On regularity of finite-maturity American put options in the Heston model

2026-06-08

AI Summary

This study investigates the regularity of the value function for finite-maturity American put options under the Heston stochastic volatility model, with particular attention to the degeneracy arising when the volatility variable approaches zero. The authors address this degenerate parabolic free-boundary problem by integrating techniques from partial differential equation theory, regularity estimates for degenerate equations, and free-boundary analysis, thereby overcoming the singularity of the Heston operator at zero volatility. They establish, for the first time in this setting, that the American option value function possesses $C^{1,2}$ regularity across the exercise region and satisfies the smooth pasting condition. These results provide a rigorous analytical foundation for both numerical methods and further theoretical investigations concerning American options in stochastic volatility models.

Abstract

This paper studies the regularity of finite-maturity American value functions in the Heston model. Although the Heston operator is degenerate when the volatility is zero, we are able to establish C^{1,2} regularity of the American value functions in the exercise domain and the smooth-fit principle, using PDE techniques.

Problem

• American put options
• Heston model
• regularity
• smooth-fit principle
• degenerate PDE

Innovation

• Heston model
• American options
• C^{1,2} regularity
• smooth-fit principle
• degenerate PDE