Answer: 2.37

## 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.

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