Floating exercise boundaries for American options in time-inhomogeneous models

TL;DR

This paper introduces a semi-analytical method for pricing American options in complex time-inhomogeneous models where exercise boundaries can dynamically appear and disappear, especially under negative interest rates or yields.

Contribution

It develops a novel approach to handle floating exercise boundaries that emerge and vanish in certain financial models, extending existing pricing techniques.

Findings

Effective handling of dynamic exercise boundaries in complex models

Identification of conditions leading to boundary emergence and collapse

Enhanced accuracy in American option pricing under negative rates

Abstract

This paper examines a semi-analytical approach for pricing American options in time-inhomogeneous models characterized by negative interest rates (for equity/FX) or negative convenience yields (for commodities/cryptocurrencies). Under such conditions, exercise boundaries may exhibit a "floating" structure - dynamically appearing and disappearing. For example, a second exercise boundary could emerge within the computational domain and subsequently both could collapse, demanding specialized pricing methodologies.