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欢欢 · 2022年01月14日

分母为什么不是除以0.02？PVBP的定义不是改变1bp吗？

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000124

问题如下：

A bond with exactly nine years remaining until maturity offers a 3% coupon rate with annual coupons. The bond, with a yield-to-maturity of 5%, is priced at 85.784357 per 100 of par value. The estimated price value of a basis point for the bond is closest to:

选项：

A.

0.0086.

B.

0.0648.

C.

0.1295.

解释：

B is correct.

The PVBP is closest to 0.0648. The formula for the price value of a basis pointis:

PVBP=(PV−)−(PV+)2PVBP=\frac{(PV-)-(PV+)}2

where:

PVBP = price value of a basis point

PV– = full price calculated by lowering the yield-to-maturity by one basis point

PV+ = full price calculated by raising the yield-to-maturity by one basis point

Lowering the yield-to-maturity by one basis point to 4.99% results in a bond price of 85.849134:

PV−=3(1+0.0499)1+⋯+3+100(1+0.0499)9=85.849134PV-=\frac3{{(1+0.0499)}^1}+\cdots+\frac{3+100}{{(1+0.0499)}^9}=85.849134

Increasing the yield-to-maturity by one basis point to 5.01% results in a bond price of 85.719638:

PV+=3(1+0.0501)1+⋯+3+100(1+0.0501)9=85.719638PV+=\frac3{{(1+0.0501)}^1}+\cdots+\frac{3+100}{{(1+0.0501)}^9}=85.719638

PVBP=85.849134−85.7196382=0.06475PVBP=\frac{85.849134-85.719638}2=0.06475

Alternatively, the PVBP can be derived using modified duration:

ApproxModDur=(PV−)−(PV+)2×(ΔYield)×(PV0)ApproxModDur=\frac{(PV-)-(PV+)}{2\times(\Delta Yield)\times(PV0)}

ApproxModDur=85.849134−85.7196382×0.0001×85.784357=7.548ApproxModDur=\frac{85.849134-85.719638}{2\times0.0001\times85.784357}=7.548

PVBP = 7.548 × 85.784357 × 0.0001 = 0.06475

考点：PVBP

解析：PVBP衡量的是利率变化1bp，带来的债券价格变化。

分别算出利率下降1个bp的债券价格PV-(85.849134)和利率上升一个bp的债券价格PV+(85.719638)，两者相减再除以2，即可得PVBP=0.0648，故选项B正确。

注意：如果直接算出PV+（或PV-），它和原本的PV之间本身就是由于利率变化1bp造成的，所以两者直接相减即可，不需要除以2。 如果分别算出PV-和PV+，那么它俩之间是由于利率相差2bps造成的，所以相减之后需要除以2。

如题。。。。。。。谢谢。
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1 个答案

笛子_品职助教 · 2022年01月15日

嗨，努力学习的PZer你好：


公式是对的，分母是2，不是0.02

含义是：可以减1个bp，也可以加1个BP，所以分子是变化了2个BP，就要除以2。


简单理解：因为PVBP考察的是变动1个BP，而公式中的分子却变动了2个BP，因此分母是2。不是0.02.

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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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2024-07-18 05:28 1 · 回答

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2022-08-04 03:47 1 · 回答

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2022-08-01 07:10 1 · 回答