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. a. 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.) (Do not round intermediate calculations. Round your answer to 2 decimal places.) 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? (Round your intermediate calculations and final answer to 2 decimal places.)

Answer 1

a.

The formula for put call parity is given below:

P = C-S+[X/(1+r)^T]

Where, C = call option price is $ 10

S = spot price is $100

X = exercise price is $100

T = time period of put option is 3 months or 1/4

R = risk free return is 10%

Putting the values in the formula we get

P = C-S+[X/(1+r)^T]

P = 10-100+[100/(1+0.10)^1/4]

P = 10-100+[100/(1.10)^1/4]

P = 10-100+[100/1.0241]

P = 10-100+97.65

P = 10-2.35

P = 7.65

b.

The straddle is a option strategy in which the investor will buy one put option and one call option

The Total cost of straddle option is = $10+$ 7.65 = $ 17.65.

This is the amount by which the stock would have to move in either direction for the profit on the call or put to cover the investment cost ignoring the time value.

If we take into consideration of time value the amount by which the stock would have to move in either direction for the profit on the call or put to cover the investment cost will be

= $ 17.65*(1.10)^1/4

^{=$ 17.65*1.0241}

^{= $ 18.07}