1. Compute the price of a zero-coupon bond (ZCB) that matures at time t = 10 and...
Question:
1. Compute the price of a zero-coupon bond (ZCB) that matures at time t = 10 and that has face
value 100.
Submission Guideline: Give your answer rounded to 2 decimal places. For example, if you
compute the answer to be 73.2367%, submit 73.24.
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.
Submission Guideline: Give your answer rounded to 2 decimal places. For example, if you
compute the answer to be 73.2367%, submit 73.24.
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.
Submission Guideline: Give your answer rounded to 2 decimal places. For example, if you
compute the answer to be 73.2367%, submit 73.24.
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.
Submission Guideline: Give your answer rounded to 2 decimal places. For example, if you
compute the answer to be 73.2367%, submit 73.24.
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.)
Submission Guideline: Give your answer rounded to the nearest integer. For example, if you
compute the answer to be -220,432.23, submit -220432.
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.)
Submission Guideline: Give your answer rounded to the nearest integer. For example, if you
compute the answer to be -220,432.23, submit -220432.