Intraday Value at Risk Estimation with Multivariate Intensity Models : An Application to Cryptocurrencies

We implement multivariate, self-exciting Peaks-over-Threshold (POT) methods to measure extremal losses in high-frequency return series of cryptocurrencies. For that purpose, we implement trivariate Hawkes-POT and the autoregressive conditional intensity ACI-POT models for Bitcoin, Ethereum, and Litecoin. By treating the intensity of the arrival of extremal events as nonconstant, we successfully capture significant excitations within and across the cryptocurrencies and thus model the clustering behavior of extremal losses. Further, we backtest the intraday VaR computation performance of both models, and observe the best performance for the ACI-POT model as well as for the most extremal risk forecast, such as 99.9 % VaR