Generalized two-barrier proportional step options

Abstract

This paper introduces a type of generalized two-barrier proportional step options. For a down-and-out step call, its payoff at expiration is defined as the payoff of an identical vanilla option discounted by a knock-out factor e−ρOTL,H, where OTL,H is the total duration of the underlying price process reaching a lower level L and remaining constantly below an upper level H up to expiration time T. Laplace transform-based analytical expressions of the option prices for exponential spectrally negative Lévy processes are derived. Finally, numerical studies are provided to show validity and applicability of our theoretical findings in practice.