Floating exercise boundaries for American options in time-inhomogeneous models

2025-02-02

AI Summary

This paper addresses the “floating” phenomenon—dynamic generation and collapse of the optimal exercise boundary—in American option pricing under negative interest rates (equities/foreign exchange) or negative convenience yields (commodities/cryptocurrencies). It provides the first systematic characterization of topological changes in the free boundary within time-inhomogeneous models, including emergence, coexistence, and synchronous disappearance of dual boundaries. We propose an adaptive solution framework integrating PDE-based semi-analytic methods, free-boundary transformations, numerical continuation tracking, and local asymptotic matching. This framework establishes rigorous existence criteria and real-time identification mechanisms for the exercise boundary. The method achieves high accuracy (boundary identification error < 0.1%) and robustness, with computational efficiency improved by a factor of three over conventional approaches. It thus delivers both theoretical foundations and practical tools for valuing American derivatives in non-standard interest-rate environments.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

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.

Problem

• Pricing American options in time-inhomogeneous models
• Handling negative rates or yields in option pricing
• Modeling floating exercise boundaries' dynamic behavior

Innovation

• Semi-analytical approach for pricing American options
• Handles floating exercise boundaries dynamically
• Addresses negative rates and yields in models