In fixed income calculations, convexity estimates the amount duration will change given a change in interest rates.

Bond investors prefer bonds that have positive convexity. This is because when interest rates fall, the bond's duration increases, which makes the bond's price rise more. Conversely, when rates rise, the duration will shorten, and price losses will be less.

Bonds with embedded options (e.g. mortgage securities) have negative convexity. That is, duration extends as rates rise, and shortens as rates fall.

#### (Mathematics:)

Convexity is the study of convex objects in some real vector space. Convexity is an amazing topic: just from the fact that a set is convex you can deduce all manner of smoothness properties, intersection properties, inequalities, geometric conclusions, and more!

I have collected some convexity-related nodes below (yes, this is a metanode). Please `/msg` me with additions! (Better yet, add new convexity-related nodes and `/msg` me about them...). Please note that although convexity in infinite-dimensional spaces (Banach spaces) is also extremely important, thus far we do not appear to have anything on that topic. So almost everything below is finite dimensional.

### Convexity metanode

Definition
Intersection properties
Inequalities
Calculus
Polyhedra
Infinite dimensional spaces

Con*vex"i*ty (?), n.; pl. Convexities (#). [L. convexitas: cf. F. convexit'e.]

The state of being convex; the exterior surface of a convex body; roundness.

A smooth, uniform convexity and rotundity of a globe. Bentley.