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kinman · 2024年01月23日

關於正負號問題

NO.PZ2023120801000104

问题如下:

An investment-grade bond with modified duration of 7 and reported convexity of 0.51 increases in price by 9.93% after a yield spread change. The value of the spread change would be closest to:

选项:

A.

−1.5%

B.

0.15%

C.

1.5%

解释:

Correct Answer: A

%∆PVFull = −(AnnModDur × ∆Spread) + 0.5 × AnnConvexity × (∆Spread)2

0.0993 = −(7 x ∆Spread) + 0.5 × (51) × (∆Spread)2

∆Spread = −0.0135−1.5%

代入-0.015進去,-7×(-0.015)+(0.5×51×(-0.015²))=0.110739

代入 0.015算出來才是正確答案,是公式負號記錯了嗎?

1 个答案

吴昊_品职助教 · 2024年01月23日

嗨,努力学习的PZer你好:


increases in price by 9.93%,现在债券价格上升,所以spread一定是下降的,因为债券价格和利率之间是反向变动的关系。所以△spread的符号一定是负的。

准确来说,∆Spread = −0.0135,-7×(-0.0135)+0.5×51×(0.0135²)= 0.0992≈9.93%

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