Modeling of Interest Rate Term Structures Under Collateralization and its Implications

by Masaaki Fujii of the University of Tokyo,
Yasufumi Shimada of the Shinsei Bank, Ltd, and
Akihiko Takahashi of the University of Tokyo

December 22, 2010

Abstract: In recent years, we have observed dramatic increase of collateralization as an important credit risk mitigation tool in over the counter (OTC) market [6]. Combined with the significant and persistent widening of various basis spreads, such as Libor-OIS and cross currency basis, the practitioners have started to notice the importance of difference between the funding cost of contracts and Libors of the relevant currencies. In this article, we integrate the series of our recent works [1, 2, 4] and explain the consistent construction of term structures of interest rates in the presence of collateralization and all the relevant basis spreads, their no-arbitrage dynamics as well as their implications for derivative pricing and risk management. Particularly, we have shown the importance of the choice of collateral currency and embedded "cheapest-to-deliver" (CTD) option in a collateral agreement.

JEL Classification: E40,E43,F31,G13.

Keywords: swap, collateral, Libor, OIS, EONIA, Fed-Fund, cross currency, basis, HJM, CSA, CVA

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Related reading: Market Review of OTC Derivative Bilateral Collateralization Practices
A Note on Construction of Multiple Swap Curves with and without Collateral,
Collateral Posting and Choice of Collateral Currency: Implications for derivative pricing and risk management

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