On the optimal exercise boundaries of swing put options

TL;DR

This paper characterizes the time-dependent optimal exercise boundaries for swing put options using probabilistic methods, providing a detailed description of the stopping regions and a formula for the option's value.

Contribution

It introduces a novel probabilistic approach to determine the optimal exercise boundaries in swing put options with coupled integral equations.

Findings

Boundaries are continuous and monotonic functions of time.

Unique solutions to the coupled integral equations are established.

A formula for the value function of the swing put option is derived.

Abstract

We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion. The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries which are continuous, monotonic functions of time and uniquely solve a system of coupled integral equations of Volterra-type. Finally we provide a formula for the value function of the problem.