There is $150 million of a 20-year mortgage with a coupon payment of 4.5% per year and paid monthly.
a. Construct 3 tranches of A with a coupon payment of 3.5% per year and least prepayment protection, B with a coupon payment of 4.5% per year, and C with equal amount of $50 million and the most prepayment protection. What is the coupon payment of Tranche C so that the mortgage above could be used as a collateral against the monthly payments of these three tranches?
b. How are the cash flows distributed if the monthly payment of $950,000 is received in the first month?