How Does an Increase in Interest Rates Affect the Price of a Put Option?

An increase in interest rates generally leads to a decrease in the price of a put option. This is because higher interest rates increase the present value of the proceeds received upon exercising the put option (selling the stock).

However, the primary effect is that the cost of carry is lower for the seller of the put option, which reduces the premium. The negative Rho of a put option mathematically confirms this inverse relationship.