docs(features): clarify that gamma * S is intentional normalization (#33)#40
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Issue cloudtrainerwork#33 flagged that calculate_gamma multiplies by S while calculate_theta and calculate_vega divide by S, and the gamma docstring's "normalized by underlying price" wording reads as if it should divide. On investigation the math is correct and the asymmetry is required: - raw gamma scales as 1/S, so gamma * S is price-scale-invariant - raw theta and vega scale as S, so theta/S and vega/S are price-scale-invariant Verified empirically: gamma*S, theta/S, vega/S/100 are identical for S=100 and S=1000 at equal moneyness/vol/time. Changing gamma to gamma / S would REINTRODUCE price dependence (a real bug), so this is a documentation-only change: reword the docstring and comment to explain why the *S is correct and warn against "fixing" it. No behavior change. Closes cloudtrainerwork#33 Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Summary
Issue #33 (which I filed) flagged that
calculate_gammamultiplies bySwhilecalculate_theta/calculate_vegadivide byS, and the gamma docstring's "normalized by underlying price" wording reads as if it should divide.On investigation, the math is correct and the asymmetry is required. This PR is documentation-only — I'm correcting my own finding rather than the code.
Why
gamma * Sis rightThe goal is price-scale-invariant features (comparable across underlyings of any price level):
gamma * Sremoves the price dependencetheta / Sandvega / Sremove itDifferent raw scalings require opposite operations to reach the same normalization.
Verification
At equal moneyness/vol/time, the normalized values are identical across price levels:
Changing gamma to
gamma / Swould reintroduce price dependence — a real bug. So the only change here is to reword the docstring/comment to explain the reasoning and warn against "fixing" it.Change
* Sis intentional and why.Closes #33.
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