FinancePy Merton jump pricing: a zero probability can erase an option value

At Poisson exposure 800, current-source FinancePy MertonJumpDiffusion returns 0 for a call with an independent value of approximately 23.50586700. The initial Poisson weight underflows, and the multiplicative recurrence cannot recover the later probabilities.

Pinned source: 7a68a8a8b3be507da6829793861d36865c98c547. Across 112 synthetic observations, discrepancies are 52 / 0 / 52 for original code, a local candidate correction, and restored code. An independent 70-digit oracle and a fresh extracted-archive replay were verified. All 12 existing upstream Merton regression functions pass on original and candidate code; the full library suite was not run.

A separate GERO synthetic worksheet values 100 hypothetical units at 0.00 instead of 2350.59 and changes the result of a chosen 2000 review threshold. No actual positions, customer losses, deployment or regulatory finding is claimed. The affected module is absent from the released PyPI 1.1.2 wheel.

The candidate changes probability weights only. Truncation-budget handling, payoff-weighted stopping and other extreme regimes remain outside its validated scope. The reproducer was sent to the official issue tracker before distribution; no acknowledgment, acceptance, reward or payment is claimed.

Independent GERO research by Xamit Kadirbekov. AI-assisted investigation and preparation, with actual code execution. Original component licenses and copyright notices are retained; see source/LICENSE and SOURCE_NOTICES.md in the archive. FinancePy source is GPL-3.0-or-later; no blanket replacement license is applied to this mixed evidence package.

Report: https://www.gero.uz/research/articles/financepy-merton-jump-poisson-underflow.html
GitHub: https://github.com/kadyrbekovhamit-cyber/gero-numerical-observatory/blob/main/catalog/reports/financepy-merton-jump-poisson-underflow.md
Evidence mirror: https://huggingface.co/datasets/XamitK/gero-research-evidence-2026-09/blob/main/financepy-merton-jump-poisson-underflow.md
Developer report: https://github.com/domokane/FinancePy/issues/273