How Does the Concept of ‘Rho’ (Interest Rate Sensitivity) Relate to the Non-Optimality of Early Exercise?
Rho measures the change in an option's price for a one-percent change in the risk-free interest rate. For an American call, a positive rho means the option's value increases with higher interest rates.
This is because higher rates increase the benefit of delaying the capital outlay (buying the asset). The positive rho reinforces the non-optimality of early exercise.