Hidden Dependence and Aggregate Tail Risk

Battle Count: 75

The paper is primarily relevant to risk management and regulatory capital rather than direct trading strategies. However, the findings about hidden dependence and tail risk underestimation are highly relevant for quantitative risk managers who need to assess portfolio tail risk, set capital buffers, and understand model risk in dependence assumptions. The results on VaR/TVaR underestimation (up to 1219% for VaR_0.999) are critical for risk-adjusted position sizing and stress testing in trading desks.

The theoretical framework requires advanced knowledge of copula theory, optimal transport (Wasserstein distances), measure-theoretic probability, and risk measure theory. The construction of hidden dependence structures and the proofs of main theorems (Theorems 10, 15, 16) are mathematically sophisticated. Practical implementation requires Monte Carlo simulation for numerical results and careful calibration of the ε-γ relationship. The credit risk application is more accessible but still requires understanding of structural models and copula-based dependence modeling.

The paper is primarily theoretical with rigorous mathematical proofs. Numerical results (Tables 1 and 2) are obtained via Monte Carlo simulation, but no code or simulation parameters are explicitly provided. The theoretical framework is fully self-contained with all definitions, lemmas, and proofs included. The asymptotic formula (20) from Vasicek (2002) is referenced for large portfolio calculations.