1a-c. Suppose we have a new type of MBS to accommodate the short term investor. This new MBS security instrument contains only 5 year mortgages (in reality are rare if non existent). ACME, a private secondary mortgage market, has pooled together ten $100, 000 5 year mortgage loans. Note: To save space in writing out your work, you can scale the ten $100,000 to $100.

Calculate the duration for this MBS pool assuming annual compounding for three years at 10 percent interest which:

a. is a "zero coupon"

b. Is an interest only MBS

c. Is fully amortizable over the three years.

2.Now assume that the interest only MBS in problem 2b. is prepayable (but not defaultable). Use the option theoretic model to price this MBS. Interest rates have a 50% chance of going up 1% each year and a 50% chance of going down 1% each year. From your results, qualitatively compare the MBS value without prepayment to the MBS value with prepayment.

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