Describe Macaulay duration, modified duration, and convexity for fixed income securities la Show that under continuous compounding the Macaulay duration is given by b Cye k 0 D P where P is the present value of the bond, A is the yield, c denotes the ki coupon paid at time .Find the derivative (dP/dA) of the present value (P) with respect to A and write it in terms of D and P. What is the financial meaning of dP/dA? Consider a bond that has a coupon rate of c paid m times a year and a yield of A 0. Show that under discrete compounding the limiting value of duration, as maturity is increased to infinity, is given by, C 1+A/ where A is the yield of the bond, and m is the number of coupon payments per year Find the convexity of a zero-coupon bond maturing at time T under continuous compounding. d c Show that when the yicld of a bond is equal to its coupon rate then its prescnt value is equal to its face value. Prove this for a bond with price P and face value Fthat makes mcoupon payments of C/m per year, and with n remaining periods The five parts carry, respectively, 20%, 20 %, 10 %, 25%, and 25% of the marks Describe Macaulay duration, modified duration, and convexity for fixed income securities la Show that under continuous compounding the Macaulay duration is given by b Cye k 0 D P where P is the present value of the bond, A is the yield, c denotes the ki coupon paid at time .Find the derivative (dP/dA) of the present value (P) with respect to A and write it in terms of D and P. What is the financial meaning of dP/dA? Consider a bond that has a coupon rate of c paid m times a year and a yield of A 0. Show that under discrete compounding the limiting value of duration, as maturity is increased to infinity, is given by, C 1+A/ where A is the yield of the bond, and m is the number of coupon payments per year Find the convexity of a zero-coupon bond maturing at time T under continuous compounding. d c Show that when the yicld of a bond is equal to its coupon rate then its prescnt value is equal to its face value. Prove this for a bond with price P and face value Fthat makes mcoupon payments of C/m per year, and with n remaining periods The five parts carry, respectively, 20%, 20 %, 10 %, 25%, and 25% of the marks