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.

a. If the risk-free interest rate is 6% per year, what must be the price of a 3-month call option on C.A.L.L. stock at an exercise price of $115 if it is at the money? (The stock pays no dividends.) (Do not round intermediate

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.)

c. 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 "0" wherever required.)

Answer 1

a) 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

b-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

c)

Position	Immediate CF	CF in 6 months
		ST<X	ST>X
Call (long)	C =14.915	0	(ST-115)
Put (Short)	P=-13.26	-(115-ST)	0
Lending Position	=115/(1+0.06)ᶺ0.25	115	115
Total	=113.3369+14.915-13.26	115	115