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逢考必过过过过过过 · 2022年07月31日

问一道题：NO.PZ2018123101000049 [ CFA II ]

  1. CFA II
  2. Fixed Income

问题如下：

Exhibit 3 presents most of the data of a binomial lognormal interest rate tree. Exhibit 4 presents most of the data of the implied values for a four-year, option-free, annual pay bond with a 2.5% coupon based on the information in Exhibit 3.

Based on the information in Exhibits 3 and 4, the bond price in euros at Node 1–2 in Exhibit 4 is to:

选项：

A.

102.7917

B.

104.8640

C.

105.2917

解释：

A is correct.

考点：考察利用利率二叉树定价

解析: 想要得到节点1-2的债券价值，用到的数据有：该节点右边的数据，即节点2-2，节点2-3的债券价值和Coupon，以及第一年末至第二年的Forward rate。通过对未来债券价值的折现求得该节点1-2的债券价值：

value = {2.5+(0.5×101.5168+0.5×102.1350)} / 1.014925 = 102.7917

这个题不对啊？我是从后面推了一下尝试的，后面从一开始到102.1350都是不含着这个时点本身的2.5的。都是只有在往前面折算的时候单独加了2.5。为什么这个点Node1-2要把2.5加在里面显示？这与其他的数字显示不一致啊
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1 个答案

pzqa015 · 2022年08月01日

嗨，从没放弃的小努力你好：


这个点的price是未来现金流的折现，具体说就是

(（101.5168+102.1350）/2+2.5)/1.014925，2.5并没有加到price上，二是加到后面两个点上面了。

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NO.PZ2018123101000049 问题如下 Exhibit 3 presents most of the ta of a binomilognorminterest rate tree. Exhibit 4 presents most of the ta of the implievalues for a four-year, option-free, annupbonwith a 2.5% coupon baseon the information in Exhibit 3.Baseon the information in Exhibits 3 an4, the bonpriin euros No 1–2 in Exhibit 4 is to: A.102.7917 B.104.8640 C.105.2917 A is correct.考点考察利用利率二叉树定价解析: 想要得到节点1-2的债券价值，用到的数据有该节点右边的数据，即节点2-2，节点2-3的债券价值和Coupon，以及第一年末至第二年的Forwarrate。通过对未来债券价值的折现求得该节点1-2的债券价值value = {2.5+(0.5×101.5168+0.5×102.1350)} / 1.014925 = 102.7917 为什么只加了一个2.5？

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