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

2026/06/08 by Khai Nguyen, Huy Chau · 1 voice
Economics, Econometrics and Finance · #q-fin.MF

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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.

Citations

• Properties of the American price function in the Heston-type models
• Variational formulation of American option prices in the Heston Model
• On American VIX options under the generalized 3/2 and 1/2 models
• Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
• C^1,1 regularity for degenerate elliptic obstacle problems
• Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions
• Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance
• Exercise Boundary of the American Put Near Maturity in an Exponential Lévy Model
• Regularity of the Optimal Stopping Problem for Jump Diffusions
• A Theory for the Term Structure of Interest Rates
• user's guide to viscosity solutions of second order partial differential equations
• User’s guide to viscosity solutions of second order partial differential equations
• The Pricing of Options and Corporate Liabilities

Discussions

• Khai Nguyen, Huy Chau: On regularity of finite-maturity American put options in the Heston model https://arxiv.org/abs/2606.10191 https://arxiv.org/pdf/2606.10191 https://arxiv.org/html/2606.10191 [bsky, 0 points, 0 comments]

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