Horizon-Adaptive Extreme Risk Quantification for Cryptocurrency Assets

Risk quantification for cryptocurrency assets is a challenging task due to their speculative nature and strongly heavy-tailed returns. Existing measures of tail risk are based primarily on the variability of extreme returns, whilst ignoring the multiple biases occurring at distinct frequencies other than the original sampling frequency. As such, they often fail to adapt to specific investment horizons and also account for the inherent microstructure frictions of cryptocurrency returns. To address this problem, we propose a novel extreme risk measure which (i) regularizes the variability of extreme returns with a confidence interval where they have a likelihood of occurring, and (ii) adapts precisely to a predefined investment horizon. To this end, we leverage the power of alpha-stable models for defining a proper confidence interval with the effectiveness of wavelet analysis for decomposing the returns at multiple frequencies. An empirical evaluation with major cryptocurrencies demonstrates improved performance of our extreme risk measure against commonly used measures based on extreme expectiles and light-tailed models.