使用即期利率的债券估值和利率二叉树中债券估值都为什么相同？

NO.PZ2018123101000060 问题如下 The following statements were ma in the course of the bate regarng the contions unrlying binomiinterest rate trees: Statement 1: The only requirements neeto create a binomiinterest rate tree are current benchmark interest rates anassumption about interest rate volatility. Statement 2: Potentiinterest rate volatility in a binomiinterest rate tree cestimateusing historicinterest rate volatility or observemarket prices from interest rate rivatives. Statement 3: A bonvalue rivefrom a binomiinterest rate tree with a relatively high volatility assumption will fferent from the value calculatescounting the bons cash flows using current spot rates. Whiof the various statements regarng binomiinterest rate trees is correct? Statement 1 Statement 2 Statement 3 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。 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。请问这三个要求分别是什么？1、volatility确定2、利率要服从log normal分布还有一个是啥？

NO.PZ2018123101000060 问题如下 The following statements were ma in the course of the bate regarng the contions unrlying binomiinterest rate trees: Statement 1: The only requirements neeto create a binomiinterest rate tree are current benchmark interest rates anassumption about interest rate volatility. Statement 2: Potentiinterest rate volatility in a binomiinterest rate tree cestimateusing historicinterest rate volatility or observemarket prices from interest rate rivatives. Statement 3: A bonvalue rivefrom a binomiinterest rate tree with a relatively high volatility assumption will fferent from the value calculatescounting the bons cash flows using current spot rates. Whiof the various statements regarng binomiinterest rate trees is correct? Statement 1 Statement 2 Statement 3 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。 从上面这个角度，risky bonvalue是有变化的。但从题目中，怎么分辩是利用二叉树计算risk-free bon是risky bon

NO.PZ2018123101000060 问题如下 The following statements were ma in the course of the bate regarng the contions unrlying binomiinterest rate trees: Statement 1: The only requirements neeto create a binomiinterest rate tree are current benchmark interest rates anassumption about interest rate volatility. Statement 2: Potentiinterest rate volatility in a binomiinterest rate tree cestimateusing historicinterest rate volatility or observemarket prices from interest rate rivatives. Statement 3: A bonvalue rivefrom a binomiinterest rate tree with a relatively high volatility assumption will fferent from the value calculatescounting the bons cash flows using current spot rates. Whiof the various statements regarng binomiinterest rate trees is correct? Statement 1 Statement 2 Statement 3 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说的应该有3个requirement，分别是什么呢？C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？

NO.PZ2018123101000060 问题如下 The following statements were ma in the course of the bate regarng the contions unrlying binomiinterest rate trees: Statement 1: The only requirements neeto create a binomiinterest rate tree are current benchmark interest rates anassumption about interest rate volatility. Statement 2: Potentiinterest rate volatility in a binomiinterest rate tree cestimateusing historicinterest rate volatility or observemarket prices from interest rate rivatives. Statement 3: A bonvalue rivefrom a binomiinterest rate tree with a relatively high volatility assumption will fferent from the value calculatescounting the bons cash flows using current spot rates. Whiof the various statements regarng binomiinterest rate trees is correct? Statement 1 Statement 2 Statement 3 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。 请问statement3在讲义的哪个位置有讲到