| Abstract [eng] |
Modeling extreme price movements in the highly volatile crypto market is a major challenge for investors. This study builds a risk model specifically for Bitcoin and Ethereum using a GARCH-Survival BB1 copula combined with Expected Shortfall. While traditional models assume that prices move together the same way during good times and bad times (symmetric dependence), the approach focuses on asymmetric tail behaviour. Analytically, it captures the crash, coupling the fact that these assets tend to collapse together much faster during market downturns than they rise together during booms. The empirical results show a high lower tail dependence of 69.52% between BTC and ETH, which proves that they move together very strongly when the market crashes. Backtesting validates the model by showing high predictive accuracy, as the actual violations match what is expected at the 95% confidence level. At first, portfolio optimization using Expected Shortfall cut down risk by 22.45% in the crypto-only mix. To test how well this framework works, the study is extended to a 3D model by adding the S&P 500 index. This comparison shows that diversifying across different asset types lowers tail risk significantly, leading to a much better risk reduction of 29.66%. Testing the framework on raw data from 2025 confirms its validity, as the model shows stable performance outside the initial estimation period. Due to the capacity for frequent adjustment, the model remains flexible enough to handle changing market shifts throughout 2026 and the upcoming years. These results prove that factoring asymmetric tail dependence into a multi-asset allocation is necessary downside risk control in both digital and traditional financial markets. |
