QUESTION 1: Compute the initial price of a futures contract on the same ZCB of the previous two questions. The futures contract has an expiration oft=4.

QUESTION 2: Compute the price of an American call option on the same ZCB of the previous three questions. The option has expirationt=6and strike=80.

Compute the initial price of a swaption that matures at timet=5and 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 att=5then the owner of the swaption will receive all cash-flows from the underlying swap from timest=6tot=11inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)

Compute the initial price of a swaption that matures at timet=5and 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 att=5then the owner of the swaption will receive all cash-flows from the underlying swap from timest=6tot=11inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)