Question

1. Suppose you buy a share of Facebook at $140, and the market also has Facebook calls and puts for sale. The price of a Facebook call with an exercise price of $143 is
   C = $5 while a Facebook put with exercise price $135 is P = $2.
   1. Draw the payoff diagram for buying the above Facebook call option (the diagram should show the level of payoffs for each future stock price). Then, illustrate (and label) the profit from buying the Facebook call option on the same diagram.
   2. Suppose you wanted to insure your Facebook stock purchase against large losses that would result if the stock price fell. What call or put option should you buy or sell (combined with the purchase of the share of Facebook stock) to achieve this result?
   3. Illustrate the resulting profit vs. stock price diagram for the combination of Facebook stock and call/put you described in part b. Be sure to indicate the maximum loss that this combination could suffer.

Answer 1

a) The CALL option on Facebook with strike price $143 has a premium of $5. It means the profit will be realized is the market price goes above $148. If the market price is $50 then the profit will be $2 and if it is $160 then the profit will be $12.
If the market price is $160 then the CALL option should be exercised.
Profit = Current Market Price - (Strike Price + Option Premium)
160 - (143 + 5) = 12

b) If there is a risk of sharp decline in the stock which could result in large losses the portfolio can be insured either by buying PUT option or selling the CALL option.
A PUT option is right to sell and so the buyer of PUT option will earn profit with the decline in the stock.
Similarly, the CALL option could be sold and the seller will earn the option premium. If the stock declines then option will expire as worthless profit could be realized from the premium.

The PUT option strategy involves cash outflow but it also has fixed amount of loss if the condition is unfavorable.
The CALL option has a cash inflow initially but it could result in large losses if the stock gains in the price sharply.

c) The PUT option has strike price of $135 and the premium is $2. Again, it means the profit will be realized if the stock price goes below $133. The maximum profit will be realized if the stock price is zero.
Profit = Strike Price - (PUT Option Premium + Current Market Price)
135 - (2 + 0) = $133
Please not that if the stock price rises then the PUT option will worthless and the maximum loss is limited to the option premium that is $2.