  We study the utility indifference price of a European option in the context
of small transaction costs. Considering the general setup allowing consumption
and a general utility function at final time T, we obtain an asymptotic
expansion of the utility indifference price as a function of the asymptotic
expansions of the utility maximization problems with and without the European
contingent claim. We use the tools developed in [54] and [48] based on
homogenization and viscosity solutions to characterize these expansions.
Finally we study more precisely the example of exponential utilities, in
particular recovering under weaker assumptions the results of [6].
