On the relationship of cryptocurrency price with us stock and gold price using copula models

Jong Min Kim, Seong Tae Kim, Sangjin Kim

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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.

Original languageEnglish (US)
Article number1859
Pages (from-to)1-15
Number of pages15
Issue number11
StatePublished - Nov 2020

Bibliographical note

Publisher Copyright:
© 2020 by the authors. Licensee MDPI, Basel, Switzerland.


  • Copula
  • Cryptocurrency
  • DCC
  • Gold
  • S&P 500


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