Interest rate modeling under multiple discounting curves

For deals denominated in a single currency, different collateralization schemes imply different accrual rates for funds posted as collateral, so that we can end up with different current accounts that accrue at different rates and their corresponding discount factors. In this paper we examine how to incorporate this multiple discounting curves environment in a pricing framework, presenting the different numeraires available and examining how the change of measure works when the corresponding numeraires are associated with different collateralization schemes. The simulation of a stochastic funding curve will also be tackled. We will assume Heath Jarrow Morton dynamics for the different discounting curves and will obtain the drift restrictions on those curves under different numeraires. Finally, we will analyze the best strategy to incorporate this multiple discounting curves framework for each single currency in a multi currency setting where different transactions following different collateral schemes are simultaneously modeled, such as a CVA pricing engine