The correct answer is: B. slight increases.
A rise in the risk-free rate will increase the value of a call option and decrease the value of a put option. This is because a higher risk-free rate makes it more expensive to borrow money, which in turn makes it more expensive to exercise a put option. It also makes it more attractive to hold a call option, as the potential payoff is greater.
Option pricing models take into account a number of factors, including the strike price, the underlying asset price, the time to expiration, the volatility of the underlying asset, and the risk-free rate. A rise in the risk-free rate will affect the value of an option by increasing the discount rate used to calculate the present value of the option’s payoff. This will make the option more valuable, as the present value of a future payoff is higher when the discount rate is lower.
The following is a brief explanation of each option:
- A. Slight time decreases: This is incorrect because a rise in the risk-free rate will actually increase the time value of an option. This is because a higher risk-free rate makes it more expensive to borrow money, which in turn makes it more expensive to exercise a put option. It also makes it more attractive to hold a call option, as the potential payoff is greater.
- B. Slight increases: This is the correct answer. A rise in the risk-free rate will increase the value of a call option and decrease the value of a put option.
- C. Slight decreases: This is incorrect because a rise in the risk-free rate will actually increase the value of an option.
- D. Slight time increases: This is incorrect because a rise in the risk-free rate will actually decrease the time value of an option.