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A Note on Construction of Multiple Swap Curves with and without Collateral

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

January 25, 2010

Abstract: There are now available wide variety of swap products which exchange Libors with different currencies and tenors. Furthermore, the collateralization is becoming more and more popular due to the increased attention to the counter party credit risk. These developments require clear distinction among different type of Libors and the discounting rates. In this brief note, we will explain the method to construct the multiple swap curves consistently with all the relevant swaps with and without a collateral agreement.

JEL Classification: C51, E43.

AMS Classification: 60H10, 91B70.

Keywords: Libor, swap, tenor, yield curve, collateral, overnight index swap, cross currency, basis spread.

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