Answer: increase the value of a long put.

## 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**.

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