Question

Suppose that you traded the following options on Facebook’s stock:

a. Sold 1 call option with an exercise price of $250 at the price of $40;

b. Sold 1 put option with an exercise price of $250 at the price of $30; and

c. Bought 1 call option with an exercise price of $300 at the price of $22.

Also, suppose that:

i. All options are European;

ii. The options expire one year from now; and

iii. As usual, each option gives the right to buy (sell) 1 share.

Construct a table with the payoffs and profits (one year from now) for your combined position. Draw the profit diagram.

Answer 1

Before solving the questions, lets first understand the each of the terms:

Call option : Buying a call option gives the buyer an option to buy assets at an agreed price on or before particular date (expiry date). Selling the call option represents an obligation to sell the underlying security at the agreed price if the option is exercised. The call option seller is paid a premium for taking on the risk associated with the obligation. If its european call option, the call can be exercised only on the particular date whereas if its american call option, the call can be exercised on or before the particular date.

A call option is exercised by the buyer when the market price prevailing on the agreed date is higher higher than the strike price.

Put option: Buying a put option gives the buyer an option to sell assets at an agreed price on or before particular date (expiry date). Selling the put option represents an obligation to buy the underlying security at the agreed price if the option is exercised. The put option seller is paid a premium for taking on the risk associated with the obligation. If its european put option, the option can be exercised only on the particular date whereas if its american put option, the option can be exercised on or before the particular date.

A put option is exercised by the buyer when the market price prevailing on the agreed date is lower than the strike price.

Table with payoffs and profits

Following information are provided in the question:

a. Sold 1 call option with an exercise price of $250 at the price of $40;

b. Sold 1 put option with an exercise price of $250 at the price of $30; and

c. Bought 1 call option with an exercise price of $300 at the price of $22.

As mentioned above, a seller of an option gets the premium (upfront) for taking on the risk associated with the obligation. Thus, a buyer of the option pays the premium (upfront) on buying the option to the seller.

Thus, premium received = $40+$30-$22 = $48.

Table with payoffs and profits:

Table with payoffs and profits is prepared below for 100 prices (at expiry) from 225 to 325.

Scenarios:

For exercise price of $250,

If the expiry price is less than 250, buyer of call option will not exercise the option and thus seller retains the premium received.

If the expiry price is higher than 250, buyer of call option will exercise the option and thus seller gain through premium received reduces to the extent of increase.

For exercise price of $300,

If the expiry price is less than 300, buyer of call option will not exercise the option and thus seller retains the premium received.

If the expiry price is higher than 300, buyer of call option will exercise the option and thus seller gain through premium received reduces to the extent of increase.

Table with payoffs and profits:

Profit Diagram:

There will be profits till the expiry price of $298 and there will be net loss if the expiry price crosses $298. The maximum loss is $2 (which is restricted since both call and put options were sold to mitigate risk). Profit will be at the maximum when the expiry price is at $250 since the net premium received will be completely retained.