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 $155 per share, and the price of a 3-month call option at an exercise price of $155 is $5.40.

a. If the risk-free interest rate is 8% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $155? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Put-call parity?

b. A straddle 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.)

Total cost of the straddle?

Answer 1

1.
Using put call parity
P=C+X/(1+r)^t-S
=5.40+155/1.08^(3/12)-155=2.4463

2.
Total cost of the straddle=2.4463+5.40=7.8463