Question

You own a put option on Ford stock with a strike price of $14. The option will expire in exactly six months time. When you bought the put, its cost to you was $2. The option will expire in exacly six months time. a. If the stock is trading at $10 in six months, what will be the payoff of the put? What will be the profit of the put? b. If the stock is trading at $25 in six months, what will be the payoff of the put? What will be the profit of the put? c. Draw a payoff diagram showing the value of the put at expiration as a function of the stock price at expiration. d. Redo (c), but instead of showing payoffs, show profits.

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Answer #1

Put Option: A put option gives the holder the right but not obligation to sell the underlying at a predetermined price (strike price) at the end of a specified time.

a)In the given case Strike price is 14 and time is 6 months. The holder of the option would benefit if the stock prices closes below 14 at the time of expiry.

Since the stock closed at 10 at the time of expiry, value (payoff) of put shall be 4 (Strike Price Less Stock Price) i.e., 14-10.

Profit on put shall be = Value of put - premium paid = 4-2 = 2.

b) Since the stock closed at 25, holder of the put will not exercise the option.

Value of put shall be zero i.e.Maximum of 0 or (Strike price - Stock price)

c) Pay off of the put option will be as below i.e., Maximum of 0 or (Strike Price Less Stock Price)

Strike Price Stock Price at expiry Pay off
14 20 0
14 19 0
14 18 0
14 17 0
14 16 0
14 15 0
14 14 0
14 13 1
14 12 2
14 11 3
14 10 4
14 9 5
14 8 6
14 7 7
14 6 8
14 5 9
14 4 10
14 3 11
14 2 12
14 1 13
14 0 14

d) Profit from holding a put option Maximum loss shall be the premium paid i.e., 2. Maximum profit is capped at 12 as show below

Strike Price Stock Price at expiry Pay off Premium paid Profit / ( Loss)
14 20 0 2 -2
14 19 0 2 -2
14 18 0 2 -2
14 17 0 2 -2
14 16 0 2 -2
14 15 0 2 -2
14 14 0 2 -2
14 13 1 2 -1
14 12 2 2 0
14 11 3 2 1
14 10 4 2 2
14 9 5 2 3
14 8 6 2 4
14 7 7 2 5
14 6 8 2 6
14 5 9 2 7
14 4 10 2 8
14 3 11 2 9
14 2 12 2 10
14 1 13 2 11
14 0 14 2 12
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