American options with gradual exercise under proportional transaction costs

TL;DR

This paper investigates American options with gradual exercise in markets with proportional transaction costs, providing tighter pricing bounds, algorithmic strategies, and dual representations for such options.

Contribution

It introduces a framework for American options with gradual exercise under transaction costs, including new algorithms and duality results not present in prior literature.

Findings

Tighter bounds on option prices compared to instant exercise models

Algorithmic methods for bid and ask price computation

Dual representations for superhedging strategies

Abstract

American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomised) stopping time. The introduction of gradual exercise leads to tighter bounds on the option price when compared to the case studied in the existing literature, where the standard assumption is that the option can only be exercised instantly at an ordinary stopping time. Algorithmic constructions for the bid and ask prices and the associated superhedging strategies and optimal mixed stoping times for an American option with gradual exercise are developed and implemented, and dual representations are established.