CSA Caps Convexity Impact on Hull & White Calibration

Prices of CSA instruments are observed in a world which is not natural for LIBOR based payoffs in the sense that LIBOR forward is not martingale under CSA-forward measure. From a theoretical perspective, pricing models for collateralized LIBOR based payoffs should account for CSA-convexity, implied when changing from CSA-forward measure to LIBOR-forward measure. In practice CSA-convexity effect is neglected. In the present paper we show how modeling jointly OIS and LIBOR using one factor guassian short rate dynamics allows to capture CSA-convexity on caps and we measure its impact on LIBOR volatility calibration in the Hull & White case