An asset has, in CoxRoss-Rubenstein notation, initial price S = 10 , up factor u = 1.5 and d = 0.7 . A forward contract is available on this asset, maturing in three time steps. A future contract is also available on this asset, and this future contract also matures in three time steps. The variable returns over the life of these two contracts are shown in the binomial tree returns below.

R(2, 2) = 1.04 R(2, 1) = 1.08 R(2, 0) = 1.08 R(1, 1) = 1.06 R(1, 0) = 1.06 R(0, 0) = 1.07

(a) Calculate all risk neutral probabilities.

(b) A zero-coupon bond matures at time T = 3 , calculate all values of this 3-zero. That is, calculate all P n j (T n) for all 0 j n 3 .

(c) For the forward contract, calculate the forward price using the n = 0 value of the zero-coupon bond and for the future contract, calculate the future price using the backward-induction formula for the future price.