Explanation

This is a standard Black-Scholes put option pricing problem. For a European put option on a non-dividend-paying stock:

$P = K e^{-rT} N(-d_2) - S_0 N(-d_1)$

Where:

• $S_0 = 50$ (current stock price)
• $K = 50$ (strike price)
• $T = 0.25$ (3 months = 0.25 years)
• $r = 0.10$ (risk-free rate)
• $\sigma = 0.30$ (volatility)

First, calculate $d_1$ and $d_2$:

$d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}} = \frac{\ln(50/50) + (0.10 + 0.30^2/2) \times 0.25}{0.30 \times \sqrt{0.25}}$ $d_1 = \frac{0 + (0.10 + 0.045) \times 0.25}{0.30 \times 0.5} = \frac{0.145 \times 0.25}{0.15} = \frac{0.03625}{0.15} = 0.2417$

$d_2 = d_1 - \sigma\sqrt{T} = 0.2417 - 0.30 \times 0.5 = 0.2417 - 0.15 = 0.0917$

Calculate the normal CDF values for the put formula:

• $N(-d_1) = N(-0.2417) \approx 0.4045$
• $N(-d_2) = N(-0.0917) \approx 0.4635$

Compute the put price: $P = 50 \times e^{-0.10 \times 0.25} \times 0.4635 - 50 \times 0.4045$ $P = 50 \times 0.9753 \times 0.4635 - 20.225$ $P = 22.60 - 20.225 = 2.375$

The price is approximately $2.37, which matches Option A.