Multi-Curve Framework with Collateral

This note is dedicated to the impact of collateral on the multi-curve framework. The pricing formulas in presence of collateral are described in a generic way encompassing several financial realities. The collateral cases covered include cash collateral, foreign currency collateral, collateral by assets (collateral square) and collateral with haircut. The change of collateral is also described, including the convexity adjustment required. The pricing of STIR futures in this framework is analysed in detail