Final answer:
Using the put-call parity theorem, the value of the put option is calculated to be approximately $5.03, given the stock price, strike price, call option price, risk-free interest rate, and time to expiration. The correct option is D. $5.03.
Step-by-step explanation:
The question is asking to calculate the value of a put option based on the put-call parity theorem, which is a concept in financial mathematics used to price options. The put-call parity theorem states that the price of a European put option and a European call option with the same strike price and expiration date should be related in a certain way, given the current stock price, strike price, risk-free interest rate, and time to expiration.
According to the put-call parity equation:
C + X/(1+r)^T = P + S
Where:
- C is the price of the call option,
- X is the exercise price,
- r is the risk-free interest rate,
- T is the time to expiration (in years),
- P is the price of the put option,
- S is the current stock price.
Given the values:
- C = $3.45,
- X = $44,
- r = 4% (or 0.04 when expressed as a decimal),
- T = 90/365 (since there are 365 days in a year),
- S = $42.
We can rearrange the equation to solve for P:
P = C + X/(1+r)^T - S
After inserting the provided values and calculating, we find that the value of the put option is approximately $5.03. Therefore, the correct option is D. $5.03.