Questions 1-6 should be answered by building an n=n =

n=10-period binomial model for the short-rate, ri,jr_{i,j}

ri,j

. The lattice parameters are: r0,0=5%r_{0,0} = 5\%

r0,0

=5%, u=1.1u = 1.1

u=1.1, d=0.9d = 0.9

d=0.9 and q=1q=1/2q =1-q = 1/2

q=1q=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
5. Compute the initial price of a swaption that matures at time t=5t 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 from times 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.)