Question

The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $145 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 $145 is $8.19. a. If the risk-free interest rate is 9% per year, what must be the price of a 6-month call option on C.A.L.L. stock at an exercise price of $145 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

Solution and Explanation:

a) Let us calculate the value of call using Put-Call Parity,

i.e. Put + Stock = Call + Present Value of Exercise Price (note that it is 6 - months time period)

$\text { i.e. } 8.19+145=\mathrm{call}+145 / 1.09^{\wedge} 0.5$

$\text { i.e. } 8.19+145=\mathrm{call}+145 / 1.044$

Therefore, Call = $ 14.31

b1) The option strategy best suited in the given condition is - Short or Sell Straddle.

In shorting a straddle, you simultaneously sell a call and a put, thereby earning premium in both the legs of the strategy. It is a neutral options strategy wherein profits can be made when stock price is expected to remain stagnant. However it is to be noted that the profits are limited to the option premium earned on call and put but the risk is unlimited. i.e. only when you are reasonably sure as to the stock price remaining more or less constant, go for short straddle.

b2) Assuming that we went for short straddle, we earn $ 8.19 premium on put and $ 14.31 premium on call i.e. we earn maximum of $ 22.50 on this stock due to our position in options.

b3) WITHOUT CONSIDERING TIME VALUE -

Now, CONSIDERING TIME VALUE - the stock price would need to swing in either direction by ($22.50 * 1.09 \times 0.5)=$ $ 23.49 for us to start incurring losses.

c) Buy the call, sell the put and lend $ 138.8848

Let 'Price' in the table below denote the stock price at the end of 6 months.

If we take a long position in call, the immediate CF is $ 14.31 (premium outflow).

If we take a short position in put, the immediate CF is $ 8.19 (premium inflow)

Position       Immediate CF      CF in 6 months         CF in 6 months

                                                         (if price < X)        (if price > X)

Call (Long)   -14.31                          0                      Price - 145

Put (Short)       8.19                         - (145 - price)               0

Lending Position  $145 / 1.09^{\wedge} 0.5=138.88$  145                     145

Total                                           Price                    Price

NOTE- FIGURES ARE SUBJECT TO ROUNDING OFF.