This study investigates the cryptocurrency market using novel multivariate risk measures based on optimal transport theory to estimate Vectors-at-Risk and Conditional-Vectors-at-Risk (Expected Shortfall). We compare the results obtained from this method with those from commonly used univariate methods for estimating Value-at-Risk and Conditional Value-at-Risk (Expected Shortfall), considering factors such as magnitude, computational time, and backtesting results. Our findings reveal that while the estimates derived from this novel approach entail significantly higher computational costs, they incorporate the correlation structure of risks among assets and and are more conservative than the usual tail risk estimation methods.
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