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 calculations. Round your answer to 2 decimal places.)

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?

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.)

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) As per Put call parity

C + PV of X = S + P

C + 115 / (1 + 0.06*3/12) = 115 + 13.26

C + 113.30 = 115 + 13.26

C = 14.96

b) We will form a short straddle by selling both call and put option of 115 Strike

c) Max profit = premium collected on both the options = 14.96 + 13.26 = 28.22

d) maximium movement = 115 +/- premium collected on options

maximum movement = 115 +/- 28.22

Upper Range = 115+28.22 = 143.22

Lower range = 86.78

We will buy a call option at 14.96 = -14.96

We will sell a put option at 13.26 = +13.26

we will lend PV of strike price 115 at 6% for 3 months = -115 / (1 + 0.06*3/12) = -113.30

Cash outflow today = 14.96 + 113.30 - 13.26 = 115