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pinzhixiaoguo · 2022年10月01日

不懂volatility到底什么时候说的是西格玛什么时候说的是r的。

NO.PZ2018122701000068

问题如下:

Jack Ma, FRM, is studying difference model, including mean-reverting models, no-drift models, models that incorporate drift, and Ho-Lee models. Ma makes the following statements about the appropriate usage of these models:

Statement 1: Both Model 1 (no drift) and the Vasicek model assume non-parallel shifts from changes in the short-term rate.

Statement 2: The Vasicek model implies decreasing volatility in short-term rates while Model 1 assumes constant volatility of future short-term rates.

Statement 3: The Model 2 (constant drift model) is a more flexible model than the Ho-Lee model.

How many of the statements is/are incorrect?

选项:

A.

0

B.

1

C.

2

D.

3

解释:

C is correct.

考点:Term structure models

解析:要求选错误的陈述有几个。

Statement 1不正确. Model 1 assume parallel shifts from changes in the short-term rate.

Statement 2 正确.

Statement 3不正确.The Ho-Lee model is actually more general than Model 2, as no drift and constant drift models are special cases of the Ho-Lee model.

因此,有2个陈述错了,答案选C。

Statement 2: The Vasicek model implies decreasing volatility in short-term rates while Model 1 assumes constant volatility of future short-term rates.


这句话V模型里面的西格玛是恒定的,但为什么是decrease?老师之前的提问里说这是r的波动率,不是西格玛,可是西格玛不就是r的波动吗?难道西格玛是什么别的东西的波动?

还有第二个问题。到底什么是平行移动?我怎么感觉有constant的drift才算平行移动?

还有第三个问题。V模型里面,(θ-r)的这个r,在第一个node运算的时候是r0,那到了第二个node,这个r要套上一步的结果变成r1还是说还带入r0?谢谢

2 个答案

李坏_品职助教 · 2022年10月01日

嗨,努力学习的PZer你好:


不好意思,我看错了。


V-model如果用在二叉树里,第二个节点的r要用r1。见原版书P188:


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

李坏_品职助教 · 2022年10月01日

嗨,努力学习的PZer你好:


首先,volatility一直都是指的sigma,也就是标准差。


  1. V模型在短期利率上是假定利率是均值回归的。均值回归的意思是短期利率不会超出长期均衡水平太多(意思是short-term rate不会一直涨或者一直跌),所以r的σ会下降。参考讲义P168:


2.FRM里面平行移动意思是各期限的利率(长期和短期利率)以相同的幅度移动,不会改变利率期限结构的斜率。

3.用r0, 看讲义P170前后的几张图,不管是哪个model 都是用r0:



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虽然现在很辛苦,但努力过的感觉真的很好,加油!

pinzhixiaoguo · 2022年10月01日

您的截图和我的基础班讲义的页码好像不一致。第三个问题当中我问的是v-model,在基础班讲义第176页,您放的画红框的截图是lognormal model的二叉树。我问的是V-model里面k(θ-r)的r,在求第二个节点的时候,用第一个节点的数值r1还是初始值r0?

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