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Coupling local currency Libor models to FX Libor models

We focus on the coupling of two existing and calibrated single currency Libor models into a joint Libor model that allows for pricing of multiple currency based structured interest rate products. Our main contribution is twofold: On the one hand we provide a method for synthesizing two local currency based correlation structures into a correctly defined joint correlation structure that describes the cross Libor correlations between the two currencies in a realistic way. On the other hand we introduce an (necessary) FX related factor X in order to describe the unified model with respect to one particular numéraire measure. In addition we propose to calibrate this factor to FX instruments in the case where X is modeled via Heston type dynamics.