Question

2. Look at the Apple options from below. Suppose you buy an October expiration call option with exercise price $100.

Apple (AAPL)	Underlying stock price, S = $102.05
Expiration	Strike (E)	Call	Put
September	95	6.20	0.21
October	95	6.35	0.33
September	100	2.20	1.18
October	100	2.62	1.55
September	105	0.36	4.35
October	105	0.66	4.75

1. If the stock price in October is $105, will you exercise your call? What are the net profit and the rate of return if you exercise the call?  
2. Will you exercise the call if you had bought the October call with exercise price $95?
3. Will you exercise the option if you had bought an October put with exercise price $100?

Answer 1

a. If  the stock price in October is $105, you will exercise your call because spot price is October is higher than than exercise price. A call option pays off to its buyer when spot price at expiration is higher than exercise price. Call option gives a right to its buyer to purchase the underlying at exercise price at expiration. If spot price is higher at expiration then buyer can purchase the underlying from seller of the option at lower exercise price and sell in the spot market at higher spot price.

Net profit = (spot price in Oct - strike price - call premium) = ($105 - $100 - $2.62) = $2.38

rate of return = net profit/call premium paid = $2.38/$2.62 = 0.91 or 91%

b. You will exercise the call if you had bought the October call with exercise price $95 because stock price in October is $105 which is higher than the exercise price of $95. there will be profit of $105 - $95 - $6.35 = $3.65.

c. You will not exercise the option if you had bought an October put with exercise price $100 and stock price in October is $105. Put option pays to its buyer only if spot price at expiration is lower than exercise price at expiration. Put option gives a right to its buyer to sell the underlying at exercise price at expiration. If spot price is lower at expiration then buyer can sell the underlying to seller of the option at higher exercise price than to sell in the spot market at lower spot price.

So stock price in October is $105 which is higher than exercise price of $100. you will not exercise the option and sell the stock at $105 in spot market.