Question

Consider an investor who owns stock XYZ. The stock is currently trading at $120. The investor worries that the outlooks for the market and the stock are not favorable. The investor decides to protect his potential losses by using derivatives.

Assume the investor decided to purchase a European call option on stock ABC. Further assume that the current price of the stock is $130. The investor paid $10 for the call with the strike price at $155.

(A)If the stock price goes up to $160, what is the payoff to the investor?

(B) Further assumes that the investor also decided to sell a European put option on the same underlying with the same strike price of $155 and option cost of $10. What is the payoff to the investor when the stock price moves to $175? Which of the following combination of answers best capture the payoffs for situations described in A and B?

Answer 1

A. Current Stock Price = $130
Exercise Price of call option = $ 155
Initial Premium paid on call option = $10

If the stock price goes up to $160, call option will be exercised and payoff will be Stock Price - Exercise Price .
Payoff from call option = $160 - $155
                                                = $5
Profit from call option    = Payoff from call option – Initial Premium Paid
Profit from call option    = 5 – 10
Profit from call option    = -5

Total Payoff = Profit from call Option + Payoff from Stock
                         = -$5 + $160
                         = $155


B) The investor is also going short the put option at Exercise price of $155.
Initial Premium Received on put option = $10
Net premium paid = Initial Premium paid on call option - Initial Premium Received on put option
                                     = 10 – 10
                                     = 0

If the stock price rises above $175,
Put option will lapse and payoff will be 0.
Payoff from call option = 175- 155 = $20
Profit from Options = Payoff from call option - Payoff from put option – Net Premium paid
Profit from Options = 20 – 0 - 0
Profit from Options = 20

Payoff from Shares = 175
Total Payoff = Profit from Options + Payoff from Stock
                         = 20 + 175
                         = 195