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Article

On the Relationship of Cryptocurrency Price with US Stock and Gold Price Using Copula Models

1
Statistics Discipline, University of Minnesota at Morris, Morris, MN 56267, USA
2
Department of Mathematics, North Carolina A&T State University, Greensboro, NC 27411, USA
3
Department of Management and Information Systems, Dong-A University, Busan 49236, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1859; https://doi.org/10.3390/math8111859
Submission received: 15 September 2020 / Revised: 19 October 2020 / Accepted: 20 October 2020 / Published: 23 October 2020
(This article belongs to the Special Issue Quantitative Methods for Economics and Finance)

Abstract

This paper examines the relationship of the leading financial assets, Bitcoin, Gold, and S&P 500 with GARCH-Dynamic Conditional Correlation (DCC), Nonlinear Asymmetric GARCH DCC (NA-DCC), Gaussian copula-based GARCH-DCC (GC-DCC), and Gaussian copula-based Nonlinear Asymmetric-DCC (GCNA-DCC). Under the high volatility financial situation such as the COVID-19 pandemic occurrence, there exist a computation difficulty to use the traditional DCC method to the selected cryptocurrencies. To solve this limitation, GC-DCC and GCNA-DCC are applied to investigate the time-varying relationship among Bitcoin, Gold, and S&P 500. In terms of log-likelihood, we show that GC-DCC and GCNA-DCC are better models than DCC and NA-DCC to show relationship of Bitcoin with Gold and S&P 500. We also consider the relationships among time-varying conditional correlation with Bitcoin volatility, and S&P 500 volatility by a Gaussian Copula Marginal Regression (GCMR) model. The empirical findings show that S&P 500 and Gold price are statistically significant to Bitcoin in terms of log-return and volatility.
Keywords: cryptocurrency; gold; S& P 500; GARCH; DCC; copula cryptocurrency; gold; S& P 500; GARCH; DCC; copula

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MDPI and ACS Style

Kim, J.-M.; Kim, S.-T.; Kim, S. On the Relationship of Cryptocurrency Price with US Stock and Gold Price Using Copula Models. Mathematics 2020, 8, 1859. https://doi.org/10.3390/math8111859

AMA Style

Kim J-M, Kim S-T, Kim S. On the Relationship of Cryptocurrency Price with US Stock and Gold Price Using Copula Models. Mathematics. 2020; 8(11):1859. https://doi.org/10.3390/math8111859

Chicago/Turabian Style

Kim, Jong-Min, Seong-Tae Kim, and Sangjin Kim. 2020. "On the Relationship of Cryptocurrency Price with US Stock and Gold Price Using Copula Models" Mathematics 8, no. 11: 1859. https://doi.org/10.3390/math8111859

APA Style

Kim, J.-M., Kim, S.-T., & Kim, S. (2020). On the Relationship of Cryptocurrency Price with US Stock and Gold Price Using Copula Models. Mathematics, 8(11), 1859. https://doi.org/10.3390/math8111859

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