In this assignment, you will explore the two different approaches of pricing MBS. Suppose as a broker we are going to issue an MBS. The MBS is backed by Mortgages with the following specification: - Initial Principal P1:$500 million. - Maturity: 5 years. - Coupon payment frequency: annual. The term structure of interest rate is given by the table below. The rates here are all annualized continuously-compounded rates. Part I: Determining the Fixed Rate Suppose the credit profile of the mortgage borrowers imply a 2% credit spread for pricing cash flow. That is, for example, for a cash flow Dt+33-years ahead, the present value is given by PV(Dt+3)=Dt+3e(4.2%+2%)3 Here 4.2% is the market rate for 3 -year zero coupon bonds and 2% is the term spread. - Suppose the mortgages backing the MBS are all fixed-rate mortgages. Calculate the fixed coupon payments C such that the present value of C 's over the five years equals the the initial principal, P1. - Based on the C you calculated, calculate the implied fixed interest rate rm for the mortgage contracts. For simplicity of calculation later, report annualized rates. - Report the cash flow of the mortgage, if there is no prepayment. Part II: Pricing the MBS using CPR Consider a pass-through MBS set up. - Suppose the MBS issuer charges a 0.5% spread between the interest payments from the mortgage borrowers and to the MBS investors. What's the interest rate for MBS investors in this case? 1 - Suppose the current market condition suggests that the mortgage borrower's repayment follows PSA150\%. Calculate the cash flow of the MBS. (Be careful: here the mortgage payment is made annually. As a result, you do not need to convert CPR to monthly terms.) You need to decompose the cash flow into 1) scheduled principal payment, 2) principal prepayment, and 3) interest payments. - The investors take into consideration of the MBS risk profile and decide that the credit spread for the MBS is 1% for pricing cash flow. Use the yield curve before and determine the fair price of the MBS. Part III: Pricing the MBS using Binomial Tree Consider a pass-through MBS set up. - Suppose the annualized volatility of interest rate change is =0.5%. Build a 5 -step binomial tree for one-year interest rate movement such that the tree would imply a yield curve as observed in data. - Suppose the mortgage borrowers know that they are facing a 2% credit spread for their mortgage borrowing. In order words, when recursively compute the discounted value of future liability, they need to use 1 -year rate plus 2%. The borrower can choose to prepay the principal in full if the principal outstanding is lower than the present value of future liability cash flow. Use the Binomial tree to characterize the borrower's prepayment decisions. - Find out the present value of the MBS, taking into consideration of the borrower's decision. Again, there is a 0.5% spread for the MBS issuer when calculating interest payments, and the investor uses a 1% spread based on the spot 1-year rate to discount the cash flow and present value recursively