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. – in your solution show the work/setup which includes the calculations for all steps.
Mortgages
A mortgage is a formal agreement in which a bank or other financial institution lends cash at interest in return for assuming the title to the debtor's property, on the condition that the obligation is paid in full.
Mortgage
The term "mortgage" is a type of loan that a borrower takes to maintain his house or any form of assets and he agrees to return the amount in a particular period of time to the lender usually in a series of regular equally monthly, quarterly, or half-yearly payments.
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. – in your solution show the work/setup which includes the calculations for all steps.
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