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In this paper we describe how to include funding and margining costs into arisk-neutral pricing framework for counterparty credit risk. We considerrealistic settings and we include in our models the common market practicessuggested by the ISDA documentation without assuming restrictive constraints onmargining procedures and close-out netting rules. In particular, we allow forasymmetric collateral and funding rates, and exogenous liquidity policies andhedging strategies. Re-hypothecation liquidity risk and close-out amountevaluation issues are also covered. We define a comprehensive pricing frameworkwhich allows us to derive earlier results on funding or counterparty risk. Somerelevant examples illustrate the non trivial settings needed to derive knownfacts about discounting curves by starting from a general framework and withoutresorting to ad hoc hypotheses. Our main result is a bilateral collateralizedcounterparty valuation adjusted pricing equation, which allows to price a dealwhile taking into account credit and debt valuation adjustments along withmargining and funding costs in a coherent way. We find that the equation has arecursive form, making the introduction of an additive funding valuationadjustment difficult. Yet, we can cast the pricing equation into a set ofiterative relationships which can be solved by means of standard least-squareMonte Carlo techniques.

Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation