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We present a general derivation of the arbitrage-free pricing framework formultiple-currency collateralized products. We include the impact on optionpricing of the policy adopted to fund in foreign currency, so that we are ableto price contracts with cash flows and/or collateral accounts expressed inforeign currencies inclusive of funding costs originating from dislocations inthe FX market. Then, we apply these results to price cross-currency swaps underdifferent market situations, to understand how to implement a feasible curvebootstrap procedure. We present the main practical problems arising from theway the market is quoting liquid instruments: uncertainties about collateralcurrencies and renotioning features. We discuss the theoretical requirements toimplement curve bootstrapping and the approximations usually taken topractically implement the procedure. We also provide numerical examples basedon real market data.

FX Modelling in Collateralized Markets: foreign measures, basis curves, and pricing formulae