Answer-first summary for fast verification
Answer: All are true
All four statements are true: - **I:** Intrinsic value is \(110 - 95 = 15\), so time value is \(20.52 - 15 = 5.52\). - **II:** With no dividends, the lower bound for a European call is \(S_0 - Ke^{-rT} \approx 110 - 95e^{-0.03} \approx 17.81\). - **III:** With dividend PV of 3.35, the lower bound becomes \(S_0 - PV(dividends) - Ke^{-rT} \approx 14.46\), which is below intrinsic value \(15\). - **IV:** For an American call on a dividend-paying stock, early exercise may be optimal. Therefore, the correct choice is **D. All are true**.
Author: Manit Arora
Ultimate access to all questions.
Q-724.3. Assume a European call option has an exercise (aka, strike) price, K = $95.00, and a time to expiration of one year. The risk-free rate is 3.0% per annum. The current stock price, S(0) = $110.00 and the stock pays a 3.0% dividend (the dividend happens to equal to the risk-free rate!) and this dividend has an equivalent lump sum present value (PV) over the life of the option equal to $3.35. Consider the following statements about this call option:
I. If the option's value is $20.52, then it's time value is about $5.52
II. If the stock does NOT pay any dividends, the minimum value (lower bound) of this European option would be about $17.81
III. If the stock pays a 3.0% dividend with a discounted present value (over the life of the option) equal to $3.35, then the minimum value of this European option is below its intrinsic value
IV. If this were instead an American option, and if the stock pays a dividend, then it might be optimal to exercise early
Which of the above statements is (are) TRUE?
A
None are true
B
Only I. is true
C
Only II. and IV. are true
D
All are true
No comments yet.