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ruby5ltc · 2023年06月11日

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NO.PZ201712110200000205

问题如下:

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.

Two methods are commonly used to estimate potential interest rate volatility in a binomial interest rate tree. The first method bases estimates on historical interest rate volatility. The second method uses observed market prices of interest rate derivatives.

Statement 1 is incorrect because there are three requirements to create a binomial interest rate tree, not two. The third requirement is an assumption regarding the interest rate model. Statement 3 is incorrect because the valuation of a bond using spot rates and the valuation of a bond from an interest rate tree will be the same regardless of the volatility assumption used in the model.

1、Statement 3 is incorrect because the valuation of a bond using spot rates and the valuation of a bond from an interest rate tree will be the same regardless of the volatility assumption used in the model.为什么呢?

2、利率模型只能是lognormal?正太分布行吗?

1 个答案

pzqa015 · 2023年06月11日

嗨,努力学习的PZer你好:


这是结论,二叉树得到的价格是无套利价格,与spot rate得到的价格一致。由于二叉树是近似对称的,如果用到的volatility更大,那么二叉树形状会更“分散”,上半部分得到的价格会下降,下半部分得到的价格会上涨,最终综合起来,与原价格几乎一致。

二叉树一个假设就是利率服从lognormal分布,而不是服从正太分布。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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NO.PZ201712110200000205 问题如下 Whiof the various statements regarng binomiinterest rate trees is correct? A.Statement 1 B.Statement 2 C.Statement 3 B is correct.Two metho are commonly useto estimate potentiinterest rate volatility in a binomiinterest rate tree. The first methobases estimates on historicinterest rate volatility. The seconmethouses observemarket prices of interest rate rivatives.Statement 1 is incorrebecause there are three requirements to create a binomiinterest rate tree, not two. The thirrequirement is assumption regarng the interest rate mol. Statement 3 is incorrebecause the valuation of a bonusing spot rates anthe valuation of a bonfrom interest rate tree will the same regaress of the volatility assumption usein the mol. 二叉树有那么多利率跟确定的spot rate怎么做比较呢?

2023-10-09 22:19 1 · 回答

NO.PZ201712110200000205 老师好, 当时我认为statement3不对是我当时觉得那个volatility的变动幅度是会改变债券在t0时刻的价格的,只是多过还是少过就不确定了,而不是像题目说的多过,所以我没选statement3. 我之所以认为volatility的变动幅度是会改变债券在t0时刻的价格的,是因为我之前做过一道题,他说两个二叉树,A比B的volatility更大,那么A的forwarrate应该比B高一些,因为upper no对forwarrate的影响比Lower no的影响大。 接下来我又想,forwarrate其实相当于upper no和lower no的中值,所以forwarrate也变了,那么后续折现到t0时刻的债券价值也会变。而不是和解析说的那样。 请问老师我哪里想错了,请老师帮忙指正,谢谢。

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