Power put-call parity
= Power put-call parity
{title2=$C_\beta-P_\beta=S^\beta e^{[\lambda_\beta-r](T-t)}-K^\beta e^{-r(T-t)}$}
The difference of the terminal power-call and power-put payoffs is $S_T^\beta-K^\beta$. <Risk-neutral pricing> and the <geometric Brownian motion> moment formula therefore give the displayed parity, with $\lambda_\beta=\beta(r-q)+\sigma^2\beta(\beta-1)/2$. At $\beta=1$ this reduces to dividend-adjusted <put-call parity>.