Cliquet option. Let \(0=T_{0}
\[
\begin{aligned}
\mathrm{e}^{-r T} \mathbb{E}^{*}\left[\left(S_{T}-\kappaight)^{+}ight]= & S_{0} \Phi\left(\frac{\log \left(S_{0} / \kappaight)+\left(r+\sigma^{2} / 2ight) T}{|\sigma| \sqrt{T}}ight) \\
& -\kappa \mathrm{e}^{-r T} \Phi\left(\frac{\log \left(S_{0} / \kappaight)+\left(r-\sigma^{2} / 2ight) T}{|\sigma| \sqrt{T}}ight), \quad T>0
\end{aligned}
\]