Consider the lognormal random variables $X_1$ and $X_2$ with $\log(X_1)\sim \mathcal{N}(0,1)$, and $\log(X_2)\sim \mathcal{N}(0,\sigma^2)$. I'm trying to calculate $\rho_{\max}$ and $\rho_{\min}$ for $\rho (X_1,X_2)$. One step in the given solution I have is: $\rho_{\max}=\rho (\exp(Z),\exp(\sigma Z))$ and $\rho_{\min}=\rho (\exp(Z),\exp(-\sigma Z))$, but they've made some references to comonotonicity and countercomonotonicity. I was hoping someone help me understand how they're relevant. (I know how to get this from the general expression but want to know specifically what the comonotonicity parts were saying.)