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Butterfly Spread: Symmetric Payoff, Two Breakevens, and Pin Risk

For educational purposes only; not investment advice.

Direct answer

Section titled “Direct answer”

A long call butterfly uses three equally spaced strikes and one expiration: buy one lower-strike call, sell two middle-strike calls, and buy one upper-strike call. It normally opens for a net debit and earns its maximum expiration profit when the underlying finishes exactly at the middle strike.

The strategy has defined losses outside both wings, but its profitable expiration interval can be narrow. It expresses a target-price and timing view, not simply a forecast that volatility will be low.

Symmetric expiration payoff

Section titled “Symmetric expiration payoff”

Let strikes be K₁ < K₂ < K₃, with K₂−K₁ = K₃−K₂ = W, and net debit D. Profit per underlying unit 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, maximum profit is W−D.
  • Between K₂ and K₃, profit declines dollar for dollar.
  • At or above K₃, loss returns to D.
  • Breakevens are K₁+D and K₃−D.

Before expiration, the position’s delta, gamma, theta, and vega vary with spot and time. Near the body strike close to expiration, gamma can be large and the mark can change sharply on a small underlying move. Volatility skew means the four legs do not necessarily offset as a simple one-volatility model suggests.

95/100/105 call butterfly

Section titled “95/100/105 call butterfly”

Buy one 95 call, sell two 100 calls, and buy one 105 call for a $1.20 net debit and 100-share multiplier.

  • Maximum loss: $1.20 × 100 = $120.
  • Wing width: $5.
  • Maximum profit: ($5 − $1.20) × 100 = $380.
  • Lower breakeven: $95 + $1.20 = $96.20.
  • Upper breakeven: $105 − $1.20 = $103.80.

At $93 or $107, all-in spread payoff is zero and loss is $120. At $98, intrinsic spread value is $3, so profit is ($3 − $1.20) × 100 = $180. At $100, value reaches $5 and profit is the maximum $380. At $102, profit is again $180.

Maximum profit occurs at a single terminal price; nearby prices still can profit, but the result falls linearly toward each breakeven.

Trade and expiration checklist

Section titled “Trade and expiration checklist”
  • Confirm equal strike spacing, identical expiration, multiplier, style, settlement, and quantity ratio 1:−2:1.
  • Use an executable complex-order debit; four leg midpoints may not trade together.
  • Include four-contract fees, slippage, and the cost of closing before expiration.
  • Stress target-price error, a gap beyond either wing, volatility/skew changes, and widening markets.
  • Monitor both short middle calls for early assignment, especially near dividends and low extrinsic value.
  • If one or both shorts are assigned, recalculate shares and remaining options immediately.
  • Near expiration, plan for pin risk around the middle strike and uncertain exercise of two short contracts.
  • Treat a roll as closing the old butterfly and opening a new one, not extending the same payoff.

Common misconceptions

Section titled “Common misconceptions”
  • “The butterfly profits whenever the stock stays between the wings.” It must also overcome the debit; the true interval is between the breakevens.
  • “Maximum profit is likely because loss is limited.” It requires expiration at the middle strike.
  • “The position is neutral at all times.” Delta and other Greeks change materially with spot and time.
  • “Four legs eliminate assignment risk.” Two short calls can be assigned independently.
  • “Cheap debit means favorable expected value.” A narrow profitable interval can justify a low price.
  • “A broken-wing butterfly is the same strategy.” Unequal wings create asymmetric tail outcomes.
Section titled “Related topics”

Authoritative sources

Section titled “Authoritative sources”