Analyticity of the Wiener-Hopf factors and valuation of exotic options in Lévy models
arXiv:0911.0373
Abstract
This paper considers the valuation of exotic path-dependent options in Lévy 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 Lévy 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 Lévy models.
22 pages, no figures. Forthcoming in the volume on "Advanced Mathematical Methods for Finance"