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% (periodic rate).
A)$2.40
B)$15.00
C)$8.25
D)$8.09

Question

Quizplus · Accepted Answer

To calculate the value of a call option, we use the formula: 
Option Value = e^(-r*t) * [p * S - K * (1-p)]
where
r = 2% (the risk-free interest rate)
t = 6/12 = 0.5 (the time to expiration)
p = probability of the stock rising = 0.5 (given that it will either rise or fall)
S = current stock price = $50
K = exercise price = $50

Plugging in the values, we get:
Option Value = e^(-0.02*0.5) * [0.5 * 80 - 50 * (1-0.5)] = $8.09

Therefore, the value of the six-month call option with an exercise price of $50 is $8.09, which is closest to option D.

Suppose ABCD's Stock Price Is Currently $50