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.