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Answer: USD 3.22
## Explanation In the Black-Scholes-Merton model for European call options with dividends, the stock price S₀ must be adjusted by subtracting the present value of expected dividends. ### Step 1: Calculate Present Value of Dividend - Dividend amount: USD 1.25 - Time to dividend payment: 1 month = 1/12 year - Risk-free rate: 3.5% per year Present Value of Dividend = $1.25 \times e^{-0.035 \times (1/12)} = 1.2464$ ### Step 2: Adjust Stock Price Adjusted S₀ = $60 - 1.2464 = 58.7536$ ### Step 3: Apply BSM Formula Call option price = $S_0 \cdot N(d_1) - K \cdot e^{-rT} \cdot N(d_2)$ Where: - S₀ = 58.7536 - K = 60 - r = 0.035 - T = 1 year - N(d₁) = 0.570143 - N(d₂) = 0.522623 Calculation: - First term: $58.7536 \times 0.570143 = 33.4978$ - Second term: $60 \times e^{-0.035 \times 1} \times 0.522623 = 60 \times 0.9656 \times 0.522623 = 30.2787$ - Call price = $33.4978 - 30.2787 = USD 3.2191 \approx USD 3.22$ Therefore, the correct call option price is USD 3.22.
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An analyst wants to price a 1-year, European-style call option on company REX's stock using the Black-Scholes-Merton (BSM) model. REX announces that it will pay a dividend of USD 1.25 per share on an ex-dividend date 1 month from now and has no further dividend payout plans. The relevant information for the BSM model inputs is in the following table:
| Current stock price (S₀) | USD 60 |
|---|---|
| Stock price volatility (σ) | 12% per year |
| Risk-free rate (r) | 3.5% per year |
| Call option exercise price (K) | USD 60 |
| N(d₁) | 0.570143 |
| N(d₂) | 0.522623 |
What is the price of the 1-year call option on the stock?
A
USD 2.40
B
USD 3.22
C
USD 3.97
D
USD 4.81
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