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:

Consider a 0.5-year floating rate note with rate 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.

Time 0 Time 0.5 0.96 Zero maturing at time 0.5 Zero maturing at time 1 0.97 0.9409 0.98 Time 0 Time 0.5 0.96 Zero maturing at time 0.5 Zero maturing at time 1 0.97 0.9409 0.98