The common stock of the C.A.L.L. Corporation has been trading in a narrow range
ID: 2786919 • Letter: T
Question
The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $135 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 $135 is $10.70 a. If the risk-free interest rate is 9% per year, what must be the price of a 3-month call option on CALL stock at an exercise price of $135 if it is at the money? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your 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 "O" wherever required. Omit the "$" sign in your response.) c. Position Immediate CF CF in 3 months Call (long) Put (short) Lending position Total (Click to select) (Click to select) (Click to select) (Click to select)Explanation / Answer
According to put call parity:
S+P=C+Xe^(-rt)
135+10.7=C+135*e^(-0.09*3/12)
So, C=135+10.7-135*e^(-0.09*3/12)
So, C=13.70358
Short straddle, sell call and put at same strike and expiry
this way if stock is more than strike, you will lose on the call which will be slightly offset by put premium
And if stock is in a range, you will pocket the premium
The maximum profit is option premium, that is option exercises at the money. profit=13.70358+10.7=24.40358
If stock goes below 135-(13.70358+10.7)=110.5964, we will lose money
If stock goes above 135+(13.70358+10.7)=159.40358, we will lose money
S=Xe^(-rt)+C-P
Call=-13.70358
Put=+10.7
Lending=-135*e^(-0.09*3/12)=-131.9964
Total or net cost is the same as that in case of buying the stock=-135
In 3 months,
St<=X
Call=0
Put=-135+St
Lending=135
Total=St
St>X
Call=St-135
Put=0
Lending=135
Total=St
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