Answer-first summary for fast verification
Answer: $3.51
For a European call on a dividend-paying stock, the lower bound is \[ c \ge S_0 - D - Ke^{-rT} \] where \(D\) is the present value of dividends paid during the life of the option. Here: - \(S_0 = 24\) - Dividend = \$1.00 paid in 4 months - \(r = 5\%\) - \(T = 0.5\) years Present value of dividend: \[ D = 1 \times e^{-0.05 \times \frac{4}{12}} \approx 0.9835 \] Then: \[ c \ge 24 - 0.9835 - 20e^{-0.05 \times 0.5} \] \[ = 24 - 0.9835 - 20e^{-0.025} \approx 24 - 0.9835 - 19.5062 = 3.5103 \] Therefore, the lower bound is approximately **$3.51**.
Author: Manit Arora
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Q-180.4. A stock will pay a $1.00 dividend in four (4) months. What is the lower bound for the price of a six (6)-month European CALL option on the stock when the stock price is $24.00, the strike price is $20.00 and the risk-free interest rate is 5.0% per annum?
A
zero (0)
B
$3.51
C
$3.65
D
$4.49
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