Dual representations for general multiple stopping problems

TL;DR

This paper develops a dual representation framework for complex multiple stopping problems, incorporating volume constraints and refraction periods, and provides a Monte Carlo method for pricing such options with practical applications in electricity markets.

Contribution

It extends existing models by simultaneously handling volume constraints and refraction periods, and introduces a flexible cashflow structure including utility-based payoffs.

Findings

Derived a dual representation for generalized multiple stopping problems.

Developed a Monte Carlo algorithm for option pricing with confidence intervals.

Applied the method to price a swing option in an electricity market.

Abstract

In this paper, we study the dual representation for generalized multiple stopping problems, hence the pricing problem of general multiple exercise options. We derive a dual representation which allows for cashflows which are subject to volume constraints modeled by integer valued adapted processes and refraction periods modeled by stopping times. As such, this extends the works by Schoenmakers (2010), Bender (2011a), Bender (2011b), Aleksandrov and Hambly (2010), and Meinshausen and Hambly (2004) on multiple exercise options, which either take into consideration a refraction period or volume constraints, but not both simultaneously. We also allow more flexible cashflow structures than the additive structure in the above references. For example some exponential utility problems are covered by our setting. We supplement the theoretical results with an explicit Monte Carlo algorithm for constructing confidence intervals for the price of multiple exercise options and exemplify it by a numerical study on the pricing of a swing option in an electricity market.