**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 ā 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.

**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.**