Iron butterfly

Definition

An iron butterfly sells an at-the-money straddle and buys a protective wing on each side, same expiry: a short call and short put at the same middle strike, plus a long call above and a long put below. It is a pin thesis — the underlying finishes near the middle strike — collecting a larger credit than a condor in exchange for a much narrower profit zone.

How it works / structure

• Legs: +1 put K1, −1 put K2, −1 call K2, +1 call K3 (K1 < K2 < K3), same expiry, K2 at or near the money.
• Credit: total credit C (large — it contains the straddle); maximum gain C at exactly K2; maximum loss = wing width − C; breakevens K2 ± C.
• Parameters (engine-executable): middle-strike placement (spot, or a target pin level such as a high-open-interest strike), wing width (wider = more credit, more risk), DTE, IV gate (iv_rank), management (mgmt-profit-target at x% of credit — full credit requires an exact pin and is rarely realized; mgmt-time-based-exit; mgmt-stop-loss).
• Greeks profile: sharper than a condor — near-zero delta at entry, strongly short gamma at the middle strike (greek-gamma), short vega, high theta; the P&L is a tent centered on K2.
• Relation to the straddle: identical to a short straddle (strategy-straddle inverted) with tail risk amputated by the wings — the wings’ cost is the price of surviving outliers.

When it applies

Strong mean/pin expectations at a specific level into expiration (event-opex pinning context), post-event IV-crush captures centered on the expected landing zone, and high-IV entries where the straddle credit is rich relative to the expected move (opt-expected-move). Narrower and more management-intensive than a condor — a precision structure.

Risk profile & failure modes

• The pin rarely lands exactly: realized P&L concentrates well below max credit; profit-target management (not hold-for-the-pin) is what the realized distribution rewards or the position round-trips.
• Gamma cliff at the middle strike: as expiry nears, small moves through K2 swing P&L violently (ms-expiration-exercise-assignment pin-risk mechanics on the short legs).
• Both-side whipsaw: management that chases the tested side in a choppy market can lose on both wings sequentially.
• Loss clustering in trend/shock regimes, same as all short- volatility structures.

Evidence & limits

Mechanics are contract arithmetic (OCC/Cboe). The premium engine is the volatility risk premium (evidence in opt-implied-volatility); no public study establishes iron butterflies specifically as an excess-return class. Pin-tendency claims around option strikes exist in the literature (event-opex carries the citations); a specific pin thesis remains per-name, per-date replay evidence.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X will close within ±C of K2 at expiry (inside the breakevens)” — falsified by a close outside them.
• “A 45-DTE iron butterfly on Y centered at the money, managed at 25% of credit, will realize its target before a 2x-credit loss in the next cycle” — falsified by the replay path.

Cross-references

• Wider sibling: strategy-iron-condor; unwinged core: strategy-straddle
• Pin mechanics: event-opex, ms-expiration-exercise-assignment, greek-gamma
• Placement: opt-expected-move, opt-iv-rank-percentile
• Management: mgmt-profit-target, mgmt-time-based-exit, mgmt-stop-loss