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金融民工阿聪 · 2021年03月07日

Statement 2的问题(2)

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。

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里面会变小吧?

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已采纳答案

小刘_品职助教 · 2021年03月08日

同学你好,

我之前表述的不太清楚。对于V-model 来说,他是以1/k 的速度向均值复归的,所以随着回归到均值之后,你可以认为他的volatility是处于一个decreasing的状态的,statement 2 是正确的。

DD仔_品职助教 · 2022年10月12日

嗨,努力学习的PZer你好:


前半句:V模型是均值复归模型,也就是说利率总是要回归均值的,那么这一期利率高于均值,就会逐渐下降想均值靠近,短期来看,因为利率会不断根据均值作出调整,所以短期的波动性相比于长期来看会比较高。所以波动性是逐渐下降的。

后半句:model1的结论 波动率是固定的

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

朵朵0927 · 2022年09月23日

老师麻烦再详细解释下2为什么不对?谢谢^

小刘_品职助教 · 2021年03月07日

同学你好,

这题的关键点在于V-model假设了均值回归,所以可以说V-model的σ比model 1 小哈~

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