Use the options prepayment model to calculate the yield on a $12 million, five-year, fully amortized mortgage passthrough where the mortgage coupon rate is 7 percent paid annually. Market yields are 8 percent paid annually. Assume that there is no servicing or GNMA guarantee fee.
a. What is the annual payment on the GNMA passthrough?
b. What is the present value of the GNMA passthrough?
c. Interest rate movements over time are assumed to change a maximum of 1 percent per year. Both an increase of 1 percent and a decrease of 1 percent in interest rates are equally probable. If interest rates fall 3 percent below the current mortgage coupon rates, all mortgages in the pool will be completely prepaid. Diagram the interest rate tree and indicate the probabilities of each node in the tree.
d. What are the expected annual cash flows for each possible situation over the five-year period?
e. The Treasury bond yield curve is flat at a discount yield of 6 percent. What is the option-adjusted spread on the GNMA pass-through?