Bottleneck Option

We consider an option whose payoff corresponds to a “capped American lookback option with floating-strike” and solve the associated pricing problem (an optimal stopping problem) in a financial market whose price process is modeled by an exponential spectrally negative Lévy process. We will present some interesting features of the solution - in fact, it turns out that the continuation region has a feature that resembles a bottleneck and hence the name “Bottleneck option”. We will also come across some well-known optimal stopping problems such as the Russian optimal stopping problem and the American lookback optimal stopping problem