  We develop an expansion approach for the pricing of European quanto options
written on LIBOR rates (of a foreign currency). We derive the dynamics of the
system of foreign LIBOR rates under the domestic forward measure and then
consider the price of the quanto option. In order to take the skew/smile effect
observed in fixed income and FX markets into account, we consider local
volatility models for both the LIBOR and the FX rate. Because of the structure
of the local volatility function, a closed form solution for quanto option
prices does not exist. Using expansions around a proxy related to log-normal
dynamics, we derive approximation formulas of Black--Scholes type for the
price, that have the benefit of giving very rapid numerical procedures. Our
expansion formulas have the major advantage that they allow for an accurate
estimation of the error, using Malliavin calculus, which is directly related to
the maturity of the option, the payoff, and the level and curvature of the
local volatility function. These expansions also illustrate the impact of the
quanto drift adjustment, while the numerical experiments show an excellent
accuracy.
