Derivatives Problem

Consider an economy in three periods, t = 0, t = 1 and t = 2. At t = 0, the market index is trading at a value of 100. At t = 1, the index either rises to 125 with 50 percent probability, or falls to 90 with 50 percent probability. Following either of these outcomes, the index either rises by 25 or falls by 10, with equal probabilities, at t=2. Thus the highest possible index value at t = 2 is 150, and the lowest is 80. The index pays a dividend yield of 5% and the risk free rate is Rf = 10 percent.

1. Find the price you could buy a forward for at t = 2. Draw the payos

2. Consider the node at t=0. Discover the price of the put payos for this node.

3. Now draw the payos from a put which has the same strike price as the forward.

4. Consider the node that has gone down to 90 at t=1. Discover the price of the put payos for this node.

5. Consider the node that has gone up to 125 at t=1. Discover the price of the put payos for this node.

6. What is the expected return of the forward?

7. You are short the index the index you are worried it is going to decrease a lot. Draw the payos if you buy the index and buy a put? What is your expected return (assuming you reinvest the dividend at t=1 in the stock)?

8. What is the expected return if instead you sell a forward?