EBF 473, Homework 4, Fall 2012
Due in class October 11, nicely typed and stapled with all your work presented. All graphs need 50 data points. Each question is worth 25 points.
- A Whoey option pays the difference between the final price and the maximum price of a stock over the period of the the option. For example, if the price of a stock is 200, 220, and 234 in the previous periods (here periods 0, 1, and 2), the maximum price is 234, the final price is 234, and the option would pay 234-234=0. If the price path is 200, 220, 200, the maximum price is 220, the final price is 200, and the option would pay 20.
So given all this, you have a Whoey option that expires in 2 periods where the stock price in period 0 is 400. The stock either moves up with u=1.2, or down with d=1/1.2. The interest rate is 1/39. What is the value of your option today in period 0?
- An Asian option pays the maximum of either 0 or the difference between the final stock price and the average stock price along the relevant price path. For example, assume that the price path is 100, 80, 100. The average price is 280/3, and the option would pay (100-(280/3))=20/3. If the price path is 100, 125, 100, the average price is 325/3, and the option would pay 0.
So given all this, you have an Asian option that expires in 2 periods where the stock price in period 0 is 500. The stock either moves up with u=1.25, or down with d=1/1.25. The interest rate is 1/19. What is the value of your option today in period 0?
- The weights of your portfolio and the characteristics of the three assets in the portfolio are given below.
| asset | Annual mean return | Annual standard deviation | correlation (asset, asset1) | weight |
| 1 | 0.08 | 0.12 | You can get this! | 15 |
| 2 | 0.06 | X | 0.7 | Not Telling! |
| Riskless | 0.04 | You should know! | Really not telling! | -4 |
Graph the standard deviation of your portfolio as X goes from 0.05 to 0.25.
- Today is March 1. You observe that 6 year treasury bills are selling for 3.1 percent. You also observe that 6.25 year bills are selling for 3.0 percent. You can go $400 million face value short in either instrument. You are sure that the two bills will converge in six months to some interest rate.
A: What is your arbitrage strategy?
B: Graph how much money you will make in six months if the interest rate converges to Z, Z between 1 and 5 percent.