Question

The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. The current price of the stock is $100 per share, and the price of a 3-month call option at an exercise price of $100 is $10.
Required:
a. If the risk-free interest rate is 5% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $140?
b. What would be a simple options strategy to exploit your conviction about the stock price?

Answer 1

Answer:

A. $7.65

B. $ 17.65

$ 18.07

Explanation:

A. Calculation to determine the price of a 3-month put option on P.U.T.T. stock at an exercise price of $100

Using this formula

P = C-S+[X/(1+r)T]

Let plug in the formula

P = 10-100+[100/(1+0.10)1/4]

P = 10-100+[100/(1.10)1/4]

P = 10-100+[100/1.0241]

P = 10-100+97.65

P = 10-2.35

P = $7.65

Therefore the price of a 3-month put option on P.U.T.T. stock at an exercise price of $100 will be $7.65

B. Calculation for the Stock price future movements

Total cost of straddle option = $10+$ 7.65

Total cost of straddle option= $ 17.65

Therefore Stock price future movements is $ 17.65

Calculation to determine the profit on your initial investment

Profit=$ 17.65*(1.10)^1/4

Profit=$ 17.65*1.0241

Profit= $ 18.07

Therefore the profit on your initial investment will be $ 18.07