Digital double barrier options: Several barrier periods and structure floors

TL;DR

This paper derives a method to price digital double barrier options with multiple barrier periods in the Black-Scholes model, and applies it to value structure floors in structured notes, linking to corridor put options.

Contribution

It introduces a novel approach for pricing digital double barrier options with multiple barrier periods and applies it to structured note valuation.

Findings

Derived pricing formulas for multi-period digital double barrier options.

Connected structure floor valuation to corridor put options.

Provided practical methods for complex barrier option structures.

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.