Explainable Deep Learning for Financial Risk: Joint VaR and ES Forecasting Using ESRNN in the Bitcoin Market

The digitisation of financial systems has led to significant growth in complex, high-dimensional financial data, making forecasting models like autoregressive integrated moving averages (ARIMA) insufficient to address nonlinearities, volatility clustering, and extreme market behaviours. Recent financial shocks, especially those stemming from the COVID-19 pandemic, have emphasised the necessity of developing more precise and adaptable risk assessment tools. This study examines the issue of underestimating tail risks in volatile cryptocurrency markets, particularly the Bitcoin/USD exchange rate, where models such as generalised autoregressive conditional heteroscedasticity (GARCH) frequently fail to predict extreme losses accurately. To achieve this, we train, validate an exponentially smoothed recurrent neural network (ESRN) architecture that jointly predicts Value-at-Risk (VaR) and Expected Shortfall (ES). Our deep learning ESRNN architecture combines exponential smoothing with recurrent neural networks, allowing it to understand both short-term changes and long-term patterns in the Bitcoin/USD exchange rate. We validated our architecture using daily adjusted Bitcoin/USD closing prices from January 2, 2015 to April 28, 2025 across rolling forecasting horizons of 5, 10, 30, and 60 days. The findings demonstrate that the 30-day forecasting horizon achieves optimal performance, evidenced by the lowest prediction errors (MSE = 0.0006868, RMSE = 0.026207). At the 99% confidence level, the ESRNN predicts losses of 1.3315% (Expected Shortfall) and 1.238% (Value at Risk); at the 95% level, the anticipated losses are 1.128% and 0.944%, respectively. The findings indicate that the ESRNN yields dependable and precise risk estimates in high-volatility markets. Its application is recommended for real-time risk monitoring systems in cryptocurrencies, with suggestions for future enhancements to incorporate intraday data and cross-asset risk modelling.