  This paper considers the valuation of exotic path-dependent options in L\'evy
models, in particular options on the supremum and the infimum of the asset
price process. Using the Wiener--Hopf factorization, we derive expressions for
the analytically extended characteristic function of the supremum and the
infimum of a L\'evy process. Combined with general results on Fourier methods
for option pricing, we provide formulas for the valuation of one-touch options,
lookback options and equity default swaps in L\'evy models.
