
Explanation:
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:
where:
So:
Thus the nearest answer is B.
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.
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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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