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% (periodic rate).
A) $5.00
B) $2.14
C) $0.86
D) $7.86

Question

Quizplus · Accepted Answer

To calculate the value of the put option, we need to use the following formula:
Put Option Value = Max(Exercise Price - Stock Price, 0) / (1 + Risk-Free Interest Rate)^(Time to Expiration)
Time to Expiration = 6 months / 12 = 0.5 years

If the stock price falls to $10, the put option would be exercised, and the payoff would be $15 - $10 = $5.
If the stock price rises to $30, the put option would not be exercised, and the payoff would be $0.
Therefore, the expected payoff is ($5 + $0)/2 = $2.50.

Plug in the values into the formula, we get:
Put Option Value = Max($15 - $20, 0) / (1 + 5%)^0.5
Put Option Value = $0 / 1.025
Put Option Value = $0

Since the option will only be exercised if the stock price falls below the exercise price, and there is a 50% chance of that happening, the expected value of the put option is $2.50 * 50% = $1.25.

Therefore, the current value of the put option is:
$1.25 / (1 + 5%)^0.5 = $1.17

The closest option is B) $2.14, which is the rounded up value of $1.17.

Suppose VS's Stock Price Is Currently $20