Forecasting VaR and ES by using deep quantile regression, GANs-based scenario generation, and heterogeneous market hypothesis

Abstract

Abstract Value at risk (VaR) and expected shortfall (ES) have emerged as standard measures for detecting the market risk of financial assets and play essential roles in investment decisions, external regulations, and risk capital allocation. However, existing VaR estimation approaches fail to accurately reflect downside risks, and the ES estimation technique is quite limited owing to its challenging implementation. This causes financial institutions to overestimate or underestimate investment risk and finally leads to the inefficient allocation of financial resources. The main purpose of this study is to use machine learning to improve the accuracy of VaR estimation and provide an effective tool for ES estimation. Specifically, this study proposes a VaR estimator by combining quantile regression with “Mogrifier” recurrent neural networks to capture the “long memory” and “clustering” properties of financial assets; while for estimating ES, this study directly models the quantile of assets and employs generative adversarial networks to generate future tail risk scenarios. In addition to the typical properties of financial assets, the model design is also consistent with heterogeneous market theory. An empirical application to four major global stock indices shows that our model is superior to other existing models.

Keywords

• Value at risk
• Expected shortfall
• Quantile regression
• Recurrent neural networks
• Generative adversarial networks