The value of convexity increases with volatility and maturity. Convexity is a measure of the curvature in the relationship between bond prices and bond yields. It provides an idea of how the duration of a bond changes as the interest rate changes. This is important because the price of a bond is not a linear function of interest rates, but a convex function. This means that as interest rates change, the sensitivity of a bond's price to further interest rate changes is not constant but varies.

Volatility refers to the degree of variation of a trading price series over time. When volatility increases, the price-yield curve becomes steeper, and thus the convexity increases. Maturity is the length of time until the principal amount of a bond is to be paid. As the maturity of a bond increases, the price-yield curve becomes steeper, and thus the convexity increases. Therefore, both volatility and maturity contribute to an increase in the value of convexity.

Choice A is incorrect. While it is true that the value of convexity increases with volatility, this option does not consider the impact of maturity on convexity. The longer the maturity, the greater the convexity of a bond.

Choice C is incorrect. This choice incorrectly suggests that yield impacts convexity. In fact, yield and convexity have an inverse relationship; as yields increase, duration decreases and thus reduces a bond’s sensitivity to interest rate changes.

Choice D is incorrect. As explained above, while volatility and maturity do increase the value of convexity, yield does not have a positive correlation with it.