Quantos and FX Skew

Abstract

We study the impact of the FX skew on quanto convexity adjustments. Using a double shifted lognormal model allows an easy calibration to the skews as well as expressing the FX skew impact analytically for quanto forwards. We conclude that under non stressed market conditions (σ^2 T≪1) the impact is negligible for short maturities and still not material for longer maturities compared to correlation risk. However, under stressed market conditions or if quanto products become liquid enough to provide market implied correlation, we would switch from a mark-to-model with uncertain correlation to a mark-to-market with implied correlation. In this situation we will need to incorporate the FX skew. In a second study, we emphasis the drawbacks of modelling FX with shifted-lognormals and as an alternative we introduce the double mixture of lognormals model as the easiest model compatible with the flat lognormal quanto adjustment formula.

Keywords: quanto, double shifted-lognormal model, FX skew, convexity adjustments, correlation uncertainty, double mixture of lognormals