If two bonds have the same maturity the same yield to maturity and the same level of risk the bonds should they sell for the same price regardless of the bond's coupon rate?

if two bonds offer the same duration and yield, then an investor should look at their levels of convexity. if one bond has greater convexity, it is less affected by interest rate changes. also, bonds with higher convexity will have higher price than bonds with lower convexity regardless whether interest rates rise or fall. Ergo, investors will have to pay more with greater convexity due to the bond's lesser sensitivity to interest rate changes.