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金融民工阿聪 · 2021年03月07日

Statement 2的问题

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。

1.Statement 2说σ会变小。但是 关于V-model,σ不是不变的吗,constant。为什么这里说它是对的呢

2.提问也有人问了,但是我看老师说,"这里的voatility不是指公式中的σ,而是收益率曲线的standard deviation。"但是这句话我不理解,因为公式中的σ本来不就是说的rate的波动率吗,这不是一个东西吗,那一会说恒定,一会说变小,怎么理解

2 个答案
已采纳答案

品职答疑小助手雍 · 2021年03月08日

嗨,努力学习的PZer你好:


所以你还是没明白这里是有两个波动率的。还是来说第一次提问的这句“1.Statement 2说σ会变小。但是 关于V-model,σ不是不变的吗,constant。为什么这里说它是对的呢

你看Vmodel的公式,一个是均值复归项,一个是波动项。你问题里的σ指的是波动项里的那个波动率,这个波动率是constant的,但是rate的公式还包含了均值复归项,这一项会在总体上减少这两项相加的总体波动率,也就是rate的波动率会比单独波动项那个σ小。

在明白了上面那句话的基础上,你才能看明白我第一次回复的rate的波动率不是波动项的波动率这句话。也就解答了你第一次提问的问题1和2。

至于追问的问题2,其实就是均值复归项会给rate整体带来一个减小波动率的效果,所以说Vmodel整体的波动率是比model1(它的σ和Vmodel波动项的σ相等)的整体波动率要小。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

品职答疑小助手雍 · 2021年03月07日

嗨,从没放弃的小努力你好:


那首先就要确定一下问题2,题目里既然说了是rate的波动率那就不是公式里波动项的波动率了。

然后再来说问题1,明确了是rate的波动率之后,那就直接用原版书的结论了(因为v-model假设了均值回归,所以利率的短期波动性下降了),当然可以通过excel画100条路径看看结果,我画过也是感觉均值复归属性的rate的波动率小一些。

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加油吧,让我们一起遇见更好的自己!

金融民工阿聪 · 2021年03月08日

还是有两个问题: 1.rate的波动率和公式里的波动率?有啥区别,两者不都是在说rate嘛,这两个rate不一样? 2.我仔细看了一下,老师提供的一个解析的图(说明v-model均值回归会有decreasing σ),里面其实说的是,如果同样的一个背景,如果假设它加上了这个均值回归,得出的σ353bps,会比不假设均值回归的模型得出的σ约390bps要小。这个小是针对不同模型(有均值回归和无均值回归)的区别,不是说它在V-model里面σ会变小吧? sta2说的是V模型里面的σ是decreasing的,而Model1的σ是constant的,实际来说应该两个都是constant吧?

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