A hybrid Markov-Functional model with simultaneous calibration to the interest rate and FX smile

In this paper we present a Markov-Functional hybrid interest rate/foreign exchange model that allows calibration to given market volatility surfaces in both dimensions simultaneously. This is achieved by extending the approach introduced by Fries and Rott by a functional for the foreign exchange rate (FX), which allows a fast, yet accurate calibration to a given market FX volatility surface. This calibration procedure comes as an additional step to the known calibration of the LIBOR functional, resulting in an efficient implementation.