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好好学习向前进 · 2023年07月31日

关于选项A和C

NO.PZ2018123101000060

问题如下:

The following statements were made in the course of the debate regarding the conditions underlying binomial interest rate trees:

Statement 1: The only requirements needed to create a binomial interest rate tree are current benchmark interest rates and an assumption about interest rate volatility.

Statement 2: Potential interest rate volatility in a binomial interest rate tree can be estimated using historical interest rate volatility or observed market prices from interest rate derivatives.

Statement 3: A bond value derived from a binomial interest rate tree with a relatively high volatility assumption will be different from the value calculated by discounting the bond’s cash flows using current spot rates.

Which of the various statements regarding binomial interest rate trees is correct?

选项:

A.

Statement 1

B.

Statement 2

C.

Statement 3

解释:

B is correct.

考点:对二叉树模型的理解

解析:通常使用两种方法来估计利率二叉树中的利率波动率。

第一种方法基于历史利率波动率的估计。

第二种方法使用观察到的利率衍生品的市场价格。

Statement 1不正确,因为创建利率二叉树有三个要求,而不是两个。第三个要求是关于利率模型的假设。

Statement 3不正确,因为无论模型中使用的波动率假设如何,使用即期利率的债券估值和利率二叉树中债券估值都是相同的。

A选项说的应该有3个requirement,分别是什么呢?

C选项说的,高波动性的算出来和用spot算出来一样,为什么呢?高波动性的话,i更分散;用spot算的话,得出f再用e^2欧米伽,为什么会一样呢?

2 个答案

pzqa015 · 2023年08月01日

嗨,努力学习的PZer你好:


高波动的话,二叉树更分散,导致上面点的利率更大,下面点的利率更小,最终上面的value更小,下面的value更大,对最终的value没有影响,这是一个结论。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

pzqa015 · 2023年08月01日

嗨,努力学习的PZer你好:


A选项除了说的那两个,还有一个假设是利率服从lognormal分布,因为lognormal分布无negative值,符合利率不能为负的实际情况。

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努力的时光都是限量版,加油!

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