41. For each of the price functions in exercise 40, compare the prices predicted by the forward di¤erence duration approximation with Di ¼ 0:01, to those predicted with the convexity adjustment, again using the convexity approximation with Di ¼

0:01, and then to the exact prices. Do this exercise shifting the original pricing yields G3%,G2%,G1%,G0.5%,G0.1%.