Questions 1-6 should be answered by building an n =n=10-period binomial model for the short-rate, r_{i,j}ri,j. The lattice parameters are: r_{0,0} = 5\%r0,0=5%, u = 1.1u=1.1, d = 0.9d=0.9 and q =1-q = 1/2q=1q=1/2.

1. Question 1 Compute the price of a zero-coupon bond (ZCB) that matures at time t=10t=10 and that has face value 100. $61.62

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

3. Question 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=4t=4.

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

5. Question 5 Compute the initial value of a forward-starting swap that begins at t=1t=1, with maturity t=10t=10 and a fixed rate of 4.5%. (The first payment then takes place at t=2t=2 and the final payment takes place at t=11t=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. Question 6 Compute the initial price of a swaption that matures at time t=5t=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=5t=5 then the owner of the swaption will receive all cash-flows from the underlying swap from times t=6t=6 to t=11t=11 inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)