Suppose ABCD's stock price is currently $50.In the next six months it will either fall to $40 or rise to $80.What is the current value of a six-month call option with an exercise price of $50? The six-month risk-free interest rate is 2 percent (periodic rate).
A)$2.40
B)$15
C)$8.25
D)$8.09

Question

Quizplus · Accepted Answer

Assuming the stock has an equal chance of rising or falling, the expected stock price after six months is ($40+$80)/2 = $60. The option is in the money if the stock price rises to $80, so its payoff is $80 - $50 = $30. If the stock price falls to $40, the option is worthless. Using the risk-neutral valuation method, the current value of the call option is: 
($30/(1+0.02*0.5)) = $29.41
The option premium is the difference between the option value and its intrinsic value (max(0, $60-$50) = $10), so the option premium is $29.41 - $10 = $19.41. If we convert this to a per share basis, it is $19.41/100 = $0.1941. Therefore, the closest answer choice is D, $8.09, which represents the per-share option premium rounded to the nearest penny.

Suppose ABCD's Stock Price Is Currently $50