答案与讲解不一致

问题如下：

The price of a three-year Treasury bond with a face value of 1 million and a coupon of 4% when the term structure is flat at 5% is 97.245937. The effective duration and convexity of the bond are 2.784703 and 9.35 resectively.

Estimate the effect of all rates increasing by 0.25% using (a) duration and (b) duration plus convexity.

选项：

A.

(a) -0.696%, (b) -0.683%

B.

(a) -0.696%, (b) -0.709%

C.

(a) 0.696%, (b) 0.683%

D.

(a) 0.696%, (b) 0.709%

解释：

The predicted change using duration is

-97.245937×2.784703×0.0025= -0.677003

Using duration plus convexity we get the estimated change as

-97.245937×2.784703× 0.0025+1/2× 97.245937 ×9.349608× 0.0025²= - 0.674161

The actual change is −0.674170, very close to this.

题目问：已知3年期的treasurybond，面值=1m，coupon rate=4%，利率=5%，利率的期限结构是flat的。这个债券的价格是97.245937，effective duration和convexity分别是2.784703和9.3。

题目要求估计一下利率上升0.25%对价格的影响，a)只考虑duration，b)考虑duration和convexity。

treasury bond一般每半年付息一次。

考虑duration的价格变化：

ΔP=-V0*Duration*ΔR

=-97.245937×2.784703×0.0025

= -0.677003

考虑duration和convexity的价格变化：

ΔP=-V0*Duration*ΔR+0.5*V0*Convexity*ΔR²

=-97.245937×2.784703× 0.0025+1/2× 97.245937 ×9.35× 0.0025²

= - 0.674161