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 $90 per share, and the price of a 3-month call option at an exercise price of $90 is $8.69.

A). If the risk-free interest rate is 7% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $90? (The stock pays no dividends.)

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?

Total cost of the straddle:

Answer 1

a]

As per the put-call parity equation, C + (K/(1 + r)^t) = P + S,

where C = price of call option,

P = price of put option,

S = current stock price

K = strike price of option

r = risk free rate

t = time to expiration in years

We plug in the values to find the price of the put option :

C + (K/(1 + r)^t) = P + S

8.69 + (90/(1 + 7%)^3/12) = P + 90

8.69 + 88.49 = P + 90

P = 7.18

Price of the put option is $7.18

b]

Total cost of the straddle = price of call + price of put

Total cost of the straddle = $8.69 + $7.18

Total cost of the straddle = $15.87

The stock would have to rise at least by  $15.87 or fall at least by  $15.87 for you to make a profit on your initial investment