Should be answered by building an n=10-period binomial model for the short-rate,

Question

Should be answered by building an n=10-period binomial model for the short-rate, n.j. The lattice parameters are:r_0, 0 = 5%, u = 1.1. d = 0.9 and q = 1 - q = 1/2 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. 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. 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. 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. 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. 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.)

Explanation / Answer

Solution 1

We have:

FV= 100

R= 5%

N= 10

We have following formula for price of a zero coupon bond:

PV= FV/ (1+r)^n

      = 100 / (1+0.05)^10

      = 100/1.628895

      = 61.39

Hence, price of the zero coupon bond would be 61.39.

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