Learning about tail risk: Machine learning and combination with regularization in market risk management

High-quality risk management is the key to ensuring the safe, efficient, and stable operation of the financial system. The current Basel Accord requires financial institutions to regularly calculate and disclose Value at Risk (VaR) and Expected Shortfall (ES) measures. However, the inaccuracy and instability of traditional risk models have reduced users' confidence. Therefore, we propose two new probabilistic deep learning frameworks for estimating VaR and ES. The trained first framework can output expectiles that are more sensitive to tail risks to map VaR and ES measures. In the second framework, we propose to approximate VaR and ES measures with spline quantile function and estimate the parameters by designing various deep learning architectures. To ensure the effectiveness of the proposed architectures, we derived the training loss and constraints for them. In addition, we solve the problem that existing machine learning risk models are difficult to estimate ES. In this way, combining various individual risk models has great potential for risk management. Therefore, we propose a regularization-based combination framework that adaptively selects and shrinks individual risk models. The developed individual methods and combinations outperform existing methods in backtesting, assisting financial institutions to allocate capital more effectively according to the Basel Capital Accord.