Explanation:
The lower bound of a European call option on a dividend-paying stock is calculated using the formula:
C >= max(0, S0 - PV(Dividends) - PV(Strike))
$5 / (1 + 0.03)^(1/6) = $4.9754$5 / (1 + 0.03)^(1/3) = $4.9510$5 / (1 + 0.03)^(1/2) = $4.9267
Total PV(Dividends) = 4.9754 + 4.9510 + 4.9267 = 14.8531Calculate the Present Value of the strike price (K = $45, T = 1 year):
PV(K) = 45 / (1 + 0.03)^1 = 43.6893
Compute the lower bound: C >= 60 - 14.8531 - 43.6893 = 1.4576 (approx USD 1.46).
Option B is correct.
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Q.20 Suppose that the current stock price is USD 60. Suppose further that the stock is expected to pay dividends of USD 5 in two months, four months, and six months. If the risk-free rate is 3% per annum (with annual compounding) for all maturities, what is the lower bound of a one-year European call option on the stock if the strike price is USD 45?
A
The European call option price must be at least USD 0.
B
The European call option price must be at least USD 1.46.
C
The European call option price must be at least USD 0.15.
D
The European call option price must be at least USD 0.22.