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Closed-form early exercise boundary in the Heston model

Derive a closed-form expression for the optimal early exercise boundary surface for American options under the Heston stochastic volatility model with constant coefficients.

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Background

Within the multidimensional diffusion setting, the authors note that for the Heston model the early exercise boundary is not known in closed form. Prior studies approximate the boundary via regressions or coarse numerical methods.

A closed-form boundary would materially simplify and accelerate semi-analytical pricing and Greek computations within the decomposition framework.

References

Since the EB for the Heston model is not known in closed form, determined it by assuming that the optimal stopping surface can be well-approximated in a log-linear fashion near the long-term variance level, i.e. as a linear function of the long-term variance model parameter.

— American options valuation in time-dependent jump-diffusion models via integral equations and characteristic functions (2506.18210 - Itkin, 23 Jun 2025) in Section 3 (Multidimensional diffusion models), discussion of prior work on Heston