Page 1 of 4 Problem Set 7: Duration and Option Pricing Submission

instructions: compute and handwrite solutions on this- submit all work/setup which calculations 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 five 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. Note:To save space in writing out your work, you can scale the ten $100,000 to $100.