Consider a par-priced 15 -year fully amortizing mortgage with a note rate of 7%. Amortize the mortgage assuming that the borrower does not curtail the loan, nor defaults, and pays off the entire balance at the end of year 5 (after the last regular payment). Use the relevant cash flows to the lender to compute the average life, the duration, and convexity of this note, all in years or years-sq. Hints: 1. You do not need a loan amount. Make up a suitable one. 2. You final principal cash flow must include the balance after the last payment has been made, so that the loan is fully paid off. 3. For average life, use tau = sum over times t of (tPCF(t))/ sum over times t of PCF(t), where PCF(t) is the principal cash flow at time t 4. For duration, use D=(P(y+dy/2)P(ydy/2))/dy/P(y), where dy is an arbitrarily small yield increment and P is the price at the corresponding yield 5. For convexity, similarly, C=(P(y+dy)2P(y)+P(ydy))/(dy2P(y)) Consider a par-priced 15 -year fully amortizing mortgage with a note rate of 7%. Amortize the mortgage assuming that the borrower does not curtail the loan, nor defaults, and pays off the entire balance at the end of year 5 (after the last regular payment). Use the relevant cash flows to the lender to compute the average life, the duration, and convexity of this note, all in years or years-sq. Hints: 1. You do not need a loan amount. Make up a suitable one. 2. You final principal cash flow must include the balance after the last payment has been made, so that the loan is fully paid off. 3. For average life, use tau = sum over times t of (tPCF(t))/ sum over times t of PCF(t), where PCF(t) is the principal cash flow at time t 4. For duration, use D=(P(y+dy/2)P(ydy/2))/dy/P(y), where dy is an arbitrarily small yield increment and P is the price at the corresponding yield 5. For convexity, similarly, C=(P(y+dy)2P(y)+P(ydy))/(dy2P(y))