<p>This study examines the cryptocurrency market by introducing novel multivariate risk measures rooted in optimal transport theory to estimate Vectors-at-Risk (VaR) and Conditional Vectors-at-Risk (CVaR). We compare these measures against traditional univariate and copula-based methods for estimating Value-at-Risk and Conditional Value-at-Risk, focusing on factors such as magnitude, computational efficiency, and backtesting performance. The findings reveal that, while the proposed method incurs significantly higher computational costs, it effectively captures the correlation structure among assets’ risks, resulting in more conservative tail risk estimates compared to conventional techniques. As financial markets continue to evolve, the implications of adopting advanced tail risk measures such as those based on Optimal Coupling will be crucial for maintaining financial stability and mitigating systemic risk. Therefore, we believe that this study can be very useful in the context of regulatory frameworks, economic stability, risk management, and portfolio selection.</p>