Does copula choice matter for FX tail risk hedging?

Abstract

Among the eight representative specifications considered, the choice of copula in foreign exchange (FX) tail-risk hedging involves a trade-off: symmetric copulas such as the Student-t may be misspecified when tail dependence is asymmetric, but flexible asymmetric copulas add parameters estimated from finite samples. Within a unified rolling Copula–GARCH–EVT framework estimated on every trading day, this letter compares eight copulas for hedging EUR/USD spot exposure with GBP/USD over 2005–2025. It estimates minimum-variance, minimum-expected-shortfall, and minimum-VaR hedge ratios, correcting the copula-implied correlation through the fitted marginal distributions. For minimum-variance hedging, Student-t delivers the largest variance reduction (41.1%), and a superior predictive ability test finds that no alternative copula outperforms it. For the minimum-ES objective, Gaussian, Frank, and BB1 achieve expected-shortfall reductions slightly above Student-t (25.0%, 25.0%, and 24.8% versus 24.4%), and on the benchmark-defined 5% worst days their average hedged losses are significantly lower though economically small. Copula choice therefore has an economically modest effect on both variance and tail-risk hedging, and the parsimonious Student-t copula remains a defensible default.