Butterfly Spread

A butterfly spread is an options strategy that uses three strike prices on the same underlying asset and expiry. In its standard long form, the trader buys one option at a lower strike, sells two options at a middle strike, and buys one option at a higher strike, with the strikes equally spaced. The position makes its largest profit if the underlying finishes exactly at the middle strike and has a small, fixed maximum loss.

The name comes from the shape of the payoff diagram: a peak in the center (the body) and two flat sections on either side (the wings). A long butterfly is a bet that the price will stay close to a chosen level, and so a bet on low realized volatility. It is an option spread with defined risk, in contrast to a short straddle, which expresses a similar view with unlimited risk.

A long call butterfly consists of four contracts: one long call option at the lower strike, two short calls at the middle strike, and one long call at the upper strike. It can be seen as two vertical spreads joined together: a bull call spread from the lower to the middle strike and a bear call spread from the middle to the upper strike.

The same payoff can be built entirely from puts. Because of put-call parity, a call butterfly and a put butterfly at the same strikes should cost almost the same. The middle strike is usually set near the current price, making the short options at the money, though it can be placed elsewhere to target a different price.

For a long butterfly with strikes $K_1$, $K_2$ and $K_3$, equally spaced:

• $K_1$, $K_2$ and $K_3$ are the lower, middle and upper strike prices.
• Net premium paid is the cost of the two options bought minus the amount received for the two sold.

A share trades at $100. A trader buys the $95 call for $7.00, sells two $100 calls for $4.00 each, and buys the $105 call for $2.00. The net premium is 7.00 + 2.00 − 8.00 = $1.00. The maximum loss is $1.00, reached if the share finishes at or below $95 or at or above $105. The maximum profit is (100 − 95) − 1.00 = $4.00, reached only at exactly $100. The break-even prices are $96 and $104.

If the share finishes at $98, the $95 call is worth $3 and the others expire worthless, giving a profit of 3 − 1 = $2 per share.

A butterfly centered on the current price starts with delta close to zero. It gains from the passing of time, measured by theta, as long as the price stays near the middle strike, and it loses when implied volatility rises. Its gamma is negative near the center, meaning that price movement away from the middle strike hurts.

These effects are weak when expiry is far away. A butterfly's value changes slowly for most of its life and then very quickly in the final days, when small price moves around the middle strike decide whether it finishes near its maximum or near zero. The full profit is rarely captured, and many traders close the position once a good part of it has been earned.

• Short butterfly. The reverse position, which sells the wings and buys the body, profits from a large move in either direction. See short butterfly.
• Iron butterfly. This uses puts below the middle strike and calls above it. The trader sells a call and a put at the middle strike and buys an out-of-the-money put and call as wings, receiving a net credit. Its payoff matches the long butterfly.
• Broken-wing butterfly. The strikes are unequally spaced, which removes the risk on one side or creates a credit, in exchange for greater risk on the other.
• Condor. A condor spread splits the body across two middle strikes, widening the profitable zone and lowering the peak. The iron condor is its credit form.

The loss on a long butterfly is small in money terms but is also the most likely result. The price has to finish inside a narrow band for the trade to pay, and the peak profit requires an exact finish. A low cost relative to the maximum payoff reflects that low probability and should not be read as a bargain.

Four contracts mean four commissions and four bid-ask spreads, which can absorb a large share of a small expected gain. With American-style options, the short middle options may be assigned early. If the price is near the middle strike at option expiry, the trader cannot be sure how many of the short options will be assigned, and may be left with an unplanned share position after the close.

Butterflies also have an analytical use. The price of a narrow butterfly at a given strike shows how much the market is willing to pay for a payoff at that price alone. Read across all strikes, butterfly prices reveal the probability distribution implied by option prices, which is closely linked to the volatility smile.