The common stock of the C.A.L Corporation has been trading in a narrow range aro
ID: 2786393 • Letter: T
Question
The common stock of the C.A.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 a. 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 $115 if it is at the money? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "S" sign in your response.) Price of a 3-month call option b-1. What would be a simple options strategy using a put and a call to exploit your conviction about the stock price's future movement? Stock price's future movement (Click to select) b-2. What is the most money you can make on this position? (Do not round intermediate calculations Round your answer to 2 decimal places. Omit the "$" 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 "S" 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 "S" 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
1a) We are going to use the put call parity to solve this problem. The put call parity formula is:
C+ Xe-rt=S+P….(1)
Where C=Price of Call Option
X= Strike Price=115
S= Stock Price=115 (since at the money call option stock price and strike price should be same)
P=Put Price=13.26
t=time to maturity=3 months= 3/12 years=0.25 years
r=risk free rate of interest= 6%
So we need to find the price of the call option (C). SO rearranging equation 1 in terms of C and then plugging the values:
C=S+P-Xe-rt
C=115+13.26-(115e-0.06*0.25)
=128.26-113.2879
=14.9721=$ 14.97
Therefore, price the call option will be $ 14.97
1b-1) We expect a range bound movement in stock in the near future. Hence we will use a “short straddle” strategy. With a short straddle strategy you sell both the call and put option.
1b-2) The maximum money on the short straddle position you can make is the sum of call and put prices. Stated in other way the maximum money you can make is the premium received for the option. Hence your max profit will be:
Price of 115 call+ Price of 115 put
=14.97+13.26
=$ 28.23
1b-3) The stock price can move $ 28.23 in either direction before your profits become 0. Thus on the upside your profits will become 0 when stock price becomes (115+28.23) = $ 143.23. On the downside your profits will become 0 when stock price become (115-28.23) =$ 86.77