Skip to content

IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Duration, convexity and immunisation

A fund holds a single zero-coupon bond paying Rs 100,000 in exactly 10 years. The effective annual yield is 5%. Using the definition of convexity as c(i) = (1/V) d²V/di², what is the convexity of the bond (to two decimal places)?

The convexity is 99.77. For a zero-coupon bond, convexity equals t(t+1)v², which is 10×11 divided by 1.05 squared. Omitting the discount factor squared gives 110, which is wrong.

  1. A90.71
  2. B99.77Correct
  3. C110.00
  4. D95.24
  5. 100.00

Explanation

V = 100000 v^10, so d²V/di² = t(t+1)v^(t+2)·100000. Dividing by V gives t(t+1)v² = 10×11/1.05² = 110/1.1025 = 99.77. Using 110 without v² ignores the discounting factor; 90.71 is t² v² and 95.24 is 100/1.05.

Did you get it right without looking?

One question tells you little. A timed set on Duration, convexity and immunisation shows your real accuracy, how long you take and where you lose marks.

Practise Duration, convexity and immunisationFree diagnostic mock

More Duration, convexity and immunisation questions