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The credit crisis and the ongoing European sovereign debt crisis havehighlighted the native form of credit risk, namely the counterparty risk. Therelated Credit Valuation Adjustment, (CVA), Debt Valuation Adjustment (DVA),Liquidity Valuation Adjustment (LVA) and Replacement Cost (RC) issues, jointlyreferred to in this paper as Total Valuation Adjustment (TVA), have beenthoroughly investigated in the theoretical papers [Cr12a] and [Cr12b]. Thepresent work provides an executive summary and numerical companion to thesepapers, through which the TVA pricing problem can be reduced to Markovianpre-default TVA BSDEs. The first step consists in the counterparty cleanvaluation of a portfolio of contracts, which is the valuation in a hypotheticalsituation where the two parties would be risk-free and funded at a risk-freerate. In the second step, the TVA is obtained as the value of an option on thecounterparty clean value process called Contingent Credit Default Swap (CCDS).Numerical results are presented for interest rate swaps in the Vasicek, as wellas in the inverse Gaussian Hull-White short rate model, also allowing one toassess the related model risk issue.

Counterparty Risk and Funding: The Four Wings of the TVA