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Note that \begin{align*} Call_{\rm BTC}=\frac{1}{S}Call_{\rm USD}. \end{align*} The premium adjusted delta $Delta_{PA}$ is defined as the change of $Call_{\rm BTC}$ with respect to the change of the spot in BTC, that is, \begin{align*} Delta_{PA} &= \lim_{\Delta S\rightarrow 0}\frac{\Delta Call_{\rm BTC}}{\frac{\Delta S}{S}}\\ &=\lim_{\Delta S\...