7. Modified duration is defined as the percentage change of a bond's price P with dp/dy respect to a one-percent change in interest rate y, i.e., | 1. It measures how sensitive the bond price is to interest rate changes, and hence is a proxy for the interest rate risk of the bond. For a coupon bond with face value M, time to maturity n (in periods), periodic coupon payment C, and periodic market interest rate y, prove its modified duration is 1 3C a. C 2C (1+y)P/(1+y) * (1+ y)2 + (1+y)' 1 ( + + C M (1+y)" '(1+y)" + 1 b. by the y?p[ (1+y)" P " 1 + n(M-Cly) (1 + y)"+lp 1 7. Modified duration is defined as the percentage change of a bond's price P with dp/dy respect to a one-percent change in interest rate y, i.e., | 1. It measures how sensitive the bond price is to interest rate changes, and hence is a proxy for the interest rate risk of the bond. For a coupon bond with face value M, time to maturity n (in periods), periodic coupon payment C, and periodic market interest rate y, prove its modified duration is 1 3C a. C 2C (1+y)P/(1+y) * (1+ y)2 + (1+y)' 1 ( + + C M (1+y)" '(1+y)" + 1 b. by the y?p[ (1+y)" P " 1 + n(M-Cly) (1 + y)"+lp 1