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Based on LIBOR Market Models, we develop a rigorous pricing framework for cross-currency exotic interest rate instruments under a uniform probability measure and in a multifactoral environment that accounts for foreign exchange skew. The model resorts to a stochastic volatility approach with volatility dynamics following a square-root process and is designed to be flexible enough to allow for the incorporation of as much as possible of market information. Using the Fourier transform, we produce closed-form formulas for FX options by analytically obtaining the characteristic function. The main focus is placed on FX markets, in terms of which the calibration of model parameters can be performed on a wide range of FX options expiries and strikes.

A Multifactoral Cross-Currency LIBOR Market Model With a FX Volatility Skew