Show that the bond prices B_p given by (8.38) and (8.39) are convex functions of the yield y.

Given the price of the bond Bp, coupon payments Pi, and maturity time T, the yield to maturity is defined as the constant value of y that satisfies the equation n P (8.38) Bp = (1 + y/m)"} n which is based on discrete compounding m times in a year. For continuous compounding we have ( Bp = Pie-yti, (8.39) i=1