Synergizing Wasserstein GANs with Constrained Schrödinger Bridges for Improved Market Risk Estimation

Abstract

This paper introduces a novel approach to market risk estimation by combining Wasserstein Generative Adversarial Networks (WGANs) with constrained Schrödinger bridges. Our framework better captures the joint distribution between portfolio components while maintaining the martingale property essential for financial time series. We incorporate financial constraints into the generation process to ensure that generated scenarios respect key properties such as the martingale condition and stylized facts of financial returns. Our comprehensive analysis of regularization techniques demonstrates that entropic regularization provides the optimal balance between model flexibility and generalization, preventing overfitting while preserving the diversity of generated scenarios. Through rigorous backtesting, we show that our approach significantly improves Value-at-Risk (VaR) and Expected Shortfall (ES) estimation across different market conditions, particularly during stress periods. The regulatory capital implications reveal that our model can help reduce capital requirements while maintaining or improving risk coverage, aligning well with current frameworks including Basel III and Solvency II.