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Extend the decomposition-and-EEP method to general time-dependent jump-diffusion and Lévy models

Determine whether the decomposition approach that represents an American option price as the sum of its European price and an early exercise premium, together with the associated Volterra integral equation for the optimal exercise boundary developed by Itkin and Kitapbayev (2025) for pure diffusion models, extends to general time-dependent jump-diffusion models and Lévy processes.

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Background

The paper advocates an integral-equation-based, semi-analytical framework for American option pricing that explicitly determines the exercise boundary and computes the early exercise premium (EEP). Prior work established this for pure diffusions.

The authors explicitly note a remaining gap: the applicability of this decomposition-and-EEP method to more general time-dependent jump-diffusion models and Lévy processes had not been explored, motivating one of the paper’s central aims.

References

Despite the advantages of the integral equation approach, several open problems remain that warrant further investigation:

  • While the method in was developed for pure diffusion models, its applicability to general time-dependent jump-diffusion models and \LY processes remains unexplored.
— American options valuation in time-dependent jump-diffusion models via integral equations and characteristic functions (2506.18210 - Itkin, 23 Jun 2025) in Introduction, paragraph beginning “Despite the advantages of the integral equation approach…”, first bullet (before Section 1)