Please show all steps and all work and hand written no excel thank you

Problem Set 7: Duration and Option Pricing

Submission instructions: compute and handwrite solutions on this 4-page worksheet

or separate paper submit all work and SHOW ALL WORK/setup with calculations

1a-c. Suppose we have a new type of MBS to accommodate the short-term investor.

This new MBS security instrument contains only 3-year mortgages (in reality are

rare if non-existent). ACME, a private secondary mortgage market, has pooled

together ten $100,000 3-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. 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 in Slide 17s Option Pricing Lecture

Write work and solution(s) continued for problem 2 on this page (if needed).