Consider a $1 billion portfolio of mortgage loans with an average loan rate of 5%. Assume for simplicity that mortgages are paid once a year for the next 3 years. Consider the following spot discount factors: Maturity, yrs. Z(0,T) 1 0.9645 2 0.9524 3 0.9327 4 0.9187 5 0.8638 Assume that a portion of the portfolio is prepaid when the interest rate falls, i.e. mortgage refinancing. The probability that the mortgage will be prepaid after the next coupon is 20%. A pass-through MBS is created at an interest rate of 4%. 1. Compute the spot discount rates for all maturities. 2. Value the pass-through MBS. 3. Compute the duration of the Pass-Through security. 4. Compute the convexity of the MBS. 5. Suppose that the interest rate falls by 1% (or 100 basis points) uniformly across for all maturities. Value the Pass-Through security.