Consider a two-period economy where the resolution of uncertainty can be represented by the tree in Fig. 2.2 in Chapter 2. Assume that three assets are traded. Their dividend processes are illustrated in Fig. 4.1, where a triple (D1, D2, D3) near a node means that asset i = 1, 2, 3 pays a dividend of Di if/when that node is reached. For example, if the economy at time 2 is in the scenario F22, assets 1 and 2 will pay a dividend of 1 and asset 3 will pay a dividend of 2. In Fig. 4.1, the numbers near the lines connecting nodes denote values of the next-period state-price deflator, that is ζ1/ζ0 = ζ1 over the first period and

ζ2/ζ1 over the second period. For example, the value of ζ2/ζ1 given that the economy is in scenario F11 at time 1 is 1 if the economy moves to scenario F21 and 2/3 if the economy moves to scenario F22. This characterizes completely the state-price deflator to be used in the computations below.

(a) Find the price processes of the three assets. (You should find that the time 0 price of asset 1 is 1.802.)

(b) Find the short-term (one-period) interest rate process. What are the one-period and the two-period zero-coupon yields at time 0?

(c) Is the market complete?