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LL77 · 2024年10月29日

为什么要rescale the convexity from 0.25 to 25?

NO.PZ2023090801000011

问题如下:

For a bond with a modified duration of 4 and a convexity of 0.25, which of the following changes in credit spread would result in a price decrease closest to 7.5%?

选项:

A.

1% decrease

B.

1% increase

C.

2% increase

解释:

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

− (4 × 0.02) + 0.5 × 25 × (0.02)^2 = –0.075 or –7.5%

The spread change is inversely related to the price effect, with a spread increase leading to a fall in bond price. Note that since duration was 4, we had to rescale the convexity from 0.25 to 25.

Note that since duration was 4, we had to rescale the convexity from 0.25 to 25. 为什么要rescale?为什么乘100?

2 个答案
已采纳答案

吴昊_品职助教 · 2024年10月30日

嗨,爱思考的PZer你好:


不是所有情况下,convexity都需要rescale的。

如果convexity不是纯小数,可以直接代入的;如果convexity很小(纯小数),convexity则需要rescale,即乘100。

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吴昊_品职助教 · 2024年10月29日

嗨,爱思考的PZer你好:


原则:当convexity很小(纯小数),convexity则需要rescale,即乘100.

convexity本身就是二阶导的影响,如果直接代入纯小数的话,0.5×convexity×(△y)^2,这一项就会很小,小到可以忽略不计了。所以在遇到convexity很小的情况下,我们需要将convexity乘以100.

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