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洁1017 · 2024年08月06日

跟基础班讲义的例题算法不一样么?

* 问题详情,请 查看题干

NO.PZ202303270300007102

问题如下:

(2) What is the approximate VaR for the bond position at a 99% confidence interval (equal to 2.33 standard deviations) for one month (with 21 trading days) if daily yield volatility is 1.50 bps and returns are normally distributed?

选项:

A.

$1,234,105

B.

$2,468,210

C.

$5,413,133

解释:

A is correct. The expected change in yield based on a 99% confidence interval for the bond and a 1.50 bps yield volatility over 21 trading days equals 16 bps = (1.50 bps × 2.33 standard deviations × 211/2). We can quantify the bond’s market value change by multiplying the familiar (–ModDur × △Yield) expression by bond price to get $1,234,105 = ($75 million × 1.040175 ⨯ (–9.887 × .0016)).

老师,我按照基础班讲义“P335-336”的例题做的,按照讲义的做法,当给出的是0.8bps,是利率变动波动率即σ(△y/y),所以需要转换成利率波动率,即σ(△y)=y×σ(△y/y)=4%×0.8%,再进行计算。

若按照基础班讲义做,此题:已知的是bps,应该也是利率变动波动率吧?则σ(△y)=2.85%×1.5%=0.0428%

VaR=2.33×0.0428%×21^½=0.4569%

VaR=(-9.887)×0.4569%×(75,000,000×104.0175/100)

    = -3,524,141.74

答案没有该选项,是我哪一块理解错了,还是答案有问题呢?


1 个答案
已采纳答案

发亮_品职助教 · 2024年08月06日

这是一道老错题了,协会前后改了很多遍,然后勘误之后,原版书例题和课后题还是2个算法。所以这块的基础课程就把2个方法都讲给大家了。


说一下例题为什么要用yield volatility×YTM,因为原来的yield volatility太大了,如果直接用Yield volatiltiy算VaR的话,会导致亏损有可能超过100%,这显然不可能。所以协会对例题的改动是,yield volatility×YTM,YTM是一个小于1的数,可以缩小yield volatility。然后算的VaR相对小一点。


课后题的勘误方法是,直接把yield volatility数字改小一点,算出来的VaR符合常理,所以没有再乘以YTM了,课后题直接用yield volatility=1.50bps乘以根号21,算出来1个月的yield volatility,即:


1.5 bps × 根号21 ×2.33×(-duration)×(market value)

= 1.5bps ×根号21×(-9.887)×(2.33)×(75,000,000×104.0175/100)

最后算下来和A的答案最接近。


说下这块怎么判断。如果Yield volatility比较大,比如0.8%,百分之几,这个yield volatility太大了,需要再乘以YTM缩小。然后再算VaR

如果Yield volatility比较小,例如只有几个Bps,这种直接算VaR即可,无需再额外乘以YTM了。


从25年的新版原版书看,现在考题大概率是比较接近课后题这种算法的,就是不再乘以YTM算VaR了。

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