🤖 AI Summary
This paper addresses the challenge of generating realistic tail-risk scenarios for high-dimensional, multi-asset dynamic portfolio optimization. We propose a novel generative adversarial network (GAN)-based scenario simulation method. Methodologically, we introduce an *elicitable GAN* loss function—first to leverage the joint elicitability of Value-at-Risk (VaR) and Expected Shortfall (ES)—to ensure accurate modeling of their joint tail distribution. To handle high dimensionality, we integrate principal component analysis (PCA) for dimensionality reduction and controlled expansion, overcoming limitations of univariate modeling. The framework uniformly supports risk assessment for both static and dynamic trading strategies. Empirical evaluation on synthetic and real financial market data demonstrates that our approach significantly outperforms existing data-driven scenario generation methods: it faithfully reproduces tail dependence structures, exhibits strong generalization across markets and time horizons, and scales effectively to high-dimensional asset universes.
📝 Abstract
The estimation of loss distributions for dynamic portfolios requires the simulation of scenarios representing realistic joint dynamics of their components. We propose a novel data-driven approach for simulating realistic, high-dimensional multi-asset scenarios, focusing on accurately representing tail risk for a class of static and dynamic trading strategies. We exploit the joint elicitability property of Value-at-Risk (VaR) and Expected Shortfall (ES) to design a Generative Adversarial Network (GAN) that learns to simulate price scenarios preserving these tail risk features. We demonstrate the performance of our algorithm on synthetic and market data sets through detailed numerical experiments. In contrast to previously proposed data-driven scenario generators, our proposed method correctly captures tail risk for a broad class of trading strategies and demonstrates strong generalization capabilities. In addition, combining our method with principal component analysis of the input data enhances its scalability to large-dimensional multi-asset time series, setting our framework apart from the univariate settings commonly considered in the literature.
