delta-symmetric strike

Whereas the choice 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 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

2000-06-11