4) At time 0, the zero maturing at time 0.5 has a price of 0.97 per $1 par, and the zero maturing at time 1 has a price of 0.9409 per $1 par. At time 0.5, there will be one of two possible states: in the "up" state, the price of $1 par of a zero maturing at time 1 will be $0.96; in the "down" state, the price of this zero will be $0.98. The risk-neutral probability of the each outcome is 50%. This information is summarized below:

Time 0

Zero maturing at time 0.5 0.97 Zero maturing at time 1 0.9409

Time 0.5 1

0.96

1 0.98

Consider a 0.5-year floating rate note withrate set in arrears. This note has a single payoff at time 0.5 equal to par plus a coupon based on the 0.5-year rate observed at time 0.5. In terms of the notation from class, for each $1 par, the cash flow at time 0.5 is 1+0.5r1/2.

a) What is the payoff of $100,000 par of this note at time 0.5, in the up state?

b) What is the payoff of $100,000 par of this note at time 0.5, in the down state? c) Use the risk-neutral probabilities to compute the value of this note at time 0.

d) Write down, but do not solve, equations that determine the par amounts N0.5and N1of the zeroes maturing at time 0.5 and time 1 to hold in a portfolio that replicates the time 0.5 payoff of the rate-set-in-arrears floater.