Analyzing the Relationship among Stock Market, International Crude Oil Prices, and Bitcoin Prices Using the Copula Models

This paper analyzed the relationships among KOSPI, WTI, and BTC using a novel technique for estimating Copula models. The main findings can be summarized as follows: First, examining the correlation coefficients revealed a significant negative correlation between the KOSPI and WTI, while a significant positive correlation was observed between KOSPI and BTC. Second, in terms of the correlation structure between KOSPI and WTI, the t-Copula model showed the best fit, and a symmetric tail structure was identified in both markets. The Kendall’s tau correlation coefficient between KOSPI and WTI ranged from -0.189 to -0.263, indicating a strong negative correlation between the two markets. In terms of the correlation structure between KOSPI and BTC, the t-Copula model also showed the best fit, and a symmetric tail structure was identified in both markets. The Kendall’s tau correlation coefficient between KOSPI and BTC ranged from 0.051 to 0.112, indicating a weak correlation between the two markets. Third, based on the results of the t-Copula 3-dimensional density function, it was observed that the left tail (extreme decline) correlation was much smaller than the right tail (extreme increase) correlation in the tail dependency analysis for KOSPI, WTI, and BTC.