Question

2.

Walt Disney Co. trading in a narrow price range for the past month, and you believe that 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 $7. If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on Walt Disney stock at an exercise price of $100? (The stock pays no dividends.) What would be a simple options strategy to exploit this profit opportunity 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

1) Put call parity is given by the formula
C0 + PV of X = P0 + S

Where C0 = Call premium
                PV of X = PV of exercise price of options
                P0 = Put premium
                S = The current share price

Therefore
= 7 + 100/(1.10)3/12 = P0 + 100
= 7 + 100/(1.10)1/4 = P0 + 100
= 7 + 100/1.0241 = P0 + 100
= 7 + 97.65 = P0 + 100
P0 = 4.65

Price of a 3month Put option at an exercise price of $100 Is $4.65.

We are expecting that the share price will be volatile but are unsure of the direction. To exploit the profit opportunity we should buy both call and put option so as to profit in case of high volatility by either share price going up or share price going down.

Price of call option at strike price of $100 = $7
Price of put option at strike price of $100 = $4.65

Total Premium paid = $7+ $4.65 = $11.65

Breakeven points :
Call Option = Exercise Price + Total Premium Paid
                      = $100 + $11.65
                  = $111.65

Put Option = Exercise Price - Total Premium Paid
                      = $100 - $11.65
                  = $88.35

So price should move more than $111.65 or move below $88.35 to earn profits.