An asset has, in CoxRoss-Rubenstein notation, initial price S = 10 , up factor u = 1.2 and d = 0.9 . A forward contract is available on this asset, maturing in two time steps. A future contract is also available on this asset, and this future contract also matures in two time steps. Returns over two time steps of a binomial model are R(0, 0) = 1.07 , R(1,1) = 1.01 and R(1,0) = 1.10.

(a) Calculate all risk neutral probabilities.

(b) A zero-coupon bond matures at time T = 2 , calculate all values of this 2-zero.

That is, calculate all Pjn(T n) for n = 0, 1, 2 and 0 j n .

(c) For the forward contract, calculate the forward price using the n = 0 value of the

zero-coupon bond Pjn(T n).

(d) For the future contract, calculate the future price using the backward-induction

formula for the future price.

(e) Say the returns over two time steps are now R(0,0) = 1.07 and R(1,1) = R(1, 0) = 1.06 .

(i) Calculate all risk neutral probabilities.

(ii) For the futures contract, calculate the futures price using the backward- induction formula for the futures price.

(iii) What is the forward price?