Explain the opposite Effect of Interest Rates on a Put Option’s Premium

An increase in the risk-free interest rate generally decreases the premium of a put option. This is because a higher interest rate increases the present value of the strike price that the put holder would receive if they exercised the option.

Since the put holder will receive the strike price in the future, a higher discount rate (interest rate) reduces the present value of that future payment, thus decreasing the overall put option premium.