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.

1. 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.)

2. 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?

Answer 1

Given Data

Spot Price=$100
3m Call option with Ex Price of $100 =$10
Stock pays no dividend
Require Put Premium
Risk free rate=10%
3 month interest=10*3/12=2.5%

Put Call Parity Theorem:

Call premium + Exercise price/(1+r)=Spot Price+ Put Premium

10+100/1.025=100+P

Solving we get P=7.56098

Now as we expect that with in a period of 3 months there will be a break out in price of stock.

if we expect that there would be a upside break out than we can but the call option @ $10 and any price above 110 would give us profit.

if we expect that there would be a downside break out than we can but the call option @ $7.56098 and any price below 92. 45 would give us profit.

However when we are not sure about which side the break out would be then we can buy both call and put option in any combination depending on our price expectation.
Suppose we buy 1 call option and 1 put option then our total premium would be $17.56098 and any price below 82.45 or above 117.60 would give us a profit.