Question

SOLVE

1. The common stock of PUTT Corp 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.
   
   1. If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on PUTT stock at an exercise price of $100? (The stock pays zero dividends.)
      
      

b.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

a.

Price of the put option will be derived using the Put-call parity equation :-

Price of the call option + Present Value of the strike price (x), discounted from the value on the expiration date at the risk-free rate = Price of Put option + Current Price of Stock

$10 + (100) / (1+0.10)^(3/12) = Price of Put option + 100

$10 + 97.64 = Price of Put option + 100

Price of Put option = 7.65

b.

To exploit the conviction about the stock price’s future movements, we will use long straddle.

Long Straddle implies buying the call and put options of the same exercise price and expiry dates. It is a non-directional options strategy which benefits when the underlying stock breaks far out of the range.

In this case, we will buy both the call and put options having the exercise price of $100, resulting into an initial outlay of

= $ (10 + 7.65) =$17.65

Break-even price on upside = $ (100 + 17.65) = $117.65

Break-even price on downside = $ (100 - 17.65) = $82.35

The Stock should either move above $117.65 or go down below $82.35 for us to make a profit on this position.