(a) Assuming a totally flat riskless term structure, what is the gross return on a riskless security over each of the intervals of length 1 15 of a year?

(b) For each possible stock price and remaining time to maturity (i.e., at each node in the tree of stock prices), calculate ? and B (i.e., the components of the replicating portfolio) and the value of the call.

(c) Suppose the stock first declines in value and then increases during each of the remaining four periods. Use a table to show at each node the value of your stock and bond portfolio both before and after any trading in stock and borrowing/repayment of debt. Show explicitly how your stock purchases are financed by additional borrowing and how the proceeds of any stock sales are used to repay borrowing. 3

Consider an American call. So = 40, X = 45, = 30% per year, erx-1.05 per year, T-4 months year. The stock will pay no dividends over the four month life of the option. The changes in the stock's price can be approximated by a series of up and down movements and let there be 5 such movements over the 4 month life of the option; i.e., divide the four months into 5 et there be 5 such movements over the 4 month life of the option; L.e., divide the four months into periods. Let n 5 . The length of each interval is then T-53-15 year. Now we need a u and a d: the best place to get them is from . Let u n-e VE and 1