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Broken-Wing Butterfly: Asymmetric Payoff, Breakevens, and Assignment Risk

For educational purposes only; not investment advice.

Direct answer

Section titled “Direct answer”

A broken-wing butterfly is a butterfly spread whose two strike intervals are unequal. A call version buys one lower-strike call, sells two middle-strike calls, and buys one higher-strike call with the same underlying, expiration, exercise style, settlement, and multiplier. The wider wing shifts cost and creates unequal losses in the two tails.

It is not merely a cheaper standard butterfly. The omitted symmetry introduces directional exposure and can make one tail materially riskier. The exact debit or credit must be combined with both wing widths before maximum profit, maximum loss, or breakevens can be stated.

Piecewise expiration payoff

Section titled “Piecewise expiration payoff”

For call strikes K₁ < K₂ < K₃ and net debit D, profit per underlying unit at expiration is:

max(S_T−K₁,0) − 2max(S_T−K₂,0) + max(S_T−K₃,0) − D

  • At or below K₁, loss is D.
  • Between K₁ and K₂, profit rises dollar for dollar.
  • At K₂, profit is (K₂−K₁)−D.
  • Between K₂ and K₃, profit declines dollar for dollar.
  • At or above K₃, profit is 2K₂−K₁−K₃−D, which can be a larger loss than the debit.

Before expiration, the position’s delta, gamma, theta, and vega change with spot, time, and the volatility skew at all three strikes. A favorable expiration graph does not imply a smooth mark-to-market path.

100/105/115 call butterfly

Section titled “100/105/115 call butterfly”

Buy one 100 call, sell two 105 calls, and buy one 115 call for a $1.00 net debit. The lower wing is $5 wide and the upper wing is $10 wide.

  • Below $100: maximum downside loss is $1.00, or $100 with a 100-share multiplier.
  • At $105: maximum profit is $5 − $1 = $4.00, or $400.
  • At or above $115: terminal spread payoff is 2×105 − 100 − 115 = −$5; after the debit, maximum upside loss is $6.00, or $600.
  • Lower breakeven: $100 + $1 = $101.
  • Upper breakeven: $105 + ($5 − $1) = $109.

At $110, intrinsic spread payoff is $0; after the debit the loss is $1.00. This illustrates why treating the structure as a symmetric butterfly produces the wrong upper-tail conclusion.

Trade and expiration checklist

Section titled “Trade and expiration checklist”
  • Write every leg, quantity, strike, expiration, multiplier, exercise style, and settlement before calculating risk.
  • Derive all four expiration regions and both tails; do not rely only on broker-displayed maximum profit.
  • Use an executable complex-order price; four favorable midpoints may not trade together.
  • Include fees and slippage across four contracts per spread.
  • Stress spot gaps through the wide wing and changes in volatility skew.
  • Monitor both short middle calls for early assignment, especially around dividends and low extrinsic value.
  • If one or both shorts are assigned, recalculate the resulting shares and remaining options immediately.
  • Plan expiration around both breakevens and the two short contracts’ pin risk.

Common misconceptions

Section titled “Common misconceptions”
  • “Broken wing means one protective option is missing.” All four contracts remain; strike spacing is asymmetric.
  • “The maximum loss is always the debit.” The wider tail can create an additional fixed loss.
  • “A net credit means no risk.” Credit changes endpoints but does not erase the wide-wing obligation.
  • “Maximum profit is likely because it is defined.” It requires expiration near the middle strike.
  • “Four legs cancel assignment risk.” Two short options can be assigned independently.
  • “Rolling preserves the original payoff.” It closes old legs and creates a new structure at new prices.
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Authoritative sources

Section titled “Authoritative sources”