The selected intervals are minimum requirements: −2% to −0.2% and +0.2% to +2% by default. A strategy that stays profitable across −2% to +2%, or across an even wider range, passes because it contains both intervals. The library first tests same-expiry convex and capped structures, then far-long/near-short calendars and double diagonals, then near-long/far-short reverse calendars/diagonals only when later-expiry protection caps every short. Same-expiry candidates are proven at endpoints and payoff kinks; mixed-expiry candidates are valued at the near expiry with residual far-option time value and searched for P/L extrema through zero-delta roots. Implied volatility supplies expected-move strike anchors; it never substitutes for the interval test.
Strategy theory and risk rules used by this search
- Same expiry: long strangles/straddles/guts, debit iron condors, butterflies, capped ratios, and capped financing layers. Their payoff is piecewise linear, so interval endpoints and all in-zone strikes prove the minimum P/L.
- Far-long time spreads: long calendars, diagonals, iron double calendars, and iron double diagonals use near shorts with equal-or-later long protection.
- Far-short time spreads: reverse calendars/diagonals always add a farther-out far-expiry cap. Paired put/call versions form protected reverse iron double calendars or diagonals; their ratios are solved from endpoint inequalities before full P/L validation.
- Mixed expiry: near legs settle intrinsically while far legs retain modeled time value at the near expiry. The scanner searches smooth P/L extrema through zero-delta roots, then rejects any candidate that misses either required interval.
- Risk: every short must have a same- or later-expiring long of the same type. A near long never counts as cover for a far short.