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Describe Macaulay duration, modified duration, and convexity for fixed income securities. Show that under continuous compounding the Macaulay duration is given by tecke-Alik D = *=0P where P is the present value of the bond, is the yield, C, denotes the kell coupon paid at time ty. Find the derivative (dP/di) of the present value (P) with respect to l and write it in terms of D and P. What is the financial meaning of dp/d/? Consider a bond that has a coupon rate of c paid m times a year and a yield of 1>0. Show that under discrete compounding the limiting value of duration, as maturity is increased to infinity, is given by, 1+1/m 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. Show that when the yield of a bond is equal to its coupon rate then its present value is equal to its face value. Prove this for a bond with price P and face value F that makes m coupon payments of Ct per year, and with n remaining periods. Describe Macaulay duration, modified duration, and convexity for fixed income securities. Show that under continuous compounding the Macaulay duration is given by tecke-Alik D = *=0P where P is the present value of the bond, is the yield, C, denotes the kell coupon paid at time ty. Find the derivative (dP/di) of the present value (P) with respect to l and write it in terms of D and P. What is the financial meaning of dp/d/? Consider a bond that has a coupon rate of c paid m times a year and a yield of 1>0. Show that under discrete compounding the limiting value of duration, as maturity is increased to infinity, is given by, 1+1/m 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. Show that when the yield of a bond is equal to its coupon rate then its present value is equal to its face value. Prove this for a bond with price P and face value F that makes m coupon payments of Ct per year, and with n remaining periods