What is the price of the put on the stock with the same exercise and strike as the call?

A stock sells for $100, and a call on the same stock for one year hence at a strike price of $100 goes for $35.

What is the price of the put on the stock with the same exercise and strike as the call? Assume the stock pays dividends at 1% per year at the end of the year and interest rates are 5% annually.
A . $41.50
B . $31.20
C . $35
D . $31.95

View Answer

Answer: B

Explanation:

We know from the put-call parity that:

Call – Put = Stock – Deposit

In the given situation,

Stock price = 100

call = 35

Put = ?

Exercise price = 100

However, we cannot use the stock price as-is, we need to adjust it for dividends that will be received during the period for which the option is valid. Dividends are $1, which need to be discounted to the present. In financial theory, dividends are often assumed to be continuously paid, though in reality they are single discrete payments at points in time. In this situation, for simplicity we assume that the dividend is paid at the end of the year, and needs to be discounted to the present and deducted from the spot price. Therefore:

Stock price adjusted for dividends = $100 – ($1/1.05) = $100 – $0.95 = $99.05

Similarly, the bank deposit amount, which is the PV of the exercise price, can be calculated as $100/1.05 = $95.24

We can now calculate the price of the put by plugging the numbers above in the put-call parity:

35 – Put = $99.05 – $95.24

Therefore the value of the put = 31.19, which is closest to 31.20 which therefore is the correct answer.