Abstract
In this talk, we address the problem of pricing credit derivatives with counterparty credit risk and funding costs. We derive a master funding equation that includes CVA, DVA, FVA and FVO. We prove a Fundamental Invariance Principle for Funding and CVA in the general setting of enlarged credit filtrations. And We show that if all the funding accrual terms originating from the three legs of the transaction (namely, ISDA, CSA, and Treasury Funding) are included, then we can discount with any short-rate that we choose. This is a generalised version of the result derived in Piterbarg (2010). We then compare the FVA term that appears on the desk balance sheet with the FAS157 FVO DVA (Fair Value Option) that appears on the Treasury balance sheet. We show that when we account for the FVO DVA, the FVA doesn’t vanish as claimed in Hull and White (2012): FVO DVA simply marks the bonds back to market and defines the correct funding rate to charge the desk through the FTP (Funds Transfer Pricing) Mechanism. We also present some interesting applications to Credit Default Swap contracts.
[PDF] Slides of the presentation.