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迷雾森林 · 2024年06月20日

问题

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NO.PZ202312080100008202

问题如下:

Given a 75 bps change in the yields-to-maturity for Bonds Y and Z, the convexity adjustment for Bond Z would be greater than the convexity adjustment of Bond Y:

选项:

A.

if the YTM change is positive

B.

if the YTM change is negative

C.

regardless of the direction of the change in YTM

解释:

Correct Answer: C

Since the convexity adjustment uses the square of the change in yield, it is always positive regardless of the direction of the change in yield-to-maturity. As a result, the convexity adjustment for Bond Z will always be greater than the convexity adjustment for Bond Y, given the same change in yields-to-maturity.

当收益率上升75个bp时,Y变动-0.064967,Z变动-0.090575,Z的变动小于Y 反之下降是,Y变动0.27636,Z变动0.100696,Z的变动大于Y 从这一点来看,C不正确

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已采纳答案

吴昊_品职助教 · 2024年06月20日

嗨,努力学习的PZer你好:


本题只考虑convexity adjustment = 0.5×Convexity×(△y)^2,无论利率上升75个bp,还是下降75个bp,(△y)^2都是正的,代入上述公式都是一样的。

1、当△y=0.75%=0.0075时,Y的convexity adjustment = 0.5×91.0278×(0.0075)^2 = 0.00256;Z的convexity adjustment = 0.5×179.8591×(0.0075)^2 = 0.00505

2、当△y= -0.75% = -0.0075时,Y的convexity adjustment = 0.5×91.0278×(-0.0075)^2 = 0.00256;Z的convexity adjustment = 0.5×179.8591×(-0.0075)^2 = 0.00505

所以,无论利率上升还是下降,只考虑convexity adjustment,Z的变化都是大于Y的变化,选C。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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