The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization as well as the associated CVA. We have presented approximate expressions for various cases using 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 the practical 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 .  We have also discussed some generic implications of asymmetric collateralization for netting and resolution of information .
The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the associated counter party credit risk. By introducing the collateral coverage ratio, our framework can handle these issues in an unified manner. Although the resultant pricing formula becomes non-linear FBSDE and cannot be solve exactly, the fist order approximation is provided using Gateaux derivative . We have shown that it allows us to decompose the price of generic contract into three parts: market benchmark, bilateral credit value adjustment (CVA), and the collateral cost adjustment (CCA) independent from the credit risk. We have studied each term closely, and demonstrated the significant impact of asymmetric collateralization through CCA using the numerical examples .
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as well as the associated CVA. We have presented approximate expressions for various cases
with the associated counter party credit risk. By introducing the collateral coverage ratio, our framework can handle these issues in an unified manner. Although the resultant pricing formula becomes non-linear FBSDE and cannot be solve exactly, the fist order approximation is provided
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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 the practical 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
A
We have shown that it allows us to decompose the price of generic contract into three parts: market benchmark, bilateral credit value adjustment (CVA), and the collateral cost adjustment (CCA) independent from the credit risk.
R
also discussed some generic implications
studied each term closely, and demonstrated the significant impact
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for netting and resolution of information
through CCA using the numerical examples