Definition of Negative convexity:
Negative convexity exists when the shape of a bond's yield curve is concave. A bond's convexity is the rate of change of its duration, and it is measured as the second derivative of the bond's price with respect to its yield. Most mortgage bonds are negatively convex, and callable bonds usually exhibit negative convexity at lower yields.
Situation in which the principal of a callable bond is returned (1) before the maturity date in declining interest rate environment or (2) after the maturity date in rising interest rate environment. The first situation may require the reinvestment of the principal at prevailing lower interest rates (call risk), the second may result in losing the opportunity to earn prevailing higher interest rates (extension risk).
Typically, when interest rates decrease, a bond's price increases. For bonds that have negative convexity, prices decrease as interest rates fall. For example, with a callable bond, as interest rates fall, the incentive for the issuer to call the bond at par increases; therefore, its price will not rise as quickly as the price of a non-callable bond. The price of a callable bond might actually drop as the likelihood that the bond will be called increases. This is why the shape of a callable bond's curve of price with respect to yield is concave or negatively convex.
Meaning of Negative convexity & Negative convexity Definition