Analyticity of the Wiener-Hopf factors and valuation of exotic options in L\'evy models

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.