The common stock of the P.U.T.T. Corporation has been trading in a narrow price

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 3 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.

If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $100? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

What would be a simple options strategy to exploit your conviction about the stock price’s future movements? How far would it have to move in either direction for you to make a profit on your initial investment? (Round your intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.)

If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $100? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Explanation / Answer

a)

C + X*EXP(-r*T) = P + S

P = C + X*EXP(-r*T) - S

= 10 + 100*EXP(-10%*3/12) - 100

= 7.53

b)

Straddle = Long call + long put

= 10 + 7.53

= 17.53

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