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PZmomo · 2024年05月02日

comment 3

NO.PZ2023040701000040

问题如下:

Hake develops a framework for valuing bonds using a binomial interest rate tree. He understands that there are several factors used in developing the tree and asks Annisquam for counsel on the correct data to use. Annisquam makes the following comments to Hake:

Comment 1: In the valuation process, the interest rate tree generates cash flows that are interest rate dependent; but does not provide the interest rates used to discount those cash flows.

Comment 2: Two assumptions must be made to create a binomial tree. The first is an interest rate model such as a lognormal model of interest rates. The second is a volatility of interest rates.

Comment 3: Volatility can be measured relative to the current level of rates. By using a lognormal distribution, interest rate movements are proportional to the level of rates and are bounded at the low end by zero.

Which of Annisquam's comments regarding binomial interest rate trees is least likely correct?

选项:

A.

Comment 1

B.

Comment 2

C.

Comment 3

解释:

Correct Answer: A

Annisquam is incorrect in Comment 1. The interest rate tree performs two functions in the valuation process: (1) generating the cash flows that are interest rate dependent and (2) supplying the interest rates used to determine the present value of the cash flows.

Volatility can be measured relative to the current level of rates. By using a lognormal distribution, interest rate movements are proportional to the level of rates and are bounded at the low end by zero. -- comment 3是什么意思?

1 个答案

pzqa31 · 2024年05月05日

嗨,爱思考的PZer你好:


comment3说的是lognormal的性质,lognormal分布一个关键特性是其等比例性。这主要体现在,当随机变量服从对数正态分布时,其变化率或百分比变化与当前的水平或数值大小无关,呈现出一种等比例的特性。具体来说,假设我们有一个服从对数正态分布的随机变量,如股票价格或资产价值。无论这些变量的当前水平是高还是低,它们的变化率或百分比变化都是等比例的。也就是说,从一个较低的水平增长到两倍,与从一个较高的水平增长到两倍,所需要的百分比变化是相同的。另外,lognormal还具有非负性,所以特别适合用于衡量如资产价格等不能为负的变量。

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