Rho – Options Sensitivity to Interest Rates

Interest rates are one of the pillars of our market economies. Hence, the pricing of options, both vanilla and exotic ones, is impacted by interest rates and their movements. Rho is one of the most common greeks when dealing with options. Indeed, it measures the sensitivity of the option price related to a change in the risk-free rate.

Call & Put Rho: It is interesting to note that a call option will always have positive Rho while a put option will always have a negative Rho. It means that if interest rates rise by 1% for example, call options will be more expensive after the surge, and put options value will decrease accordingly.

For example:

XYZ call option with K = 100 and Dec21 maturity have a Rho of 0.25 and cost \$2.00.

XYZ put option with K = 100 and Dec21 maturity have a Rho of -0.30 and cost \$2.20.

If the risk-free rate rises by 1%:

XYZ call option value will be: 2.00 + (0.25*1) = \$2.25

XYZ put option value will be: 2.20 + (-0.30*1) = \$1.90

If the risk-free rate drops by 1%:

XYZ call option value will be: 2.00 + (0.25*(-1)) = \$1.75

XYZ put option value will be: 2.20 + (-0.30*(-1)) = \$2.50

Additionally, Rho is larger for ITM options and drops steadily as the option changes to become OTM. Also, rho increases as the time to expiration increases. Then, long-dated options will have a bigger Rho compared to short-dated options.