4. ABC Subprime Corporation is currently trading at $45, with volatility =40%, r=3%, and no dividends. Assume that the ABC stock price can be modeled according to the two period binomial approach with T=1 and n=2, so that the stock price moves every 6 months.

Suppose an investment banker holds a European put option with strike price of $100 on ABC. She wants to sell but cannot find a buyer for the option. She then tries to securitize the option by creating a vehicle called a Collateralized Option Obligation (COO), where the underlying collateral is the one year put option on ABC stock with a strike price of $100. She would like two tranches of COO securities---a senior tranche that is paid first and is CERTAIN to get all of its money, and a junior tranche that gets whatever is left over from the payoff of the put option and is thus risky. Thus, note that the senior tranche and junior tranche taken together will receive all of the payout from the option. Ignore any counterparty risk on the option payoff when answering this question.

a) First, build the binomial tree for ABC stock.

b) What are the possible payoffs for the put option?

c) Assume that the banker wants to make the senior tranche as large as possible when structuring the deal. Use your answer in (b) to determine what the senior tranche will be paid after one year. What would a fair price for the senior tranche be today?

d) What common security is the junior tranche equivalent to? Be as specific as you can.

e) What is a fair price for the junior tranche today?

f) Suppose the deal is done, and immediately after the deal happens, the volatility of ABC stock rises. What happens to the fair values of the senior and junior tranches? What if volatility falls?