American options under periodic exercise opportunities

TL;DR

This paper analyzes perpetual American options with periodic exercise opportunities within exponential Lévy models, demonstrating the optimality of barrier strategies and providing explicit solutions for certain jump processes.

Contribution

It introduces a model for American options with periodic exercise times and proves the optimality of barrier strategies, offering explicit solutions for one-sided jump Lévy processes.

Findings

Barrier strategies are optimal under the model.

Explicit solutions are derived for one-sided jump Lévy processes.

The model extends traditional American option analysis to periodic exercise scenarios.

Abstract

In this paper, we study a version of the perpetual American call/put option where exercise opportunities arrive only periodically. Focusing on the exponential L\'evy models with i.i.d. exponentially-distributed exercise intervals, we show the optimality of a barrier strategy that exercises at the first exercise opportunity at which the asset price is above/below a given barrier. Explicit solutions are obtained for the cases the underlying L\'evy process has only one-sided jumps.