building an n = 10 - period binomial model for the short - rate, ri,j . The lattice parameters are: r0,0 = 5%, u = 1.1, d = 0.9 and q = 1- q = 1/2.

1) Compute the price of a zero - coupon bond (ZCB) that matures at time t = 10 and that has face value 100.

2) Compute the price of a forward contract on the same ZCB of the previous question where the forward contract matures at time t = 4.

3) Compute the initial price of a futures contract on the same ZCB of the previous two questions.The futures contract has an expiration of t = 4.

4)Compute the price of an American call option on the same ZCB of the previous three questions. The option has expiration t = 6 and strike = 80.

5) Compute the initial value of a forward- starting swap that begins at t = 1 , with maturity t = 10 ,& a fixed rate of 4.5%(The first payment that takes place at t = 2 and the final payment takes place at t = 11 as we are assuming, as usual, that payments take place in arrears. You should assume a swap notional of 1 million,and assume that you receive floating and pay fixed.)

6) Compute the initial price of a swaption that matures at time t = 5 and has a strike of 0 . The underlying swap is the same swap as described in the previous question with a notional of 1 million. To be clear, you should assume that if the swaption is exercised at t = 5 then the owner of the swaption will receive all cash-flows from the underlying swap fromtimes t = 6 to t = 11 inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)