Tail-GAN: Learning to Simulate Tail Risk Scenarios

The estimation of loss distributions for dynamic portfolios requires the simulation of scenarios representing realistic joint dynamics of their components, with particular importance devoted to the simulation of tail risk scenarios. We propose a novel data-driven approach that utilizes Generative Adversarial Network (GAN) architecture and exploits the joint elicitability property of Value-at-Risk (VaR) and Expected Shortfall (ES). Our proposed approach is capable of learning to simulate price scenarios that preserve tail risk features for benchmark trading strategies, including consistent statistics such as VaR and ES. We prove a universal approximation theorem for our generator for a broad class of risk measures. In addition, we show that the training of the GAN may be formulated as a max-min game, leading to a more effective approach for training. Our numerical experiments show that, in contrast to other data-driven scenario generators, our proposed scenario simulation method correctly captures tail risk for both static and dynamic portfolios.
Comment: 39 pages, 17 figures, 11 tables. An earlier version of this paper circulated under the title "TailGAN: Nonparametric Scenario Generation for Tail Risk Estimation". First draft: March 2022