and are positive. The result reflects a significant one-way spillover from stock to gold. Table 7 shows the spillover relation between oil and stock index. The index of S&P, Dow Jones, NASDAQ, and FTSE have two-way spillover to oil price. The Brent oil future price causes the one-way spillover to 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.


NodeMeanSDMC error2.50%5.00%10.00%Median97.50%is it significant

0.091380.058040.00147−0.01010.0042410.021160.08710.2177Not significant
0.0073110.020830.00054−0.03462−0.02706-0.018880.0075230.04801Not significant
0.072170.076890.00188−0.06467−0.04413−0.020240.066620.2394Not significant
0.027780.029330.00078−0.02335−0.01526−0.0064210.025060.09253Not significant
0.092080.0490.001890.01980.027790.037820.084270.2093Significant
0.037360.031130.00097−0.01791−0.009137.33E-040.034910.1062Not significant


NodeMeanSDMC error2.50%5.00%10.00%Median97.50%is it significant

0.03330.045310.00093−0.04887−0.03595−0.021790.030730.1307Not significant
0.018520.019690.00047−0.02023−0.01362−0.0062690.018450.05747Not significant
0.027310.04390.00083−0.05429−0.04121−0.026480.025410.1199Not significant
0.018940.019350.00047−0.01839−0.0122−0.0053430.018750.05812Not significant
0.03920.051640.00111−0.0547−0.04006−0.023410.036190.1494Not significant
0.010180.018660.00046−0.02656−0.0203−0.013320.010070.04773Not significant
−0.065470.089550.00237−0.2596−0.2204−0.1788−0.059890.09509Not significant
-0.01640.026210.00065−0.07173-0.06052−0.04901−0.015510.03298Not significant
0.03590.073720.00186−0.09611−0.07636−0.053020.031120.1961Not significant
0.016460.018020.00051−0.01713-0.01162−0.0052880.015680.05464Not significant
0.044220.060160.00145−0.06457-0.04782-0.02850.040710.1735Not significant
0.021460.020130.00054−0.01625−0.01018−0.003160.020680.06322Not significant
0.00820.054720.00119−0.09453-0.07761−0.058640.0060910.1233Not significant
0.023410.017840.00041−0.01174−0.0057390.0011060.023350.05894Not significant


NodeMeanSDMC error2.50%5.00%10.00%Median97.50%is it significant

0.094190.046930.001810.022310.030250.040320.087540.204Significant
0.042430.035320.00115−0.02026−0.01088−1.39E-040.039920.1196Not significant
0.10750.052730.002100.027670.035880.046730.10040.2316Significant
0.026770.033280.00095−0.03251−0.02359−0.013180.024480.09864Not significant
0.12860.066460.002740.033350.042980.055130.11670.2915Significant
0.042020.039850.00142−0.02514−0.01551−0.0045930.038340.1302Not significant
0.032690.034470.00096−0.03706−0.02348−0.0092210.03260.1026Not significant
−0.029410.026480.00067−0.08281−0.0725-0.06166−0.029440.02366Not significant
0.092060.059710.002480.0028510.012630.024880.082830.2343Significant
0.025220.031620.00124−0.02382−0.0173−0.0097970.020560.09874Not significant
0.17340.096290.004360.041570.053990.070540.15340.4118Significant
0.045250.043870.00163−0.02623−0.0163−0.0050770.039860.1469Not significant
0.21940.093510.003960.075830.091480.11260.20580.4397Significant
0.044030.045380.00163−0.03077−0.02058−0.0085290.03910.1466Not significant


NodeMeanSDMC error2.50%5.00%10.00%Median97.50%is it significant

0.23110.11480.005270.070380.086230.1060.2080.5111Significant
0.069490.044010.00160−0.0023450.0063820.01740.064670.1691Subsignificant
0.36810.14060.006120.11790.14640.18640.36380.6645Significant
0.12160.076190.003270.0045980.018450.034680.11070.3041Significant
0.16640.089670.004040.048580.061130.075830.14670.4111Significant
0.050740.035310.00125−0.0060180.0014380.010320.046640.1334Subsignificant
0.032920.024930.00071−0.01775−0.0079940.0019540.033120.08241Not significant
−0.011330.019260.00048−0.0499−0.04269−0.03493−0.011470.02766Not significant
0.089450.099930.00467-0.03178-0.01846−0.0018410.067520.3702Not significant
0.17620.091360.004140.036270.049270.067660.1650.3844Significant
0.58330.21770.010000.18670.24010.30590.57521.035Significant
0.085720.071220.00305-0.01649−0.0071840.0055360.073340.2571Not significant
0.4890.20330.009460.11990.16870.2280.48180.9241Significant
0.18190.12610.006630.021890.037250.056040.15080.5201Significant

4. Conclusion

The empirical results of DC-GC-MSV model are logically correct and convergent. The 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. The 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, medium-correlation 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

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare there are no conflicts of interest regarding the publication of this paper.

Authors’ Contributions

All authors contributed equally to the study.

Acknowledgments

This work was supported by the Major Projects of Social Sciences in Anhui Universities (SK2020ZD006) and the General Project of Anhui Natural Science Foundation (1908085MG232).

References

  1. C. Baek, “Bitcoins as an investment or speculative vehicle? a first look,” Applied Economics Letters, vol. 22, p. 30, 2015. View at: Google Scholar
  2. F. B. Aurelio, “The inefficiency of bitcoin revisited: a dynamic approach,” Economics Letters, vol. 161, p. 1, 2017. View at: Google Scholar
  3. L. Salim, B. Stelios, and S. Antonio, “Long-range memory, distributional variation and randomness of bitcoin volatility,” Chaos, Solitons, and Fractals, vol. 107, p. 43, 2018. View at: Google Scholar
  4. E. Demir, S. Simonyan, C. D. Garca-Gmez, and C. K. M. Lau, “The asymmetric effect of bitcoin on altcoins: evidence from the nonlinear autoregressive distributed lag (nardl) model,” Finance Research Letters, p. 101754, 2020. View at: Google Scholar
  5. A. Y. Khamis Hamed, M. Walid, and M. Y. Seong, “Efficiency, multifractality, and the long-memory property of the bitcoin market: a comparative analysis with stock, currency, and gold markets,” Finance Research Letters, vol. 27, p. 228, 2018. View at: Google Scholar
  6. J. Alvarez-Ramirez, E. Rodriguez, and C. I. Valdez, “Long-range correlations and asymmetry in the bitcoin market,” Physica A: Statistical Mechanics and Its Applications, vol. 492, p. 948, 2018. View at: Google Scholar
  7. L. Wu and S. Chen, “Long memory and efficiency of bitcoin under heavy tails,” Applied Economics, vol. 52, pp. 5298–5309, 2020. View at: Google Scholar
  8. B. Stjepan, K. Zvonko, H. E. Stanley, and Podobnik B., “Scaling properties of extreme price fluctuations in bitcoin markets,” Physica A: Statistical Mechanics and Its Applications, vol. 510, p. 400, 2018. View at: Google Scholar
  9. W. Zhang, P. Wang, X. Li, and D. Shen, “Some stylized facts of the cryptocurrency market,” Applied Economics, vol. 50, pp. 5950–5965, 2018. View at: Google Scholar
  10. X. Wen and H. Cheng, “Which is the safe haven for emerging stock markets, gold or the us dollar?” Emerging Markets Review, vol. 35, pp. 69–90, 2018. View at: Google Scholar
  11. T. Choudhry, S. S. Hassan, and S. Shabi, “Relationship between gold and stock markets during the global financial crisis: evidence from nonlinear causality tests,” International Review of Financial Analysis, vol. 41, pp. 247–256, 2015. View at: Google Scholar
  12. S. J. Hussain Shahzad, N. Raza, M. Shahbaz, and A. Ali, “Dependence of stock markets with gold and bonds under bullish and bearish market states,” Resources Policy, vol. 52, pp. 308–319, 2017. View at: Google Scholar
  13. J. Iqbal, “Does gold hedge stock market, inflation and exchange rate risks? an econometric investigation,” International Review of Economics & Finance, vol. 48, pp. 1–17, 2017. View at: Google Scholar
  14. M. Hood and F. Malik, “Is gold the best hedge and a safe haven under changing stock market volatility?” Review of Financial Economics, vol. 22, pp. 47–52, 2013. View at: Google Scholar
  15. E. Bouri, D. Lien, D. Roubaud, and S. J. H. Shahzad, “Directional predictability of implied volatility: from crude oil to developed and emerging stock markets,” Finance Research Letters, vol. 27, pp. 65–79, 2018. View at: Google Scholar
  16. S. A. Basher and P. Sadorsky, “Hedging emerging market stock prices with oil, gold, vix, and bonds: a comparison between dcc, adcc and go-garch,” Energy Economics, vol. 54, pp. 235–247, 2016. View at: Google Scholar
  17. W. Chkili, “Dynamic correlations and hedging effectiveness between gold and stock markets: evidence for brics countries,” Research in International Business and Finance, vol. 38, pp. 22–34, 2016. View at: Google Scholar
  18. W. Mensi, B. Hkiri, K. H. Al-Yahyaee, and S. H. Kang, “Analyzing timecfrequency co-movements across gold and oil prices with brics stock markets: a var based on wavelet approach,” International Review of Economics & Finance, vol. 54, pp. 74–102, 2018. View at: Google Scholar
  19. G. J. Wang, C. Xie, D. Wen, and L. Zhao, “When bitcoin meets economic policy uncertainty (epu): measuring risk spillover effect from epu to bitcoin,” Finance Research Letters, vol. 31, 2019. View at: Google Scholar
  20. M. Qin, C. W. Su, and R. Tao, “Bitcoin: a new basket for eggs?” Economic Modelling, vol. 94, pp. 896–907, 2021. View at: Google Scholar
  21. T. Bollerslev, “Generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, vol. 31, pp. 307–327, 1986. View at: Google Scholar
  22. R. Liesenfeld and J. F. Richard, “Univariate and multivariate stochastic volatility models: estimation and diagnostics,” Journal of Empirical Finance, vol. 10, pp. 505–531, 2003. View at: Google Scholar
  23. D. Chun, H. Cho, and J. Kim, “Crude oil price shocks and hedging performance: a comparison of volatility models,” Energy Economics, vol. 81, pp. 1132–1147, 2019. View at: Google Scholar
  24. S. Kim, N. Shephard, and S. Chib, “Stochastic volatility: likelihood inference and comparison with arch models,” The Review of Economic Studies, vol. 65, pp. 361–393, 1998. View at: Google Scholar
  25. J. B. Liu and S. N. Daoud, 2019, Number of Spanning Trees in the Sequence of Some Graphs COMPLEXITY.
  26. H. Ghosh and B. Gurung, “Kalman filter-based modelling and forecasting of stochastic volatility with threshold,” Journal of Applied Statistics, vol. 42, pp. 492–507, 2015. View at: Google Scholar
  27. D. B. Nugroho and T. Morimoto, “Boxccox realized asymmetric stochastic volatility models with generalized student’s t-error distributions,” Journal of Applied Statistics, vol. 43, pp. 1906–1927, 2016. View at: Google Scholar
  28. S. Chib, F. Nardari, and N. Shephard, “Analysis of high dimensional multivariate stochastic volatility models,” Journal of Econometrics, vol. 134, pp. 341–371, 2006. View at: Google Scholar
  29. Y. Omori, S. Chib, N. Shephard, and J. Nakajima, “Stochastic volatility with leverage: fast and efficient likelihood inference,” Journal of Econometrics, vol. 140, pp. 425–449, 2007. View at: Google Scholar
  30. K. Jacobs and X. Li, “Modeling the dynamics of credit spreads with stochastic volatility,” Management Science, vol. 54, pp. 1176–1188, 2008. View at: Google Scholar
  31. J. Yu and R. Meyer, “Multivariate stochastic volatility models: bayesian estimation and model comparison,” Econometric Reviews, vol. 25, pp. 361–384, 2006. View at: Google Scholar
  32. R. S. Tsay, Analysis of Financial Time Series, John Wiley & Sons, Hoboken, New Jersey, USA, 2005.

Copyright © 2021 Jing Zhang and Qi-zhi He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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