Consider a world with two time periods and two possible states at cacti time t = 0, 1. 2. There are only to assets to invest. One is risk-free burrowing and lending at the risk-free rate ri, i = 0, 1. The other is to buy a two period bond with current price B0. The bond pays $1 at time t = 2 when it matures.

(a) Set up a 2 x 4 system with crate prices ??ij = i, j = u, that gives the arbitrage-free prices of a savings account and of the bond B.

(b) Show how one can get risk-neutral probabilities, P, in this setting.

(c) Show chat if one adopts a savings account normalization, the arbitrage-free price of the bond will be givenby

B = E (1+1 +). li