1.Using an options prepayment model, calculate the yield on the following fully amortizing MBS Term (yrs) 3 PV MBA $ 50,000,000 Coupon (%) 6.5% Market Yield (%) 6.8% Assume no servicing or guarantee fee applies a. What is the annual payment on the GNMA passthrough? b. What is the present value of the GNMA passthrough?

c. Interest rates change + or - .5% per year and are equally likely If interest rates fall 1% below the current mortgage coupon rate all mortgages in the pool will prepay. Diagram the interest rate tree and indicate probabilities of each node in the tree

e. The Treasury Bond yield curve is flat
Discount yield	6%
What is the OAS on the MBS?
Hint try and use Excel's Solver Add-in to calculate

d. What are the expected annual cash flows for each possible situation over the three-year period?

2.Consider a pool of mortgages with the following characteristics What are the quarterly mortgage payments, interest and principal payments over the first year of life of the pool? Pool Size $ 375000000 Coupon (%) 5% Term (Yrs) 30

3.Calculate the term structure of default probabilities over 3 years using the following spot rates from the Treasury strip and corporate bond (pure discount) yield curves. You need to compute annual marginal and cumulative default rates Spot 1 year Spot 2 year Spot 3 year Treasury Strips 4.5% 5.6% 6.7% BB-rated bonds 7.3% 7.9% 8.8%

You have the following Yields on Securities in Percent US Treasuries (i) 1-year Discount Bonds (k) 1-year 5.00 7.75 2-year 5.75 9.80 a. Calculate the one-year forward rate on the Treasuries and the corporate bond. b. Using the current and forward one-year rates, calculate the marginal probability of repayment on the corporate bond in years 1 and 2, respectively. c. Calculate the cumulative probability of default on the corporate bond over the next two years