Suppose VS's stock price is currently $20.In the next six months it will either fall by 50 percent or rise by 50 percent.What is the current value of a call option with an exercise price of $15 and expiration of one year? The six-month risk-free interest rate is 5 percent (periodic rate).Use the two-stage binomial method.
A)$5
B)$2.14
C)$7.86
D)$8.23

Question

Quizplus · Accepted Answer

The correct answer is D.The current value of the call option can be calculated using the two-stage binomial method. The first step is to calculate the value of the option at the end of the first six months. There are two possible scenarios: the stock price either falls by 50 percent or rises by 50 percent. If the stock price falls by 50 percent, the value of the option will be zero. If the stock price rises by 50 percent, the value of the option will be $5.The next step is to calculate the value of the option at the end of the second six months. There are again two possible scenarios: the stock price either falls by 50 percent or rises by 50 percent. If the stock price falls by 50 percent, the value of the option will be zero. If the stock price rises by 50 percent, the value of the option will be $10.The final step is to discount the value of the option at the end of the second six months back to the present using the six-month risk-free interest rate of 5 percent. The present value of the option is $8.23.

Suppose VS's Stock Price Is Currently $20