We are given the data in a two year two-step recombining tree model, S(0,0)=10, S(1,0)=8, S(1,1)=14, S(2,0)=5, S(2,1)=11, S(2,2)=16. The interest rates are R(0,0) = 1.04, R(1,0) = 1.03 and R(1,1) = 1.06. The risk neutral probabilities are (0,0) = 0.4, (1,0) = 0.54 and (1,1) = 0.768.

(a) Use Jamshidian's Forward Induction formula to calculate the Arrow-Debreu prices, (2,2), (2,1) and (2,0).

(b) Using the values for (2,2), (2,1) and (2,0) obtained in part (a) calculate P(0,2), the present value of the asset that pays $1 in all states at t=2.

(c) Calculate the time 2 forward price F(0,0) of S.

(d) Calculate the time 2 futures price G(0,0) of S.