Abstracts

We present a unified model for a generalised bilateral CVA with funding and collateral costs derived using semi-replication. The model is generalised in two ways. First it is formulated in terms of general boundary conditions that include, amongst others, bilateral close-outs with one-way and two-way CSAs, extinguishers and set-offs. Second it makes only weak assumptions on the own bonds available to the issuer and how these bonds can be traded, and we prove that any valuation adjustment that includes counterparty risk, funding and collateral is given by the classical (generalised) bilateral CVA plus a funding cost adjustment. This term is shown to be equal to the expected value of the issuer hedge error at own default. This proves that each issuer bond / strategy combination has it unique set of economic valuation adjustment formulas, resulting in non-symmetric prices.
We also show how funding aware close-outs can be incorporated into the framework and discuss the impact of derivative assets and funding liabilities on the balance sheet of the derivative issuer and theoretical and practical effects thereof.
Finally we present three concrete models with different assumptions on issuer bonds and trading strategies and give their specific CVA, DVA, FCA, FVA and collateral adjustments. We show that under certain assumptions set-off close-outs result in vanishing funding cost adjustments and symmetric prices. The models are illustrated by practical examples.