Derivative Pricing with Two Collateral Rates

This note analyses derivative pricing in the context of a collateral rate switch during the life of a financial product or the existence of two overnight rates. In particular we analyse the impact of forward change of collateral, the impact on OISs when the collateral rate is different from the OIS underlying, and the impact of bilateral swaptions collateral rate different from the one implied by the cleared market. In each case, we evidence new convexity adjustment impacts previously not accounted for. The order of magnitude of those impacts is also proposed for realistic values of model parameters; the individual relative impacts are not huge, but when applied on trillions of notional, as it is the case, the monetary impacts can be substantial.