Valuing Switching options with the moving-boundary method

Shaunak S Dabadghao,Arun Chockalingam,Taimaz Soltani,Jan Fransoo

doi:10.1016/j.jedc.2021.104124

Shaunak S Dabadghao, Arun Chockalingam + Show 2 more

Open Access

https://doi.org/10.1016/j.jedc.2021.104124

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Abstract

Switching options can be deployed in various complex switching problems such as tolling agreements and the offshoring–backshoring problem. Closed form solutions to valuing switching options are not only hard, but also computationally intensive when solving numerically. We develop a new computational method to value switching options based on the moving boundary method. We show how the free boundary problem arising from switching options can be converted into a sequence of fixed boundary problems. We formulate the problem, and solve the optimal switching problem in two regimes over a finite time horizon. We establish the theoretical guarantees for this method (maximum principles, uniqueness and convergence). We demonstrate this with a numerical example and show the sensitivity of the solution with respect to problem parameters.

Highlights

Managerial problems typically boil down to answering the following question: “What action should be taken, and when?”
We develop a new computational method to value switching options based on the moving boundary method
We show how the free boundary problem arising from switching options can be converted into a sequence of fixed boundary problems

Summary

Introduction

Managerial problems typically boil down to answering the following question: “What action should be taken, and when?”. Given the frequency with which these decision-making problems occur in practice, and the impact that some of these decisions could have, managers would benefit by knowing the switching times and the associated optimal actions Such decision rules are obtained by solving optimal-switching problems. We focus our attention on the two-regime switching problem, because while a manager may theoretically be faced with selecting one action from a set of two or more actions, practically, a substantial number of managerial decisions can be cast as real options with two possible actions. We first formulate a 2-regime switching problem that can be solved using an extension of the earlier moving boundary method developed by Chockalingam and Muthuraman (2011).

Literature Review

The Switching Model

Method

Numerical Studies

Effect of volatility and switching costs on the Optimal Policy

Discussion and Conclusion