The butterfly spread: delta

By roma, 10 January, 2021

Butterfly spread has certain characteristics that depend on sensitivity to price variations in the underlying asset, its delta ∆.

Butterfly spread is easy to implement and, when bought, offers the prospect of significant but limited gains in exchange for a small investment.

Butterfly as the sum of two spreads 

The butterfly spread can be broken down into two spreads, one spread needs to be bought and one to be sold. For example, let's take a call butterfly 80/100/120 1 year, this is the purchase of 1 call 80, the sale of 2 calls 100 and the purchase of 1 call 120.

The strategy can be broken down into two:
- buying one call spread 80/100
- sale of a 100/120 call spread

The key idea of this decomposition will appear later when we study the butterfly spread in depth, in particular its behavior with respect to movements in the implied volatilities of the options that compose it, when the volatilities are not identical in value or movement.

Sensitivity to spot variations, the DELTA ∆ of the butterfly spread

Butterfly spread is sensitive to spot variations in that it generates highest profit when the spot is at the level of the sold strike (middle strike). As soon as you move away from this strike, the butterfly loses value. But this loss is limited.

butterfly spread price

 

Implicitly we deduce that the value of the butterfly is 0 at the extremities.

Translated in trading terms, "The delta must be zero at the ends and the center of the butterfly."

The butterfly gains value between 0 and the center of the butterfly, and then loses value until it reaches 0.

The graphical representation of the delta ∆ of the butterfly (10 days to expiration date) is shown here:

The butterfly delta

Note that the more distant the expiration date, the delta of the butterfly is less important.

Why is this? Because the longer the maturity is, the more the option deltas are similar. The purchases and sales offset each other and the final result is almost zero: very small delta.

On the other hand, the longer the expiration, the less expensive the butterfly is.

Conclusion

We can take advantage of the spot variations on a butterfly if expiration date is not far away. As we approach the expiration date, delta will react the most, in one direction or the other (increase in value, loss of value).

As far as the butterflies with expiration far away, it is clear that delta makes almost no impact on the butterfly spread price. There is certainly another factor, and we will see that soon.