4.The Australian Treasury is currently selling a coupon bond for $100. This bond expires in two years, has face value $100, and coupon rate 6%, with coupons paid at the end of the year. The current return over one year is R(0,0)=1.02.

(a) How much does the bond pay each year?

(b) Use the coupon bond and the return R(0,0) to determine the zero-coupon bond values P(0,1) and P(0,2).

(c) Use the Ho-Lee model and the zero-coupon bond values calculated in (b) to determine the returns over the second year, R(1,0) and R(1,1), correct to four decimal places. The Ho-Lee model parameters are= 0.5 and= 0.95.

(d) A future contract is available with expiry in two years and underlying asset described in Cox-Ross-Rubenstein notation S = $20, u = 1.15 and d = 0.90. Given that the risk neutral probabilities are(0,0) = 0.48,(1,0) = 0.9329 and(1,1) = 0.7063, use the backward-induction formula to calculate the future price for this future contract.

(e) A forward contract is available with maturity in two years and with the same underlying asset as the future contract in (d). What is the forward price for this forward contract?