Question

Apple currently trades at $433.

1.You can buy a 3-month put option on Apple stock with a strike price of $428 for $24.8. How much do you have to pay to establish a protective put position for a single unit?

2.In reality, you cannot buy a single option, only an option contract. According to the CBOE website, how many shares of the underlying stock are covered by 1 option contract for equity options?

3.From now on, assume you bought 1 put option contract (and no stocks). What is your option payoff at expiration if the stock price has risen to $435?

4.What is your option payoff at expiration if the stock price has fallen to $424?

5.Ignoring the time value of money, what is your total profit with a stock price of $424?

6.What is your total profit if you consider the time value of money? The risk-free rate is 0.007 (EAR).

Answer 1

1) We know that Protective Put = Stock + Put option

= $433 +$24.8 = $ 457.8

3) Here is the trick for you : Ask yourself to the following questions to get answer to such type of question:

a) I have the right to sell @X = $428

b) Price in the market is $435

c) Will I sell ? NO

d) Therefore payoff = 0

4) Again the same set of questions as above :

a) I have the right to sell @X = $428

b) Price in the market is $ 424

c) Will I sell ? YES

d) Therefore payoff = $(428-424) = $4

5) e) Premium = $24.8 (assuming same )

f) Profit /Loss = ($4 - $24.8) = Loss of $20.8

6) Considering TVM = 20.8 / (1.007)^(3/12) = Loss $20.764