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月之流离 · 2020年01月15日

问一道题:NO.PZ2016031001000128

问题如下:

A bond has an annual modified duration of 7.140 and annual convexity of 66.200. The bond’s yield-to-maturity is expected to increase by 50 basis points. The expected percentage price change is closest to:

选项:

A.

–3.40%.

B.

–3.49%.

C.

–3.57%.

解释:

B is correct.

The expected percentage price change is closest to 3.49%. The convexity adjusted percentage price change for a bond given a change in the yield-to-maturity is estimated by:

%ΔPV  Full[AnnModDur×ΔYield]+[0.5×AnnConverxity×(ΔYield)2]\%\Delta PV\;Full\approx\lbrack-AnnModDur\times\Delta Yield\rbrack+\lbrack0.5\times AnnConverxity\times(\Delta Yield)^2\rbrack

%ΔPV  Full[7.10×0.005]+[0.5×66.200×(0.005)2]\%\Delta PV\;Full\approx\lbrack-7.10\times-0.005\rbrack+\lbrack0.5\times66.200\times(-0.005)^2\rbrack= -0.034873 or -3.49%

看不懂?这题为什么这样计算?

1 个答案

吴昊_品职助教 · 2020年01月15日

嗨,努力学习的PZer你好:


这道题考察的是综合考虑duration和convexity对债券价格的影响,具体公式参考基础班讲义P315页。

现在题目说利率上升50bp,即△yield=0.5%=0.005,duration=7.14,Convexity=66.2,代入公式得到价格的变化率为=(-7.14)×0.005+0.5×66.2×(0.005)^2=-3.49%,选B。解析中给出的数字有些问题,马上进行调整。


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虽然现在很辛苦,但努力过的感觉真的很好,加油!