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Gaussian copulas are widely used in the industry to correlate two randomvariables when there is no prior knowledge about the co-dependence betweenthem. The perturbed Gaussian copula approach allows introducing the skewinformation of both random variables into the co-dependence structure. Theanalytical expression of this copula is derived through an asymptotic expansionunder the assumption of a common fast mean reverting stochastic volatilityfactor. This paper applies this new perturbed copula to the valuation ofderivative products; in particular FX quanto options to a third currency. Acalibration procedure to fit the skew of both underlying securities ispresented. The action of the perturbed copula is interpreted compared to theGaussian copula. A real worked example is carried out comparing both copulasand a local volatility model with constant correlation for varying maturities,correlations and skew configurations.

Perturbed Copula: Introducing the skew effect in the co-dependence