Barrier options and their application to structure floors

Abstract

We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black-Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose individual coupons are digital double barrier options. This value can also be approximated by the price of a corridor put. We also address the issue which arises when using Monte Carlo simulation to price a barrier option, namely the discretization bias inherent when using a discrete setting in a continuously monitored model. This work is largely based on the paper Digital Double Barrier Options: Several Barrier Periods and Structure Floors of Altay, Gerhold, Haidinger and Hirhager, published in the International Journal of Theoretical and Applied Finance, Volume 16, 2013, which the author has co-authored.