⏱ 1-Minute Summary Butterflies are defined-risk, three-strike structures built in a 1:2:1 ratio. Long butterflies profit when the stock settles near the middle strike (great when IV is low); short butterflies profit when it breaks out. The unbalanced (broken-wing) variants shift the risk to one side to lower cost. This is the full family the simulator supports.
1. The Butterfly Family
All butterflies combine three strikes of the same option type in a 1:2:1 structure: buy one, sell two at the middle, buy one. The family branches by:
- Type: call butterflies vs put butterflies.
- Direction: long (range-bound) vs short (breakout).
- Spacing: balanced wings vs unbalanced (broken-wing) wings.
The chart above shows gamma, how much delta changes per $1 move in the stock, across the underlying price. It assumes a strike of 200 and a fixed implied volatility (IV) of 25% as the baseline; the lines show 14, 45 and 90 days to expiry. At a stock price of 200, gamma is highest for the shortest-dated line: about 0.046 at 14 days, 0.027 at 45 days, and 0.019 at 90 days. Every line peaks at the money and falls toward zero away from it, with the shorter-dated peaks much taller and narrower. For a butterfly this is where convexity lives: gamma concentrates at the middle strike and nearly vanishes at the wings, and it sharpens sharply as expiry approaches.
The chart above shows how gamma changes as expiration approaches. It assumes a stock price of 200 and a fixed implied volatility (IV) of 25% as the baseline; the blue line is the 200 strike (at the money), the red line the 180 strike, and the green line the 220 strike. The at-the-money line explodes near expiry: about 0.046 with 15 days to expiry, 0.032 at 30 days, and 0.019 at 90 days. The 180 and 220 lines stay low and nearly flat, around 0.01 at 90 days. For a butterfly this is the expiration-week effect: the short middle strike carries its most gamma in the final weeks, which is when a long butterfly's edge is sharpest, while the wings stay low-gamma.
The chart above shows gamma against moneyness (S divided by K) instead of the absolute price. It assumes a stock price of 200, a fixed implied volatility (IV) of 25% as the baseline, and lines for 30, 45 and 90 days to expiry. At the money gamma is highest: about 0.032 at 30 days, 0.027 at 45 days, and 0.019 at 90 days; it falls toward the wings (in the money or out of the money) to roughly 0.014. This normalized view is why butterflies work at any price level: the convexity always concentrates at the middle strike, regardless of the stock's absolute level.
2. Call Butterfly (Long & Short)
- Long call butterfly: buy low call, sell 2 middle calls, buy high call. Profits if the stock settles near the middle strike.
- Short call butterfly: the opposite. Profits if the stock breaks out above or below the range.
| Long call butterfly | Short call butterfly | |
|---|---|---|
| Max profit | At middle strike | Beyond the wings |
| Max loss | Net debit | Wing width − credit |
| Best when | Low IV, range-bound | Breakout expected |
The charts above show the long and short call butterfly's profit and loss against the underlying price at expiry. They assume a stock price of 200, 45 days to expiry, and a fixed implied volatility (IV) of 25% as the baseline; both use the $190 / $200 / $210 strikes. The long butterfly buys the $190 call (about $12.6), sells two $200 calls (about $6.2 each), and buys the $210 call (about $2.5), paying a net debit of about $2.6; the short butterfly is the exact opposite, collecting a net credit of about $2.6. At expiry the long butterfly peaks at the middle strike, about +$7.4 at $200, +$5.4 at $198 or $202, +$2.4 at $195 or $205, and is capped at about -$2.6 beyond $190 or $210, so the risk is defined by the strike width. The breakevens sit at about $192.6 and $207.4. The short butterfly is the mirror image: it loses about -$7.4 at $200 and pays about +$2.6 flat outside the wings.
The dashed lines show the same positions 10 days in (35 days to expiry). Both curves flatten dramatically because the two short middle legs still carry time value: the long butterfly is only about +$0.3 at $200, and the breakevens tighten to about $193.4 and $206.5; the short butterfly is about -$0.3 at $200. The maximum profit of the long version is only realized at expiry if the stock pins exactly at $200, so butterflies must be held into expiration or carefully manage the risks.
The charts above show how the 10-days-in P&L changes if implied volatility moves 10 points from the 25% baseline. The gray line is the baseline, the red dashed line is with IV 10 points higher (35%), and the blue dashed line is with IV 10 points lower (15%). A long butterfly is net short vega (the two sold middle strikes carry more vega than the wings), so higher IV pushes the curve down: at $200 the long version is about -$0.5 instead of +$0.3, while lower IV lifts it to about +$1.9. The short butterfly mirrors this: higher IV helps it, about +$0.5 at $200, while lower IV hurts it, about -$1.9. This is why long butterflies prefer low and falling IV, and short butterflies prefer high IV or an IV crush into a breakout.
3. Put Butterfly (Long & Short)
- Long put butterfly: buy low put, sell 2 middle puts, buy high put. Identical payoff shape to the call version thanks to put-call parity.
- Short put butterfly: profits on a breakout; limited risk.
The charts above show the long and short put butterfly's profit and loss against the underlying price at expiry. They assume a stock price of 200, 45 days to expiry, and a fixed implied volatility (IV) of 25% as the baseline; both use the $190 / $200 / $210 strikes. Thanks to put-call parity, the payoff shapes are identical to the call versions: the long put butterfly buys the $190 put (about $1.9), sells two $200 puts (about $5.5 each), and buys the $210 put (about $11.8), paying a net debit of about $2.6; the short put butterfly collects about $2.6. At expiry the long version peaks at about +$7.4 at $200 and is capped at about -$2.6 outside $190 to $210, with breakevens at about $192.6 and $207.4; the short version mirrors it, losing about -$7.4 at $200.
The dashed lines show the same positions 10 days in (35 days to expiry). Both curves flatten dramatically: the long put butterfly is only about +$0.3 at $200, and the breakevens tighten to about $193.4 and $206.5. As with the call version, the long maximum is only reached at expiry with the stock pinned at $200.
The charts above show how the 10-days-in P&L changes if implied volatility moves 10 points from the 25% baseline. The gray line is the baseline, the red dashed line is with IV 10 points higher (35%), and the blue dashed line is with IV 10 points lower (15%). The long put butterfly is net short vega, so higher IV pushes it down, about -$0.5 at $200 instead of +$0.3, while lower IV lifts it to about +$1.9; the short version mirrors that, gaining about +$0.5 at $200 when IV rises and losing about -$1.9 when IV falls. The put and call versions share the same IV behavior, so choose the one with the better liquidity and bid-ask.
4. Unbalanced (Broken-Wing) Butterflies
An unbalanced butterfly keeps the 1:2:1 ratio but makes one wing wider than the other. The simulator supports all four combinations:
- Long unbalanced call butterfly: buy low, sell 2 middle, buy higher call with a wider upper wing.
- Short unbalanced call butterfly: mirrored short version.
- Long unbalanced put butterfly: buy low put, sell 2 middle, buy higher put with a wider lower wing.
- Short unbalanced put butterfly: mirrored short version.
The wider wing creates an asymmetric loss zone, which lowers the net cost (or increases the credit) but leaves one side exposed to a larger loss.
The charts above show the four unbalanced (broken-wing) butterfly variants against the underlying price at expiry. They assume a stock price of 200, 45 days to expiry, and a fixed implied volatility (IV) of 25% as the baseline. The long unbalanced call buys the $190 call (about $12.6), sells two $200 calls (about $6.2 each), and buys a wider $215 call (about $1.5), paying a reduced net debit of about $1.5; it peaks at about +$8.5 at $200, but the wider upper wing leaves a larger loss zone above: about -$6.5 from $215 up, with breakevens at about $191.6 and $208.5. The short unbalanced call is the mirror, collecting about $1.5 and losing about -$8.5 at $200 while paying about +$6.5 above $215. The long unbalanced put buys the $185 put (about $1.0), sells two $200 puts, and buys the $210 put (about $11.8), paying about $1.6; it peaks at about +$8.4 at $200 but carries the wider loss zone below $185, about -$6.6, with breakevens at about $191.7 and $208.4. The short unbalanced put mirrors it.
The dashed lines show the same positions 10 days in (35 days to expiry). The peaks flatten dramatically and the breakevens tighten: the long call version is only about +$0.5 at $200 with breakevens near $185.7 and $203.4, while the long put version is about +$0.5 at $200 with breakevens near $196.5 and $214.1. As with the balanced versions, the maximum is only realized at expiry if the stock pins near the middle strike.
The charts above show how the 10-days-in P&L changes if implied volatility moves 10 points from the 25% baseline. The gray line is the baseline, the red dashed line is with IV 10 points higher (35%), and the blue dashed line is with IV 10 points lower (15%). The long unbalanced butterflies are net short vega: higher IV pushes the curve down, about -$0.7 at $200 instead of +$0.5, while lower IV lifts it to about +$2.6. The short versions mirror that, gaining about +$0.7 at $200 when IV rises and losing about -$2.6 when IV falls. The broken wing lowers the entry cost or raises the credit, but it does not change the vega sign: long versions still prefer low IV and short versions still prefer high IV.
5. Choosing Strike Spacing
- Balanced, tight wings: cheapest, smallest profit, best for a very precise price target.
- Balanced, wide wings: more expensive, larger profit zone, more forgiving.
- Unbalanced (broken-wing): lower cost or higher credit, but one side carries a much larger loss; choose the wider wing on the side you believe will not be hit.
6. Risk Management
- Butterflies are defined risk (the worst case is a few strikes of width) but the profit zone is narrow, so theta works against long versions until the pin.
- Avoid earnings and other IV events unless you specifically want the IV crush effect.
- Wide bid-ask on the outer strikes can eat the edge; verify liquidity in the simulator’s option data before sizing.
- All results reflect T-1 EOD data and are educational, not signals.
⚠️ Research Use Only: This article is educational. Options trading involves substantial risk of loss, especially when selling options. Nothing here is a buy or sell signal. Use this platform's backtests as historical statistical reference only; past performance does not guarantee future results.