Question

Suppose you write a May expiration call option on Delta Airlines with exercise price $50 and at the same time, write a Delta Airline put option with exercise price $50. The premium of the call option is $0.91 and the premium of the put option is $0.54. Assume Delta Airlines will not pay any dividend before these options expire in May.

a. Draw the payoff of this option portfolio at option expiration as a function of Delta Airlines stock price at that time.

b. What will be the profit/loss on your option portfolio if Delta Airlines is selling at $53 on the option expiration date? What if Delta Airlines is selling at $60?

c. At what two stock prices will you just break even on your investment?

d. What kind of “bet” is this investor making, that is, what must this investor believe about Delta Airline's stock price to justify this position?

Answer 1

Part a)-

Writer of call option has obligation to sell stock & writer of put option has obligation to buy stock at the option of the holder. When the exercise price is less than actual price, holder of call option will exercise the call else allow to lapse it whereas when the exercise price is more than actual price then only holder of put option will exercise else he will allow to lapse it.

	Call	Put
Strike price	Exercise price	Exercise or Lapse	Loss	Premium received	Payoff	Exercise or Lapse	Loss	Premium received	Payoff	Net Payoff
$         46	$       50	Lapse	$     -	$         0.91	$     0.91	Exercise	$ 4.00	$        0.54	$ -3.46	$   -2.55
$         48	$       50	Lapse	$     -	$         0.91	$     0.91	Exercise	$ 2.00	$        0.54	$ -1.46	$   -0.55
$         50	$       50	Either	$     -	$         0.91	$     0.91	Either	$     -	$        0.54	$   0.54	$    1.45
$         52	$       50	Exercise	$ 2.00	$         0.91	$    -1.09	Lapse	$     -	$        0.54	$   0.54	$   -0.55
$         54	$       50	Exercise	$ 4.00	$         0.91	$    -3.09	Lapse	$     -	$        0.54	$   0.54	$   -2.55

Note : Strike price is assumed

Part B

	Call option	Put option
Strike price	Exercise price	Exercise or Lapse	Loss	Premium received	Payoff	Exercise or Lapse	Loss	Premium received	Payoff	Net Loss
$         53	$       50	Exercise	$ 3.00	$         0.91	$    -2.09	Lapse	$     -	$        0.54	$   0.54	$   -1.55
$         60	$       50	Exercise	$10.00	$         0.91	$    -9.09	Lapse	$     -	$        0.54	$   0.54	$   -8.55

In part b, Exercise price is less than market price hence holder of call option will exercise whereas holder of put option allow to lapse it. In both the prices, writer will incur losses only.

Part C;-

Since he is a net writer, net premium should be deducted from exercise price.

Breakeven Price = Exercise price - Net premium

= $50 - $1.45 = $48.55

Part D;-

Investor expecting the stock price would be between $48.55 to $51.45.