Question

You enter into a 6-month long forward contract on XYZ stock. The forward price is 50. What is the payoff to your long forward if XYZ stock rises to 53 at 6 months? You enter into a 6-month short forward contract on XYZ stock. The forward price is 50. What is the payoff to your short forward if XYZ stock rises to 51 at 6 months? You purchase a European call option on XYZ stock with strike price 50. What is the payoff to the option if XYZ stock is trading at 48 on the expiration day?

Answer 1

(a) Forward Price = 50, Forward Position: Long which implies that the investor has bought the forward contracts and hence has the OBLIGATION to honor the same.
Stock Price at Expiry = 53

Under the long forward position, the investor is OBLIGED to purchase the stocks at the forward price of 50 irrespective of the original market price of the stock.

Therefore, Stock Payoff = (53 - 50) = 3

(b) Forward Price = 50, Forward Position: Short which implies that the investor has sold the forward contracts and hence has the OBLIGATION to honor the same.
Stock Price at Expiry = 51

Under the short position, the investor is OBLIGED to sell the stocks at the forward price of 50 irrespective of the original market price of the stock

Therefore, Stock Payoff = (50 - 51) = - 1

(c) Call Option Strike Price = 50, The investor is long on the call option as he/she purchases the option. Under a long call position, the call buyer has the RIGHT TO but NOT THE OBLIGATION to buy the underlying asset at the strike price.

Hence, if the stock's market price is below the strike price, it is more beneficial to the call holder to purchase the stock directly at the lower market rates, instead of the higher strike price. A call option has a positive pay off to the call buyer only if the strike price is below the existing price of the underlying asset.

Hence, if the underlying asset price is 48, the call Payoff = 0