Suppose VS's stock price is currently $20. In the next six months it will either fall to $10 or rise to $30. What is the current value of a put option with an exercise price of $15? The six-month risk-free interest rate is 5 percent per six-month period.
A)$5.00
B)$2.14
C)$0.86
D)$7.86

Question

Quizplus · Accepted Answer

To solve this problem, we need to calculate the put option's intrinsic value at both possible stock prices ($10 and $30) and discount each value back to the present using the risk-free interest rate of 5% per six-month period.

If the stock price falls to $10, the put option will be worth $5 ($15 - $10), so the present value of this payoff is 5/1.05 = $4.76. 
If the stock price rises to $30, the put option will be worthless, so the present value of this payoff is zero.

The fair price of the put option is the average of these two present values: 
($4.76 + 0)/2 = $2.38

Therefore, the current value of a put option with an exercise price of $15 is $2.38, which is closest to choice (B): $2.14.

Suppose VS's Stock Price Is Currently $20