Interior smoothness and zero-variance geometry for finite-maturity Heston American puts

By Junkee Jeon, Takwon Kim, Jehan Oh

Rating

1803
Battle Count: 50

Relevance

8/10
Highly relevant for sophisticated derivatives desks and risk management teams dealing with stochastic volatility models. Understanding the smoothness and behavior of the exercise boundary near zero variance is critical for accurate pricing and hedging of American options in the Heston framework, especially for deep out-of-the-money or near-expiry scenarios.

Implementation Complexity

9/10
The theoretical analysis is highly complex, involving advanced PDE theory (obstacle problems, blow-up analysis, Hopf lemmas) and stochastic calculus (local times, CIR processes). Implementing the numerical scheme described requires careful handling of the degenerate boundary at y=0 and the mixed derivative term.

Reproducibility

3/5
The paper provides full theoretical derivations and specifies numerical parameters for the illustrative finite difference scheme. However, the code is not publicly hosted in a repository URL within the text, though it is stated to be available from the corresponding author upon request. The simulation parameters are fully specified.

Abstract

We study finite-maturity American puts in the Heston model without the Feller condition. At positive variance, the exercise boundary is smooth and strictly decreasing in remaining maturity and variance. At zero variance, the endpoint is locally Lipschitz in remaining maturity, the boundary moves with bounded speed in maturity uniformly down to zero variance, and it extends continuously to the axis. Each boundary slice at positive maturity has a regular C^1 closure tangent to the zero-variance axis, its stock threshold has variance derivative tending to minus infinity, and both partial derivatives of the inverse boundary graph vanish along the slice. The continuation premium at the axis contact stock is of order variance, and as a consequence smooth fit fails in the variance direction at the axis. At expiry the whole boundary, including its axis edge, converges to the strike. We give quantitative boundary gap bounds, an exact limiting weighted boundary Hessian, and vertical identities retaining the maturity term. Exact boundary gap equivalents remain open.

Links

arXiv:2610.20000 ยท Paper rankings

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