In this paper authors Alexander Antonov and Han Lee present a discrete framework on event time grid for a cross-currency term structure modelling. The discrete model is generic, in the sense that it can link together any single currency model to form a multi-factor cross currency model, provided that it is known (analytically or numerically) in a rolling-spot measure.

As an example we present a construction of a Markov-Functional model in this framework. For the discrete cross-currency extension, transitional probabilities between adjacent time slices for the FX process can be explicitly calculated if the respective underlying interest rate models have known transitional probabilities for their states.

A calibration of the discrete cross-currency model including FX volatility is also discussed in the paper. Namely, we present an analytical FX-rate volatility approximation and a construction of its efficient numerical solution.