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Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA

by Masaaki Fujii of the University of Tokyo, and
Akihiko Takahashi of the University of Tokyo

March 31, 2011

Abstract: 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.

JEL Classification: C02, C63, E43, G13, G33.

AMS Classification: 60H10, 60J75, 91B70, 91G40.

Keywords: swap, collateral, derivatives, Libor, currency, OIS, EONIA, Fed-Fund, CCS, basis, risk management, HJM, FX option, CSA, CVA, term structure, SSA, one-way CSA.

Previously titled: Asymmetric and Imperfect Collateralization, Derivative Pricing, and CVA

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