Answer-first summary for fast verification
Answer: $14.32
For a forward-start **at-the-money** call, the value today is the current value of the corresponding ATM call with the same remaining term, discounted by the dividend yield over the start period. A useful shortcut here is: $$V_0 = e^{-qT_1} C_{1}$$ where: - $q = 5\%$ is the continuous dividend yield, - $T_1 = 1$ year, - $C_1 = 15.05$ is the one-year ATM European call price today. So: $$V_0 = e^{-0.05} \times 15.05 \approx 0.95123 \times 15.05 \approx 14.32$$ Thus the nearest answer is **B**. ### Why this works The forward-start ATM call begins in one year, and at the start date its strike is set to the then-current stock price. Under standard lognormal assumptions, the option’s value scales with the stock and the initial price is the one-year ATM call price adjusted for dividends over the waiting period.
Author: Manit Arora
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The price of a vanilla (non-exotic) at-the-money European call option, today, with a one-year maturity is $15.05; if we extend the maturity to two years, the price of the option is $22.58. Now consider a forward start at-the-money European call option, on the same underlying stock, that will start in one year ( year) and mature one year later, two years from today ( year = 2.0 years). The continuous dividend yield on the underlying stock is 5.0% per annum, and the risk-free rate is 3.0% per annum; both are expressed with continuous compounding. Which is NEAREST to today’s price of the forward start option?
A
$13.89
B
$14.32
C
$14.61
D
$21.48
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