Question

Q.4.At the Chicago Board of Options Trading, stock ABC is currently trading at $64, and 3 months ‘At the
Money’ puts on this stock are trading at $3. If you buy one of these puts today and hold on to it until

expiry a) Explain with the help of a profit graph what price of the stock at expiry will allow you to break-
even? b) What will be your maximum profit? Label the profit area in the graph. c) What will be your

maximum loss? Label the loss area in the graph. d) Draw the profit graph for a call with same strike and
expiry which is priced at $2.

I know the question is so long but can you plese answer all the parts A-B-C and D Thank You

Answer 1

Don't worry even if the questions are too long. I am here to help you. I have answered all the questions with the help of graphs, please find the answers to the questions below:

The top graph labeled, "Put Option", are for parts a, b, and c.(A single graph suffices for all 3 parts). The bottom graph labeled "Call Option" answers part d.

The current price is $64. Hence, the strike price of "At the Money" option is also $64. I pay $3 for the put option.

a) At expiry, the payoff from the put will depend on the closing price. If the stock closes above $64, the option will not be exercised hence no payoff. At prices below $64, the payoff will be the difference between the closing price and the strike price. Note: the payoff is what you get when you exercise the option. It is not the profit. Profit is given by the difference between the original cost of the option and the pay-off for example.

If Share closes at $62, the payoff is 64-62=$2. Profit is$2-$3=-1$ (negative indicates a loss of $1). If share closes at $55, the payoff is $64-$55=$9. Profit is $9-$3=$6. Since I paid$3 for the put, I will need $3 to break even.

The break-even share price at expiry will be given by the equation:

Hence a price of $61 at expiry will allow me to break even.

b) The theoretical minimum price any share can close at expiry is $0. Hence, maximum profit for the put option will be when the stock price at expiry is $0. The pay-off at $0 can be calculated using the same method in part a, i.e. $64-$0=$64. Since, the option was originally priced at $3, the total profit is$64-$3=$61.

c) No matter what price the share closes, the maximum loss is limited to the price of the put option i.e. $3. This area extends to infinite on the right side of the line BX. Remember; the option buyer has the right and not the obligation to exercise the option.

d) For a call with same strike price priced at $2 (Refer to the2nd graph labeled "Call Option":

For, all prices below $64, the option will not be exercised. For all prices, above $64, the call will be exercised, and the payoff will be the difference between the exercise price and the strike price. For e.g., if the share closes at $70, the payoff will be$70-$64=$6. The profit will be the difference between the pay-off and the original cost of the option (Here $2). Hence, profit (at$70 closing price) = $6-$2= $4.

For a call option, the profit area extends to infinite on the right of the point B. There is no theoretical upper limit on the profit you can earn. The loss is to the left of the line BX. The maximum loss is limited to $2.

You're welcome!

Thank you.