Efficient estimation of extreme value-at-risks for standalone structural exchange rate risk

The standalone structural exchange rate risk depends on the product of the future foreign currency earning and the change in the exchange rate. Its Value-at-Risk (VaR) implying an extremely high survival probability, usually exceeding 99.9%, is used in practice to determine its economic capital. This paper proposes a new conditional method to calculate such extreme VaRs that is shown to be more efficient than the conventional method of directly simulating from the joint distribution of the future foreign currency earning and the change in the exchange rate. The intuition of the proposed method is that, conditional on either the future foreign currency earning or the change in the exchange rate, the distribution of the structural exchange rate risk is usually analytically tractable. The proposed method can be implemented by solving a nonlinear equation via a simple one-dimensional numerical integration and is generally applicable under the distributional assumptions commonly employed in practice.