1.

Compute the price of a zero-coupon bond (ZCB) that matures at timet = 10and 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 timet = 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 oft = 4

4.

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

5.

Compute the initial value of a forward-starting swap that begins att=1

t=1, with maturityt = 10and a fixed rate of 4.5%. (The first payment then takes place att = 2

and the final payment takes place att = 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.

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 = 5 then the owner of the swaption will receive all cash-flows from the underlying swap from timest = 6

tot = 11inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)