  We provide a general HJM framework for forward contracts written on abstract
market indices with arbitrary fixing and payment adjustments. We allow for
indices on any asset class, featuring collateralization in arbitrary currency
denominations. The framework is pivotal for describing portfolios of interest
rate products which are denominated in multiple currencies. The benchmark
transition has created significant discrepancies among the market conventions
of different currency areas: our framework simultaneously covers
forward-looking risky IBOR rates, such as EURIBOR, and backward-looking rates
based on overnight rates, such as SOFR. In view of this, we provide a thorough
study of cross-currency markets in the presence of collateral, where the cash
flows of the contract and the margin account can be denominated in arbitrary
combinations of currencies. We finally consider cross-currency swap contracts
as an example of a contract simultaneously depending on all the risk factors
that we describe within our framework.
