Greeks
Rho
Rho measures the change in an option's price for a one-percentage-point change in the risk-free interest rate. Calls have positive rho and puts negative rho, and the effect is largest for long-dated options.
Rho is usually the least influential Greek. For short-dated options it is negligible, but for LEAPS on a high-priced stock a one-point rate change can move prices by meaningful dollars, because higher rates raise the cost of carrying the shares a call replaces and lower the present value of the strike a put protects.
Rate changes also feed put-call parity and the forward price, so persistent rate shifts show up as a change in the fair relationship between calls and puts at the same strike.
Formula
Rho = ∂V / ∂r
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Frequently asked questions
When does rho matter?
For options with a year or more to expiration during periods when central banks are moving rates. For weeklies and monthlies it is almost always immaterial.