Convexity

(noun)

As interest rates change, the price does not change linearly, but rather is a convex function of interest rates. Convexity is a measure of the curvature of how the price of a bond changes as the interest rate changes. Specifically, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question, and the convexity as the second derivative.

Related Terms

Examples of Convexity in the following topics:

  • Image Formation by Spherical Mirrors: Reflection and Sign Conventions

    • Spherical mirrors can be either concave or convex.
    • A convex mirror has a negative focal length because of this.
    • A summary of the properties of convex mirrors is shown below:
    • A convex mirror with three rays drawn to locate the image.
    • For a convex mirror, the image is virtual and upright.

  • Refraction and Magnification

    • In general, two types of lenses exist: convex lenses, which cause parallel light rays to converge, and concave lenses, which cause parallel light rays to diverge.
    • The former property of convex lenses is of special interest to microbiologists.
    • In essence, a convex lens allows magnification.
    • A magnifying glass is one convex lens, and this by itself allows the magnification of objects.
    • Note also that many of the lenses are convex, thus the light that goes through a specimen is focused and therefore magnified.

  • The Compound Microscope

    • A compound microscope is made of two convex lenses; the first, the ocular lens, is close to the eye, and the second is the objective lens.
    • It is made of two convex lenses: the first, the ocular lens, is close to the eye; the second is the objective lens.
    • shows a diagram of a compound microscope made from two convex lenses.

  • The Magnifying Glass

    • A magnifying glass is a convex lens that lets the observer see a larger image of the object being observed.
    • Since a magnifying glass uses its convex shape to focus light in a certain position, it can be used to converge the sun's radiation at the focus, causing hot spots.
    • A magnifying glass is a convex lens that lets the observer see a larger image of the object under observation.
    • A magnifying glass is a convex lens that lets the observer see a larger image of the object under observation.

  • The Spine

    • Lordosis is an exaggerated convex (lordotic) curvature of the lumbar region; it is commonly known as "swayback."
    • The cervical curve convexes forward and begins at the apex of the odontoid (tooth-like) process.
    • The thoracic curve convexes dorsally, begins at the middle of the second thoracic vertebra, and ends at the middle of the 12th thoracic vertebra.
    • It is convex anteriorly with the lower three vertebrae much more convex than the upper two.

  • Properties of Indifference Curves

    • Almost all indifference curves will be negatively sloped, convex, and will not intersect.
    • Nearly all indifference lines will be convex, or curving inwards at the center (towards the bottom left).
    • Consumers naturally desire a bundle of goods that is varied (hence the convex curves for most comparisons) in order to maximize their utility.

  • The Lensmaker's Equation

    • A lens is biconvex (or double convex, or just convex) if both surfaces are convex.
    • The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave.
    • The sign convention used to represent this varies, but for our treatment if R1 is positive the first surface is convex, and if R1 is negative the surface is concave.
    • The signs are reversed for the back surface of the lens: if R2 is positive the surface is concave, and if R2 is negative the surface is convex.

  • Refraction Through Lenses

    • The word lens derives from the Latin word for lentil bean—the shape of which is similar to that of the convex lens (as shown in ).
    • The convex lens is shaped so that all light rays that enter it parallel to its axis cross one another at a single point on the opposite side of the lens.
    • Such a lens is called a converging (or convex) lens for the corresponding effect it has on light rays.
    • Compare the effect of a convex lens and a concave lens on the light rays

  • Newton's Rings

    • Newton's rings seen in two plano-convex lenses with their flat surfaces in contact.
    • One surface is slightly convex, creating the rings.

  • Combinations of Lenses

    • Note the sign convention: a telescope with two convex lenses (f1 > 0, f2 > 0) produces a negative magnification, indicating an inverted image.
    • A convex plus a concave lens (f1 > 0 >f2) produces a positive magnification and the image is upright.
    • The most common type of achromat is the achromatic doublet, which is composed of two individual lenses made from glasses with different amounts of dispersion Typically, one element is a negative (concave) element made out of flint, which has relatively high dispersion, and the other is a positive (convex) element made of crown glass, which has lower dispersion.