Efficient Nested Estimation of CoVaR: A Decoupled Approach

Faster CoVaR Estimation via a Decoupled Approach CoVaR is a widely used measure of systemic financial risk, capturing the risk of a portfolio conditional on another portfolio being under distress. In the paper “Efficient Nested Estimation of CoVaR: A Decoupled Approach,” Nifei Lin, Yingda Song, and L. Jeff Hong address two central challenges in CoVaR estimation: The conditioning event has zero probability, and portfolio losses often require costly simulation-based repricing. Their key insight is that, in nested simulation, the computational cost of outer simulations is negligible compared with that of inner simulations. The proposed approach decouples the nested estimation task by first learning approximations of portfolio loss functions using smoothing techniques and then evaluating the learned functions over a large outer-level sample to handle the zero-probability event. The framework is plug-and-play: Different smoothing techniques can be incorporated, and when their [Formula: see text]approximation rates are available, the paper’s theory directly yields the convergence rate of the resulting CoVaR estimator. The authors also establish smoothness of portfolio loss functions, a key foundation for efficient learning. Under suitable conditions, the estimator achieves the favorable near-square-root convergence rate [Formula: see text], where [Formula: see text]is the inner-level simulation budget.