What Role Does the Risk-Free Rate Play in Options Pricing Models like Black-Scholes for Long-Dated Contracts?

The risk-free rate is used to discount the expected future payoff of the option back to its present value. For long-dated contracts, this discounting effect is more pronounced.

A higher risk-free rate generally increases the theoretical price of a call option and decreases the theoretical price of a put option, reflecting the time value of money.