Integral equation formulation for shout options

Abstract

We use an integral equation formulation approach to value shout options, which are exotic options giving an investor the ability to ``shout†and lock in profits while retaining the right to benefit from potentially favourable movements in the underlying asset price. Mathematically, the valuation is a free boundary problem involving an optimal exercise boundary which marks the region between shouting and not shouting. We also find the behaviour of the optimal exercise boundary for one- and two-shout options close to expiry. doi:10.1017/S1446181118000160