Let us check if and by how much using convexity improves the approximation of the bond price changes that we have considered in Example 6.1. As we have seen there, the prices of two zeros maturing in 3 and 20 years, respectively, are

When yield is 3%, and they drop to 

when there is an increase by 100 basis points. If we use both duration and convexity, we find the approximations

These approximations are definitely more accurate than those provided by a first-order expansion. For the second zero, the percentage error drops (in absolute value) from \(228 \%\) in Example 6.1 to

when adding the second-order term.

Data From Example 6.1

Data From Equation (6.3)

Transcribed Image Text:

Pz (0, 0.03; 3) = 100 x e-0.03x3 = 91.39312, P(0, 0.03; 20)=100 x e-0.0320 = 54.88116,