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delta-symmetric strike

Whereas the choice $K=f$ produces identical values for call and put, we seek the strike $\check{K}$ which produces absolutely identical deltas (spot, forward or driftless). This condition implies $d_+=0$ and thus

\begin{displaymath} \check{K}=fe^{\frac{\sigma^2}{2}T}, \end{displaymath} (27)

in which case the absolute delta is $e^{-r_f\tau}/2$. In particular, we learn, that always $\check{K}>f$, i.e., there can't be a put and a call with identical values and deltas. Note that the strike $\check{K}$ is usually chosen as the middle strike when trading a straddle or a butterfly. Similarly the dual-delta-symmetric strike $\hat{K}=fe^{-\frac{\sigma^2}{2}T}$ can be derived from the condition $d_-=0$.



2000-06-11
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