Assignment Task: Questions 1-6 should be answered by building an n = 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.
Question 1 - Compute the price of a zero-coupon bond (ZCB) that matures at time t = 10 and that has face value 100.
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 = 4.
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 = 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 = 6 and strike = 80.
Question 5 - Compute the initial value of a forward-starting swap that begins at t = 1, with maturity t = 10 and a fixed rate of 4.5%. (The first payment then 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.)
Question 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 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.)