问一道题：NO.PZ2019070101000050

问题如下：

A bond has a par of $100 and a coupon rate of 10% paid semiannually. The bond has a YTM of 10% and a maturity of 10 years. If the yeild change by 10 basis point, the effective duration and convexity of the bond  are closest to:

选项：

解释：

C is correct

考点：Bond Duration and Convexity

解析：

利率上涨0.1%，债券价格等于：

$$N=20; PMT=5; FV=100; I/Y=10.1/2=5.05;  CPT PV= 99.3795

利率下跌0.1%，债券价格等于：

N=20; PMT=5; FV=100; I/Y=9.9/2=4.95;  CPT PV= 100.6258

Δy=0.001

$\begin{array}{l}D\text{uration=}\frac{100.6258\text{-}99.3795}{2\times \mathrm{100\times }0.001}\text{=}6.231\\ C\text{onvexity=}\frac{100.6258\text{+}99.3795\text{-}200}{₤100₤₤0.001{₤}^2}\text{=}53\end{array}$