Consider a 2 year bond with 10% semi-annual coupon payments. Assume that its yield is equal to 10%. Assume F = 100 for face value.

(a) Take the first derivative of the bond price with respect to yield.

(b) Calculate the first derivative by using price and duration. Check that you obtain the same result as in (a).

(c) Find the second derivative of the bond price with respect to yield.

(d) Prove that the price of the bond is a convex function of the yield.