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Modeling of the Bitcoin Volatility through Key Financial Environment Variables: An Application of Conditional Correlation MGARCH Models

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  • Ángeles Cebrián-Hernández

    (Department of Applied Economics, Universidad de Sevilla, 41018 Seville, Spain)

  • Enrique Jiménez-Rodríguez

    (Department of Financial Economics and Accounting, Universidad Pablo de Olavide, 41013 Seville, Spain)

Abstract

Since the launch of Bitcoin, there has been a lot of controversy surrounding what asset class it is. Several authors recognize the potential of cryptocurrencies but also certain deviations with respect to the functions of a conventional currency. Instead, Bitcoin’s diversifying factor and its high return potential have generated the attention of portfolio managers. In this context, understanding how its volatility is explained is a critical element of investor decision-making. By modeling the volatility of classic assets, nonlinear models such as Generalized Autoregressive Conditional Heteroskedasticity (GARCH) offer suitable results. Therefore, taking GARCH(1,1) as a reference point, the main aim of this study is to model and assess the relationship between the Bitcoin volatility and key financial environment variables through a Conditional Correlation (CC) Multivariate GARCH (MGARCH) approach. For this, several commodities, exchange rates, stock market indices, and company stocks linked to cryptocurrencies have been tested. The results obtained show certain heterogeneity in the fit of the different variables, highlighting the uncorrelation with respect to traditional safe haven assets such as gold and oil. Focusing on the CC-MGARCH model, a better behavior of the dynamic conditional correlation is found compared to the constant.

Suggested Citation

  • Ángeles Cebrián-Hernández & Enrique Jiménez-Rodríguez, 2021. "Modeling of the Bitcoin Volatility through Key Financial Environment Variables: An Application of Conditional Correlation MGARCH Models," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:267-:d:489289
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    References listed on IDEAS

    as
    1. Tiwari, Aviral Kumar & Jana, R.K. & Das, Debojyoti & Roubaud, David, 2018. "Informational efficiency of Bitcoin—An extension," Economics Letters, Elsevier, vol. 163(C), pages 106-109.
    2. Cheah, Eng-Tuck & Mishra, Tapas & Parhi, Mamata & Zhang, Zhuang, 2018. "Long Memory Interdependency and Inefficiency in Bitcoin Markets," Economics Letters, Elsevier, vol. 167(C), pages 18-25.
    3. Baur, Dirk G. & McDermott, Thomas K., 2010. "Is gold a safe haven? International evidence," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1886-1898, August.
    4. Marie Briere & Kim Oosterlinck & Ariane Szafarz, 2015. "Virtual Currency, Tangible Return: Portfolio Diversification with Bitcoins," Post-Print CEB, ULB -- Universite Libre de Bruxelles, vol. 16(6), pages 365-373.
    5. Selgin, George, 2015. "Synthetic commodity money," Journal of Financial Stability, Elsevier, vol. 17(C), pages 92-99.
    6. Hui, Cho-Hoi & Lo, Chi-Fai & Chau, Po-Hon & Wong, Andrew, 2020. "Does Bitcoin behave as a currency?: A standard monetary model approach," International Review of Financial Analysis, Elsevier, vol. 70(C).
    7. Nan, Zheng & Kaizoji, Taisei, 2019. "Market efficiency of the bitcoin exchange rate: Weak and semi-strong form tests with the spot, futures and forward foreign exchange rates," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 273-281.
    8. Dirk G. Baur & Brian M. Lucey, 2010. "Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold," The Financial Review, Eastern Finance Association, vol. 45(2), pages 217-229, May.
    9. Selmi, Refk & Mensi, Walid & Hammoudeh, Shawkat & Bouoiyour, Jamal, 2018. "Is Bitcoin a hedge, a safe haven or a diversifier for oil price movements? A comparison with gold," Energy Economics, Elsevier, vol. 74(C), pages 787-801.
    10. Gardebroek, Cornelis & Hernandez, Manuel A., 2013. "Do energy prices stimulate food price volatility? Examining volatility transmission between US oil, ethanol and corn markets," Energy Economics, Elsevier, vol. 40(C), pages 119-129.
    11. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    12. Bouri, Elie & Gupta, Rangan & Tiwari, Aviral Kumar & Roubaud, David, 2017. "Does Bitcoin hedge global uncertainty? Evidence from wavelet-based quantile-in-quantile regressions," Finance Research Letters, Elsevier, vol. 23(C), pages 87-95.
    13. Hung, Jui-Cheng & Liu, Hung-Chun & Yang, J. Jimmy, 2020. "Improving the realized GARCH’s volatility forecast for Bitcoin with jump-robust estimators," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    14. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    15. Gao, Chun-Ting & Zhou, Xiao-Hua, 2016. "Forecasting VaR and ES using dynamic conditional score models and skew Student distribution," Economic Modelling, Elsevier, vol. 53(C), pages 216-223.
    16. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    17. Lanza, Alessandro & Manera, Matteo & McAleer, Michael, 2006. "Modeling dynamic conditional correlations in WTI oil forward and futures returns," Finance Research Letters, Elsevier, vol. 3(2), pages 114-132, June.
    18. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    19. Urquhart, Andrew, 2016. "The inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 148(C), pages 80-82.
    20. Bariviera, Aurelio F., 2017. "The inefficiency of Bitcoin revisited: A dynamic approach," Economics Letters, Elsevier, vol. 161(C), pages 1-4.
    21. Luther, William J. & Salter, Alexander W., 2017. "Bitcoin and the bailout," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 50-56.
    22. Kristoufek, Ladislav, 2018. "On Bitcoin markets (in)efficiency and its evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 257-262.
    23. Urquhart, Andrew & Zhang, Hanxiong, 2019. "Is Bitcoin a hedge or safe haven for currencies? An intraday analysis," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 49-57.
    24. Hussain Shahzad, Syed Jawad & Bouri, Elie & Roubaud, David & Kristoufek, Ladislav, 2020. "Safe haven, hedge and diversification for G7 stock markets: Gold versus bitcoin," Economic Modelling, Elsevier, vol. 87(C), pages 212-224.
    25. Garcia-Jorcano, Laura & Benito, Sonia, 2020. "Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying," Research in International Business and Finance, Elsevier, vol. 54(C).
    26. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    27. Smales, L.A., 2019. "Bitcoin as a safe haven: Is it even worth considering?," Finance Research Letters, Elsevier, vol. 30(C), pages 385-393.
    28. Bouri, Elie & Molnár, Peter & Azzi, Georges & Roubaud, David & Hagfors, Lars Ivar, 2017. "On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier?," Finance Research Letters, Elsevier, vol. 20(C), pages 192-198.
    29. Guesmi, Khaled & Saadi, Samir & Abid, Ilyes & Ftiti, Zied, 2019. "Portfolio diversification with virtual currency: Evidence from bitcoin," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 431-437.
    30. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
    31. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    32. Yu, Miao, 2019. "Forecasting Bitcoin volatility: The role of leverage effect and uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    33. Ardia, David & Bluteau, Keven & Rüede, Maxime, 2019. "Regime changes in Bitcoin GARCH volatility dynamics," Finance Research Letters, Elsevier, vol. 29(C), pages 266-271.
    34. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    35. Balcilar, Mehmet & Bouri, Elie & Gupta, Rangan & Roubaud, David, 2017. "Can volume predict Bitcoin returns and volatility? A quantiles-based approach," Economic Modelling, Elsevier, vol. 64(C), pages 74-81.
    36. White, Reilly & Marinakis, Yorgos & Islam, Nazrul & Walsh, Steven, 2020. "Is Bitcoin a currency, a technology-based product, or something else?," Technological Forecasting and Social Change, Elsevier, vol. 151(C).
    37. Kumar, Anoop S. & Anandarao, S., 2019. "Volatility spillover in crypto-currency markets: Some evidences from GARCH and wavelet analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 448-458.
    38. Nadarajah, Saralees & Chu, Jeffrey, 2017. "On the inefficiency of Bitcoin," Economics Letters, Elsevier, vol. 150(C), pages 6-9.
    39. Brauneis, Alexander & Mestel, Roland, 2018. "Price discovery of cryptocurrencies: Bitcoin and beyond," Economics Letters, Elsevier, vol. 165(C), pages 58-61.
    40. Jesús Fernández-Villaverde & Daniel R. Sanches, 2018. "On the Economics of Digital Currencies," Working Papers 18-7, Federal Reserve Bank of Philadelphia.
    41. Hazlett, Peter K. & Luther, William J., 2020. "Is bitcoin money? And what that means," The Quarterly Review of Economics and Finance, Elsevier, vol. 77(C), pages 144-149.
    42. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    43. Katsiampa, Paraskevi, 2017. "Volatility estimation for Bitcoin: A comparison of GARCH models," Economics Letters, Elsevier, vol. 158(C), pages 3-6.
    44. Elie Bouri & Naji Jalkh & Peter Molnár & David Roubaud, 2017. "Bitcoin for energy commodities before and after the December 2013 crash: diversifier, hedge or safe haven?," Applied Economics, Taylor & Francis Journals, vol. 49(50), pages 5063-5073, October.
    45. Beat Weber, 2016. "Bitcoin and the legitimacy crisis of money," Cambridge Journal of Economics, Oxford University Press, vol. 40(1), pages 17-41.
    46. Conlon, Thomas & Corbet, Shaen & McGee, Richard J., 2020. "Are cryptocurrencies a safe haven for equity markets? An international perspective from the COVID-19 pandemic," Research in International Business and Finance, Elsevier, vol. 54(C).
    47. Gronwald, Marc, 2019. "Is Bitcoin a Commodity? On price jumps, demand shocks, and certainty of supply," Journal of International Money and Finance, Elsevier, vol. 97(C), pages 86-92.
    48. C. Baek & M. Elbeck, 2015. "Bitcoins as an investment or speculative vehicle? A first look," Applied Economics Letters, Taylor & Francis Journals, vol. 22(1), pages 30-34, January.
    49. Jarjour, Riad & Chan, Kung-Sik, 2020. "Dynamic conditional angular correlation," Journal of Econometrics, Elsevier, vol. 216(1), pages 137-150.
    50. Dyhrberg, Anne Haubo, 2016. "Hedging capabilities of bitcoin. Is it the virtual gold?," Finance Research Letters, Elsevier, vol. 16(C), pages 139-144.
    51. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    52. Koutmos, Dimitrios, 2018. "Liquidity uncertainty and Bitcoin’s market microstructure," Economics Letters, Elsevier, vol. 172(C), pages 97-101.
    53. Baur, Dirk G. & Hong, KiHoon & Lee, Adrian D., 2018. "Bitcoin: Medium of exchange or speculative assets?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 54(C), pages 177-189.
    54. Dyhrberg, Anne H. & Foley, Sean & Svec, Jiri, 2018. "How investible is Bitcoin? Analyzing the liquidity and transaction costs of Bitcoin markets," Economics Letters, Elsevier, vol. 171(C), pages 140-143.
    55. Chan, Wing Hong & Le, Minh & Wu, Yan Wendy, 2019. "Holding Bitcoin longer: The dynamic hedging abilities of Bitcoin," The Quarterly Review of Economics and Finance, Elsevier, vol. 71(C), pages 107-113.
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