The common stock of the C.A.L.L. Corporation has been trading in a narrow range

Question

The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $115 per share for months, and you believe it is going to stay in that range for the next 3 months. The price of a 3-month put option with an exercise price of $115 is $13.26 If the risk-free interest rate is 6% per year, what must be the price of a 3-month call option on CALL stock at an exercise price of $115 if it is at the money? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your a. response.) Price of a 3-month call option b-1. What would be a simple options strategy using a put and a call to exploit your conviction about the stock price's future movement? Stock price's future movement (Click to select) b-2. What is the most money you can make on this position? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.) Amount b-3. How far can the stock price move in either direction before you lose money? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.) Stock price How can you create a position involving a put, a call, and riskless lending that would have the same payoff structure as the stock at expiration? What is the net cost of establishing that position now? (Do not round intermediate calculations. Round your answers to 2 decimal places. Leave no cells blank - be certain to enter"" wherever required. Omit the "$" sign in your response.) c.

Explanation / Answer

a)

Put-call parity

C + X/(1+r)^t = S0 + P

C = call premium

P = Put premium

X = strike price

S0 = underlying price

Hence

rearrange

C = P + S0 - X/(1+r)^t

= 13.26 + 115 - 115/ (1.06)^0.25

= 14.915

b-1)

Strategy which can be used is

Sell a straddle

sell a call and Put to get the income of

P+c

= 13.26 + 14.915

= 28.175

b-2)

Suppose the stock price becomes $130, both of the options wont be used and the profit for the seller of the option will be 24.97. This is the maximum possible profit since, at any other stock price, you will have to pay off on either the call or the put.

b-3)

The stock price can move by 24.97 in either direction before the profits become negative.

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