In this article, we introduce analytic approximation formulae for FX options in the Libor market model (LMM). The method to derive the formulae is an asymptotic expansion technique introduced in Kawai [Kaw03].

We first apply the method to the lognormal LMM and lognormal FX model. Then, the method is applied to the displaced diffusion LMM and the displaced diffusion FX model. Some numerical examples show that the derived formulae are sufficiently accurate for practical applications.

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