Question

The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $40 per share for months, and you believe it is going to stay in that range for the next 6 months. The price of a 6-month put option with an exercise price of $40 is $8.49.

a. If the risk-free interest rate is 8% per year, what must be the price of a 6-month call option on C.A.L.L. stock at an exercise price of $40 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?

Answer 1

a.

According to the put call parity theorem:

Where

• C is price of call option
• X is the strike price
• P is the price of put option
• S is the current stock price
• r is the annual interest rate
• n is the time till maturity in years

Substituting the values, we get

(Since, the option is at the money S = X = 40)

or, C = $1.26

b.

If the stock price is going to stay in a narrow range around $40, an investor could sell both call and put options at a strike price of a little greater than $40 (for call option) and a little less than $40 (for the put option). In this way, the investor would end up with the premiums earned on both the options and since the stock price is not going to move abruptly on either side, each option would remain out of the money.