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.)

Price of a 6 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? Sell a straddle

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.)

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.)

Stock Price =

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.)

	Position Immediate CF Call (long) Put (short) Lending position Total

Answer 1

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)

i.e. 8.19+145 = call + 145/1.09^0.5

i.e. 8.19+145 = 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 -

We have taken a short position in call and put i.e. if the market price goes up, the call will be exercised by the buyer and we will have to buy the stock at the exercise price of $ 145 as against the then prevailing higher market price, the put in that case will lapse. However we have already earned a total premium of $ 22.50 so to the extent price goes up by $ 22.50, we do not incur any loss. If price goes up by more than $ 22.50 i.e. if price is more than $ 167.50, we start incurring losses.

Similarly, if the price of the stock goes down, the call will lapse but the put will be exercised by the buyer. We will have to buy stock from him at $ 145 as against the then prevailing lower market price. However, since we have already earned a total premium of $ 22.50, we do not incur any loss till the extent price goes down by $22.50 i.e. if price falls below $ 122.50, we start incurring losses.

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

c) Buy the call, sell the put and lend $ 138.8848 (i.e. 145/1.09^0.5)

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 (if price < X)	CF in 6 months (if price > X)
Call (Long)	-14.31	0	Price - 145
Put (Short)	8.19	- (145 - price)	0
Lending Position	145/1.09^0.5 = 138.88	145	145
Total		Price	Price

NOTE- FIGURES ARE SUBJECT TO ROUNDING OFF.