Prove that [begin{aligned}C_{E}(x, K ; r, delta ; T-t) & =P_{E}^{*}left(K e^{-mu(T-t)}, x e^{mu(T-t)} ; T-t ight)

Prove that

\[\begin{aligned}C_{E}(x, K ; r, \delta ; T-t) & =P_{E}^{*}\left(K e^{-\mu(T-t)}, x e^{\mu(T-t)} ; T-t\right) \\& =e^{-\mu(T-t)} P_{E}^{*}\left(K, x e^{2 \mu(T-t)} ; T-t\right),\end{aligned}\]where \(\mu=r-\delta\) is called the cost of carry.