Butterfly spread (options)
A butterfly spread buys one option at a low strike, sells two at a middle strike and buys one at a high strike, all of the same type and expiry. It costs little, pays most if the underlying settles exactly at the middle strike, and its price is tied to the probability the market assigns to that region.
Senzoukria · Glossary · Updated September 2026
At a glance
- Construction
- Long 1 low strike, short 2 middle strike, long 1 high strike
- Max payoff
- Distance between adjacent strikes, at the middle strike
- Risk (long)
- Limited to the debit paid
Worked example
Underlying at 100, 30 days, 20% implied volatility, zero rates. Buy the 95 call for 5.57, sell two 100 calls for 2.29 each, buy the 105 call for 0.64: the butterfly costs 5.57 − 4.57 + 0.64 = 1.64. At expiry it is worth 5 if the underlying is exactly at 100, declines linearly to 0 at 95 and 105, and is worthless outside. Breakevens are 96.64 and 103.36; the maximum gain is 5 − 1.64 = 3.36.
| Underlying at expiry | Value | P&L |
|---|---|---|
| 95 or below | 0 | −1.64 |
| 96.64 | 1.64 | 0 |
| 100 | 5.00 | +3.36 |
| 103.36 | 1.64 | 0 |
| 105 or above | 0 | −1.64 |
What the price of a butterfly says
Because a narrow butterfly pays off only if the underlying finishes near the middle strike, its price divided by its maximum payoff approximates the risk-neutral probability of that region, discounted. In the limit of very close strikes, the butterfly price per unit of width squared converges to the risk-neutral density of the terminal price. This is why no-arbitrage requires butterfly prices to be non-negative, a constraint that fitted volatility smiles must respect.
Greeks and uses
- Near the middle strike and close to expiry, a long butterfly is short gamma and long theta: it wants the underlying to stay still.
- Far from the middle strike, it becomes long gamma: it needs price to move back toward the centre.
- Traders use butterflies to target a price at expiry cheaply, for example near a large strike, and short-dated index butterflies are popular because their cost is low.
- The 1-2-1 ratio means the legs do not share a size, which matters for detecting them on a flow tape.
In Senzoukria
Senzoukria does not price butterflies. On its Option Flow tape, a butterfly's legs print in a 1-2-1 ratio, so the MULTI tag, which groups different contracts of the same size printed within 25 milliseconds, groups the two wings but not the doubled middle leg; the middle leg can then look like a large directional sale. The documentation notes that spread legs priced separately can defeat the detection rules.
Related
In the same section
- Buy-side and sell-side liquidity
- Bridge
- Buying and selling pressure
- Breakeven win rate
- CAGR
- Breakeven stop
- Calendar spread
- Bracket order
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Frequently asked questions
- Why are butterflies so cheap?
- Because they pay only in a narrow range around the middle strike, which the market assigns a limited probability. The cost reflects that probability; a cheap butterfly is not a bargain by default.
- Is a butterfly the same as the 25-delta butterfly in volatility markets?
- No. The 25-delta butterfly is a volatility quote measuring the curvature of the smile. The butterfly spread is a traded structure of three strikes. The names are related because both describe the relationship between the wings and the centre.