Collateralization with daily margining and the so-called OIS-discounting have become a new standard in the post-crisis financial market. Although there appeared a large amount of literature to deal with a so-called multi-curve framework, a complete picture for a multi-currency setup with currency funding spreads, which are necessary to explain non-zero cross currency basis , can be rarely found since our initial attempts 9, 10, 11 . This note gives an extension of these works regarding a general framework of interest rates for a fully collateralized market. We provide a new formulation of the currency funding spread which is more suitable in the presence of non-zero correlation to the collateral rates. In particular, the last half of the paper is dedicated to develop a discretization of the HJM framework including stochastic collateral rates, LIBORs, foreign exchange rates as well as currency funding spreads with a fixed tenor structure, which makes it readily implementable as a traditional Market Model of interest rates .
Collateralization with daily margining has become a new standard in the post-crisis market. Although there appeared vast literature on a so-called multi-curve framework, a complete picture of a multi-currency setup with cross-currency basis can be rarely found since our initial attempts . This work gives its extension regarding a general framework of interest rates in a fully collateralized market. It gives a new formulation of the currency funding spread which is better suited for the general dependence. In the last half , it develops a discretization of the HJM framework with a fixed tenor structure, which makes it implementable as a traditional Market Model .
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