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QuantLib: deterministic ITM probabilities and cap/floor deltas

Authors: Kadirbekov, Xamit;

QuantLib: deterministic ITM probabilities and cap/floor deltas

Abstract

Two implementation defects in QuantLib 1.43 and pinned current C++ source ca953b7ebdb400f2839d86f18eeb0d4a2a4a30a4. At zero standard deviation, Black asset ITM probabilities are reversed, while Bachelier returns a payoff amount instead of a probability (20 instead of 1 for a call with forward 120 and strike 100). Actual released code and complete upstream C++ translation units were executed. Candidate corrections remove 90 discrepancies across 660 helper inputs and 6 delta failures across 16 direct cap/floor engine cases. Restoring the original source reproduces the failures. All 12 focused upstream BlackFormula test cases pass after correction; the full library suite was not run. Tested prices remain unchanged. Separate released full-instrument examples confirm incorrect normalized optionlet deltas. The archive contains pinned source, minimal reproducers, independent references, raw outputs, build commands, regression patch, mutation evidence, dependency hashes and a bounded duplicate review. No exact earlier report was found in that review. No production portfolios, customer losses, bank deployment or upstream acceptance are claimed. Report and canonical evidence: https://github.com/kadyrbekovhamit-cyber/gero-numerical-observatory/blob/main/catalog/reports/quantlib-zero-stddev-itm-probabilities.md Independent GERO research by Xamit Kadirbekov. AI-assisted research and preparation. Report CC BY 4.0; original GERO harness MIT; bundled QuantLib source retains its original license.

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