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The importance of collateralization through the change of funding cost is nowwell recognized among practitioners. In this article, we have extended theprevious studies of collateralized derivative pricing to more genericsituation, that is asymmetric and imperfect collateralization as well as theassociated CVA. We have presented approximate expressions for various casesusing Gateaux derivative which allow straightforward numerical analysis.Numerical examples for CCS (cross currency swap) and IRS(interest rate swap)with asymmetric collateralization were also provided. They clearly show thepractical relevance of sophisticated collateral management for financial firms.The valuation and the associated issue of collateral cost under the one-way CSA(or unilateral collateralization), which is common when SSA (sovereign,supranational and agency) entities are involved, have been also studied. Wehave also discussed some generic implications of asymmetric collateralizationfor netting and resolution of information.

Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA