Answer: 2.37

## Explanation This is a Black-Scholes option pricing problem for a European put option. The key parameters are: - **Stock price (S)**: $50 - **Strike price (K)**: $50 - **Time to expiration (T)**: 3 months = 0.25 years - **Risk-free rate (r)**: 10% = 0.10 - **Volatility (σ)**: 30% = 0.30 - **Dividend yield**: 0 (non-dividend-paying stock) ### Black-Scholes Formula for Put Option: \[ P = Ke^{-rT}N(-d_2) - SN(-d_1) \] Where: \[ d_1 = \frac{\ln(S/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}} \] \[ d_2 = d_1 - \sigma\sqrt{T} \] ### Calculations: 1. **Calculate d₁**: \[ d_1 = \frac{\ln(50/50) + (0.10 + 0.30^2/2) \times 0.25}{0.30 \times \sqrt{0.25}} = \frac{0 + (0.10 + 0.045) \times 0.25}{0.30 \times 0.5} = \frac{0.145 \times 0.25}{0.15} = \frac{0.03625}{0.15} = 0.2417 \] 2. **Calculate d₂**: \[ d_2 = d_1 - \sigma\sqrt{T} = 0.2417 - 0.30 \times 0.5 = 0.2417 - 0.15 = 0.0917 \] 3. **Calculate N(-d₁) and N(-d₂)**: \[ N(-d_1) = N(-0.2417) = 0.4045 \] \[ N(-d_2) = N(-0.0917) = 0.4634 \] 4. **Calculate put option price**: \[ P = 50 \times e^{-0.10 \times 0.25} \times 0.4634 - 50 \times 0.4045 \] \[ P = 50 \times e^{-0.025} \times 0.4634 - 20.225 \] \[ P = 50 \times 0.9753 \times 0.4634 - 20.225 \] \[ P = 22.59 - 20.225 = 2.365 \] Rounded to two decimal places, the put option price is **$2.37**, which corresponds to option A. ### Verification: This result makes sense because: - The option is at-the-money (S = K) - With 3 months to expiration and 30% volatility, there's significant time value - The put-call parity relationship also confirms this result

Author: LeetQuiz .