HOMEWORK.

Assignment 1, due Friday, January 19, 2008, in class.
1. Chapter 1, exercise 1.
2. Suppose that a stock is currently selling for $20 per share. A (long position in a) forward contract is available to buy 100 shares of stock 3 months from now for $20.20 per share. Suppose that a bank is offering interest at the rate of 5% per annum (continuously compounded) on a 3-month deposit. Describe a strategy for creating an arbitrage profit and establish the amount of the profit.
3. A combination option called a strangle is obtained by taking a long position in a (European) call and a (European) put option with the same expiration date but differing strike prices, all based on the same underlying asset. A strangle is similar to a straddle in that the investor who buys the strangle is betting that there will be a large movement in the price of the underlying, but is uncertain whether it will involve an increase or a decrease in the price. Typically the price has to move further for the investor to make a profit from a strangle, but the downside risk is typically less than with a straddle. Find a formula for the payoff for a strangle where the put has a strike price of K1 and the call has a strike price of K2 and K1 < K2. Draw a graph of this payoff as a function of the final price of the underlying asset. (Make sure to label your axes on the graph.)

Assignment 2, due Friday, February 2, 2008, in class.
From Chapter 2, Exercises 1, 2 (part (d) is optional), 3 (part (d) is optional), 4, 5 (note that you can use the result from Exercise 4 if you wish - there is a typo in the book at the end of Exercise 5, it should read "Exercise 4" rather than "Exercise 3").

Assignment 3, due Wednesday, February 14, 2008, in class.
1. Consider the CRR model described in Exercise 2 of Chapter 2 as the model for a stock and a bond. A forward contract is to be offered under which the holder of a long position in the forward contract will buy 100 shares of stock at time T=2 for a fixed price F. (Here F is the total amount to be paid for the 100 shares). Remember that no money changes hands at time zero when a forward contract is written. What value should F take in order that there is no arbitrage opportunity for the investor who holds a long or a short position in the contract? Explain your reasoning fully (in particular, identify an associated European contingent claim and derive the value of F using arbitrage pricing for the contingent claim).
2. Exercise 6 (except part (d)) from Chapter 2.
3. Exercise 7 from Chapter 2.

Assignment 4, due Monday, February 26, 2007, in class.
Exercises 2, 3, 4 from Chapter 3.

Extra credit project: This is a challenging project. You do not need to do this project. If you do it well, it will count for extra credit.
Consider a finite market model that is viable and complete. Show that there is a minimal hedging strategy for any American contingent claim in this setting. (Hint: you may need to use the martingale representation property.) Use your analysis to find the initial arbitrage free price for an American contingent claim. Part of your answer will involve showing that this price is indeed arbitrage free.

Please note that class on Friday, March 9 only will meet in AP&M 6402.
Assignment 5, due Wednesday, March 14, 2007, in class.
Exercises 1, 2, 3, 4, 5 from Chapter 4.