Butterfly Spread

Overview

The Butterfly Spread is the strategy for the trader who has a "Pin" target. It is a neutral strategy that uses three different strike prices to create a sharp "peak" of profit.

If you think a stock will be exactly $100 in two weeks—not $105, and not $95—the Butterfly is the most capital-efficient way to express that view.

[!TIP] Think of a Butterfly as a "tent." The peak of the tent is where you make the most money. If the stock wanders away from the tent poles (the wings), you lose your entry fee.

The Setup

A Long Call Butterfly consists of:

1. Lower Wing ($K_L$): Buy 1 Call (OTM or ITM)
2. Body ($K_M$): Sell 2 Calls at the middle strike (ATM)
3. Upper Wing ($K_H$): Buy 1 Call (further OTM)

Mechanics of the "Pin"

Why sell two calls in the middle?

• You want the stock to stay right at the strike of those two calls.
• If the stock ends at exactly $K_M$, your lower call is profitable, and your two short calls expire worthless.
• The cost to enter a Butterfly is very low because the two short calls you sold pay for almost all of the two long calls you bought.

Payoff and Break-even

Max Profit

The distance between the strikes minus the debit paid:

$$\text{Max Profit} = (\text{Strike Width}) - \text{Net Debit}$$

Max Loss

Simply the net debit you paid to enter the trade.

Break-even Points

• Lower BE: $K_L + \text{Debit}$
• Upper BE: $K_H - \text{Debit}$

The "Micro-Greeks"

Butterfly spreads have very unusual Greeks because the three strikes are so close together.

1. Delta: Directionally Indifferent

At the start, a Butterfly has nearly zero Delta. However, as the stock moves, the Delta flips sign.

• If the stock is below the peak, Delta is positive (you want it to go up toward the peak).
• If the stock is above the peak, Delta is negative (you want it to come back down to the peak).

2. Theta: The Closing Window

Theta is your friend if the stock is inside the tent. As expiration approaches, the "tent" gets taller and narrower. This is called "Time Decay working for the pin."

3. Vega: Sensitivity to Calm

Butterfly buyers are Short Volatility. If the market starts swinging wildly, the probability of the stock "pinning" a specific price drops, and the value of your butterfly will fall.

Strategic Variations

• Broken Wing Butterfly: You make one wing wider than the other. This removes the risk on one side of the trade, but increases it on the other.
• Iron Butterfly: Use both puts and calls. It results in the same payoff but is entered for a credit.

Checklist for Entry

• Do I have a high-conviction Target Price?
• Is the risk/reward attractive? (Butterflies often have 1:10 or better R/R).
• Is the stock stable? (Avoid butterflies on meme stocks or high-beta names).

Interpreting the 'Tent' with ProbabilityRead more

In quantitative finance, the price of a butterfly is used to estimate the Probability Density Function (PDF) of the stock's future price.

If butterflies at a certain strike are becoming more expensive, it means the market "believes" more strongly that the stock will finish at that specific price. By buying a butterfly, you are essentially buying a narrow slice of the probability distribution.