# How to understand broken wing butterfly option strategies?

I feel very confused about the greeks analysis for the broken wing butterfly strategy.

Let's say for the stock ABC, we enter into a such strategy: we long a put option with strike $$k_1$$ and another put option with strike $$k_3$$，and at the same time short two put options with strike $$k_2$$, where $$k_2-k_1>k_3-k_2$$.

Then what I read tells me that this position is possibly a net debit or a net credit when starting with. Intuitively, if $$k_1$$ is too low, then the strategy should be a net credit. Intuitively, if the stock price is above $$k_3$$, the $$\Theta$$ should be positive since I profit from time decay. At expiration all puts will become worthless. But if $$k_1$$ is not that low, I can imagine it would be a net debit position when entering, then the $$\Theta$$ would be negative since I will lose money from time decay.

How to understand such behavior of this strategy. And another confusion is, if I enter the strategy with net debit, I will have two break even price; but if I enter with net credit, I will have only one. This also seems strange to me. So what determines if I enter with debit or credit, and how to understand the behavior of this strategy? Thank you so much!

• although it uses no math, I found this article useful tickertape.tdameritrade.com/trading/… especially the idea of starting from a butterfly (which we already understand) and adding a vertical spread to "move" one of the legs away. So a broken butterfly (bbf) is a combination of two things: bf+vertical spread. – noob2 Jul 13 at 20:18

Intuitively, if $$k_1$$ is too low, then the strategy should be a net credit.
That is an incorrect conclusion. The lower that $$k_1$$ is, the larger the credit will be or the lower the debit cost will be. Bear in mind that $$k_3$$ also affects cost. The deeper ITM it is, the more it costs, and vice versa..
The distance of $$k_1$$ and $$k_3$$ from $$k_2$$ determines the cost of the respective legs. The further away from $$k_2$$ they are, the less $$k_1$$ costs and the more $$k_3$$ costs. The more that $$k_3$$ is ITM, the greater its cost, eventually exceeding $$k_2 - k_1$$, resulting in a debit spread.
IOW, if the spread credit is greater than $$k_3 - k_2$$, there is no upside risk and there is only one break-even.