Bottleneck Options

Abstract

In the spirit of Kyprianou and Ott (in Acta Appl. Math., to appear, 2013) and Ott (in Ann. Appl. Probab. 23:2327–2356, 2013) 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 modelled by an exponential spectrally negative Lévy process. Despite the simple interpretation of the cap as a moderation of the payoff, it turns out that the optimal strategy to exercise the option looks very different compared to the situation without a cap. In fact, we show that the continuation region has a feature that resembles a bottleneck and hence the name “bottleneck option”.