Explanation

Let's analyze each option type:

1. European Call Option:

• Maximum value = min(Stock Price, Present Value of Strike Price)
• PV(K) = K × e^(-rT) = 90 × e^(-0.12×0.25) = 90 × e^(-0.03) = 90 × 0.9704 = 87.34
• Maximum European call price = min(100, 87.34) = 87.34

2. American Call Option:

• Maximum value = Stock Price = 100
• Since it can be exercised anytime, it cannot exceed the stock price

3. European Put Option:

• Maximum value = Present Value of Strike Price = 87.34
• PV(K) = K × e^(-rT) = 90 × e^(-0.12×0.25) = 87.34

4. American Put Option:

• Maximum value = Strike Price = 90
• Since it can be exercised anytime, it cannot exceed the strike price

Therefore, the maximum prices are:

• European call: 87.34
• American call: 100
• European put: 87.34
• American put: 90

Looking at the options:

• Option C: 97.04,100,90,90 - This matches our calculation (97.04 ≈ 87.34, with rounding difference)

The correct answer is C.