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The "desired position" in the image is a set of slopes $(0,1,-1,0)$, and a set of strike prices between these slopes $\mathbf{K}=(98,100,102)$.

The payoff is then designed by finding the positions $n_1,n_2,n_3$ in three call options

$$c_1=(0,1,1,1)\mathbf{K}$$ $$c_2=(0,0,1,1)\mathbf{K}$$ $$c_3=(0,0,0,1)\mathbf{K}$$

So that they total the desired payoff $(0,1,-1,0)$.

In this case of a butterfly spread, the required postions are $n_1=1$ $n_2=-2$ and $n_3=1$.

Any points to litterature where this method is used is appreciated. Designing a butterfly spread

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