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Butterfly Spread: Payoff Geometry, Execution, and Assignment

Build long and short option butterflies, prove their expiration payoffs, and separate headline breakevens from executable pricing, assignment, settlement, and account risk.

Updated

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

A standard long butterfly uses three equally spaced strikes on one matched option claim: buy one lower-strike option, sell two middle-strike options, and buy one upper-strike option. With K_1 < K_2 < K_3, equal wing width W = K_2 − K_1 = K_3 − K_2, and positive net debit D, its expiration profit per underlying unit is max(S_T − K_1, 0) − 2max(S_T − K_2, 0) + max(S_T − K_3, 0) − D for calls. Maximum loss is D in either tail, maximum profit is W − D at K_2, and breakevens are K_1 + D and K_3 − D when 0 < D < W.

A matched long put butterfly has the same terminal intrinsic-payoff shape, while a short butterfly reverses every leg and typically receives a credit. Those statements do not make their lifecycles identical: American exercise, physical delivery, independent assignment of the two body options, dividends, borrow, margin and broker action can produce different interim shares and cash. A narrow target-price payoff is not merely a generic low-volatility forecast, and a defined expiration loss is not a guarantee about account funding or executable exit value.

Seven-step construction and lifecycle test

  1. Lock the strategy family and matched series. Record long or short, call or put, underlying, K_1 < K_2 < K_3, expiration, exercise style, settlement, multiplier, deliverable, currency, adjustment status and quantity. A standard symmetric butterfly requires equal spacing and ratio +1:−2:+1 for the long position; an iron butterfly, broken-wing butterfly or mixed specification is a different claim.
  2. Build the complete timeline. Map trade, ex-dividend, last-trading, customer and broker exercise cutoffs, expiration, official valuation, assignment notification and cash or physical settlement. Define S_T from the contract rather than substituting a stock close, after-hours print, live index, ETF or futures quote.
  3. Prove the terminal payoff by region. Evaluate S_T ≤ K_1, K_1 < S_T ≤ K_2, K_2 < S_T < K_3, and S_T ≥ K_3. A long equal-wing butterfly has gross intrinsic value 0, S_T − K_1, K_3 − S_T, and 0 across those regions. Unequal strikes cannot use +1:−2:+1 as a zero-tail identity; a weighted construction instead uses quantities proportional to (K_3 − K_2):−(K_3 − K_1):(K_2 − K_1).
  4. Price the executable package. Use a synchronized ratio-correct complex-order bid or ask, displayed size and actual fills. For a long butterfly, D is the executable net debit per underlying unit, not a sum of favorable leg midpoints. Verify 0 < D < W; otherwise recheck signs, units, stale quotes, leg specifications and whether any apparent credit represents a genuine executable opportunity.
  5. Convert the graph to account dollars. Multiply payoff, debit or credit by the actual multiplier and complete-package quantity, then include commissions, exchange and clearing charges, financing, borrow, dividend, settlement and tax costs. Distinguish option payoff, strategy profit, premium cash, margin requirement and return on capital.
  6. Stress the live position. Revalue delta, gamma, theta, vega, skew and event exposure across spot and time. Test zero, partial and full body assignment, long-wing disposition, pin and after-hours moves, exercise-by-exception, contrary instructions, halts, partial fills, legging, house margin, short stock, strike cash and broker liquidation.
  7. Reconcile every outcome. Save quotes, order ratio, limit, fills, fees and assignment notices; then reconcile remaining options, shares, dividends, cash, official settlement, margin, tax lots and next-session exposure. A roll is a close plus a new opening trade, not an extension of the original butterfly.

Worked examples

  • Long call butterfly at expiration. Buy the 95 call, sell two 100 calls, and buy the 105 call for D = $1.20 with multiplier 100. Maximum loss is $1.20 × 100 = $120; maximum profit is ($5 − $1.20) × 100 = $380; breakevens are $96.20 and $103.80. At S_T = $93/$98/$100/$102/$107, profit is −$120/$180/$380/$180/−$120. The $380 peak occurs at one official terminal value, not throughout the wing interval.
  • Short put butterfly is the reverse payoff. Sell the 95 put, buy two 100 puts, and sell the 105 put. Premiums $1.50/$3.00/$5.70 produce credit $1.50 − 2 × $3.00 + $5.70 = $1.20. Maximum tail profit is $120, maximum body loss is −$380, and breakevens are $96.20/$103.80. At S_T = $93/$98/$100/$102/$107, profit is $120/−$180/−$380/−$180/$120. Put assignment and stock delivery remain different lifecycle events from the call construction.
  • Executable package and all-in cost. Synchronized calls quote 6.10/6.30, 2.85/3.05, and 0.90/1.05. Their midpoint debit is 1.275, while the natural executable-leg debit is 6.30 − 2 × 2.85 + 1.05 = 1.65. If a complex order fills three butterflies at 1.45, gross premium paid is 3 × $1.45 × 100 = $435. Twelve contracts at $0.65 per contract cost $7.80, so total cost is $442.80, all-in debit per package is $1.476, maximum all-in profit is ($5 − $1.476) × 100 = $352.40, and breakevens are $96.476/$103.524 before later costs and tax.
  • Cash settlement versus physical assignment. A matched European cash-settled 95/100/105 call butterfly with D = $1.20 and official S_T = $103 pays ($8 − 2 × $3 + $0) × 100 = $200 and earns $200 − $120 = $80, with no shares or strike cash. In an American physically settled version, assignment of one short 100 call creates −100 shares and $10,000 strike proceeds while the other body call and both wings remain separate. Holding those shares short across a $0.75 ex-dividend creates a $75 dividend obligation; assignment of both body calls would create −200 shares, $20,000 proceeds and a $150 dividend obligation. Long wings do not act automatically.

Risks and validation controls

  • Confirm long or short direction and whether the legs are calls, puts or a different butterfly family.
  • Match underlying, expiration, exercise style, settlement, currency, multiplier and deliverable across all legs.
  • Verify strike order and equal wing spacing before using the +1:−2:+1 ratio.
  • Use a weighted construction for unequal strikes; do not disguise a broken-wing tail as a symmetric butterfly.
  • Keep debit positive and credit positive by stated convention; validate 0 < D < W for a standard long butterfly.
  • Define S_T from the contract’s official exercise-settlement source and time.
  • Use executable complex-package quotes, not independent midpoints, last trades or theoretical marks.
  • Check ratio-correct size and complete-package depth before scaling the order.
  • Treat order acceptance, partial execution and full execution as different states.
  • Include four-leg commissions, exchange, clearing, routing, financing, borrow, settlement and tax costs.
  • Distinguish regulatory minimum margin from strategy, portfolio and broker house requirements.
  • Model each short body option as independently exercisable and assignable where the contract permits.
  • Reconcile shares and strike cash immediately after partial or full assignment.
  • Compare sale and exercise of each long wing; exercise can destroy remaining extrinsic value.
  • Check ex-dividend timing, short-stock dividend obligations, borrow availability and recall risk.
  • Verify exercise-by-exception thresholds, contrary instructions, broker cutoffs and removed or halted securities.
  • Stress pin risk, after-hours moves and the next-session gap for zero, one or two body assignments.
  • Recalculate after splits, mergers, distributions or other adjusted-deliverable events.
  • Treat Greek signs and magnitudes as state-dependent local sensitivities, not guaranteed daily P&L.
  • Reconcile close, roll, expiration, assignment, cash, shares, fees and tax lots from final broker files.

Common misconceptions

  • “Any terminal price between the wings is profitable.” The position must first recover the debit, so profit exists only between the breakevens.
  • “Limited expiration loss makes the peak likely.” Maximum profit requires the official terminal value to land at the body strike, while the profitable interval can be narrow.
  • “Long call and long put butterflies are identical trades.” Matched European terminal values can agree, but quotes, cash flows, American exercise and assignment paths can differ.
  • “Four legs automatically exercise and offset one another.” Every leg and each of the two short body contracts can produce a separate account event.
  • “A low debit or nonnegative terminal graph proves favorable value.” Execution, depth, fees, margin, settlement, liquidity and the probability distribution determine the actual economics.

Authoritative sources

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