The rise of cryptocurrencies, led by Bitcoin, has transformed the financial landscape. In this paper the volatility characteristics of cryptocurrencies are studied and their relation to traditional financial assets is explored. The study investigates the volatility of four major cryptocurrencies—Bitcoin, Ethereum, Cardano, and Litecoin—over three distinct time periods using various GARCH-type models, including EGARCH, TGARCH, and IGARCH. Additionally, using Dynamic Conditional Correlation (DCC) GARCH models, the study explores the relationships of these cryptocurrencies with eight traditional financial indices and commodities, namely Gold, Brent Oil, Gas, Economic Policy Uncertainty (EPU), Standard’s and Poor’s 500 (S&P 500), Nasdaq, VIX and EuroStoxx 50. The best-fitting models are determined using the Akaike Information Criterion, the Bayesian Information Criterion, and the Hannan-Quinn Criterion as these are considered by the literature as the appropriate criteria. The results show that IGARCH frequently provides the best fit for cryptocurrency data, highlighting thus the impact of new information on variance. Furthermore, significant long-term correlations are revealed, between certain cryptocurrencies and traditional financial assets, suggesting potential hedging opportunities. The practical implications of our findings extend to portfolio managers and investors, who can use our results to plan a strategy to mitigate their risk exposure. The significance of this study lies in its potential to provide valuable insights for investors and policymakers by identifying the most suitable models for analyzing cryptocurrency volatility under different market conditions.