Explanation

For options pricing using the Black-Scholes model:

Call options:

• Higher risk-free rates increase call option values
• Lower risk-free rates decrease call option values

Put options:

• Higher risk-free rates decrease put option values
• Lower risk-free rates increase put option values

This relationship exists because:

• For calls: Higher rates reduce the present value of the strike price, making calls more valuable
• For puts: Higher rates reduce the present value of the expected future stock price, making puts less valuable

Therefore, a decrease in the risk-free rate will increase the value of a long put.