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 "cheapestto-
deliver" (CTD) option in a collateral agreement.
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