1. Suppose you bought a stock with a current price of S and a put option on the stock with an exercise price of E. Show that the payoff of this position is always higher or equal to E. 2. Suppose that markets are efficient. Show that the price w of a warrant cannot be lower than So-E, where So is the current price of the underlying stock and E is the exercise price, We assume So-E>0. 3. Let S be the current price of a commodity. Show that buying a call with one year maturity on the commodity at an exercise price and selling a put with one year maturity on the commodity at an exercise price E has the same payoff as buying a one-year forward contract on the commodity at a delivery price E. 1. Suppose you bought a stock with a current price of S and a put option on the stock with an exercise price of E. Show that the payoff of this position is always higher or equal to E. 2. Suppose that markets are efficient. Show that the price w of a warrant cannot be lower than So-E, where So is the current price of the underlying stock and E is the exercise price, We assume So-E>0. 3. Let S be the current price of a commodity. Show that buying a call with one year maturity on the commodity at an exercise price and selling a put with one year maturity on the commodity at an exercise price E has the same payoff as buying a one-year forward contract on the commodity at a delivery price E