Instructions: Term Structure Models

Instructions: Term Structure Models

Questions 1-6 should be answered by building an n=10-period binomial model for the short-rate, ri,jā€‹. The lattice parameters are: r0,0 = 5%, u= 1.1, d = 0.9 and q = 1 āˆ’ q = 1/2.

1. 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. 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.

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. 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.

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. 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.

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. 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.)

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. 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.)

Submission Guideline: Give your answer rounded to the nearest integer. For example, if you compute the answer to be -220,432.23, submit -220432.

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