Bitcoin, Gold, and Stock Market Volatility Including COVID-19 Periods: Comparative Analysis Using GARCH and DCC-MGARCH Models

This study investigates the volatility dynamics and time-varying correlations between Bitcoin (BTC) and major financial markets, including gold, oil, NASDAQ, NIKKEI, FTSE, DAX, and the USD Index. Using daily data and GARCH-family models, we quantify persistence, asymmetry, and memory in BTC volatility. The EGARCH model was identified as the most suitable for capturing conditional variance. A DCC-MGARCH framework was then employed to estimate evolving cross-market correlations. Results indicate that BTC volatility is highly persistent with strong reactions to negative shocks. Gold displays the lowest persistence, confirming its role as a stable diversifier. DCC-MGARCH estimates reveal weak positive BTC-Gold correlations and negative BTC-USDINX correlations, implying significant diversification potential. Notably, BTC-NIKKEI and BTC-Gold correlations strengthened during the COVID-19 period. These findings underscore the importance of dynamic portfolio strategies, as optimal weights shift with evolving conditional covariances, rendering static allocations suboptimal. For policymakers, these results can inform leverage and exposure limits, particularly when linkages between BTC and traditional assets intensify.. © 2025 Universidad Catolica de Colombia. All rights reserved.