Bond convexity

Convexity is a measure of financial mathematics to describe the behavior of a bond with interest rate changes. It's an extension and improvement of the duration and - like this - only an estimate of the change in the present value.

The course of the present value of bonds in the case of interest rate changes is convex. Since the duration of only the first derivative - ie the slope - into account, it is to be used only for small changes in interest rates or will become less accurate the greater the interest rate goes down.

Takes account of the convexity of the second derivative of - the curvature of - and is therefore a more accurate approximation of the actual value change. The formula for calculating the convexity is:

Where P0 represents the value of the bond at time 0 and i0 the corresponding interest rate.

If P0 ( i0 ), for example,

N = nominal, c = coupon and i = interest rate, then the first derivative in this case

And the second derivative

The change in the present value of a bond in accordance with the principle of convexity is as follows:

In which

• Financial Mathematics
• Financing