Questions 1-6 should be answered by 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=1q=1/2.

Q1. Compute the price of a zero-coupon bond (ZCB) that matures at time t=10 and that has face value 100.

Q2. Compute the price of a forward contract on the same ZCB of the previous question where the forward contract matures at time t=4.

Q3. 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.

Q4. 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.

Q5. Compute the initial value of a swap with expiration t = 11 and a fixed rate of 4.5%. (The first payment takes place at t = 1 and the final payment takes place at t = 11.) You should assume a swap notional of 1 million and assume that you receive floating and pay fixed.)

Q6. 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.)

Q7. Briefly explain the conditions under which we can guaranty no arbitrage when pricing the above derivative securities.

ANSWER QUESTION 7 ONLY