We are currently working on payoff diagrams in my intro to investments class. Was wondering if anyone could help me draw a payoff diagram to the following problems. Is there any easy way to do this?
(3) Determine the payoff at maturity for the following portfolio: A long forward contract on a stock (with a forward price = F0) and a long European put on the same stock with the same maturity as the forward and a strike price X = F0. Show that this portfolio has the same payoffs as a European call on the stock with a strike price of F0. Draw the payoffs of each the contracts (i.e. the forward, the put and the call) on the same diagram.
(4) A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the same maturity. The call costs $3 and the put costs $4. Draw a diagram showing the payoff and the profits to holding these options.
(5) Assume that the risk-free rate is 9% per year with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August and November dividends are paid at a rate of 5% per year. In other months, dividends are paid a rate of 2% per year. Suppose that the value of the index on July 31, 2006 is 300. What is the futures price for a contract deliverable on December 31, 2006? Hint: You need to calculate the average dividend yield.
(6) Suppose that the risk free interest rate is 10% per year with continuous compounding and that the dividend yield on a stock index is 4% per year. The level of the index is 400, and the futures price for a contract deliverable in four months is 405. Isopportunity? If so, what positions would you take?