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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.

How Does the ‘Rho’ Greek Relate to Long-Term Inventory Risk?
How Does ‘Rho’ (The Interest Rate Greek) Impact Long-Term Options Pricing?
How Does an Increase in Interest Rates Generally Affect the Price of a Call Option?
Why Is the Interest Rate a More Significant Factor in the Early Exercise of an American Put than a Call?