Consider a world with two time periods and two possible states at each time t = 0, 1, 2. There are only two assets to invest. One is risk free borrowing 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 × 4 system with state prices ψij, i, j = u, d that gives the arbitrage-free prices of a savings account and of the bond B.
(b) Show how one can get risk-neutral probabilities in this setting.
(c) Show that if one adopts a savings account normalization, the arbitrage-free price of the bond will be given by

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