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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年08月17日

bond price是不是错了?

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000063

问题如下：

A European put option, which would be expired in two years, has a strike price of $101.00. The underlying bond has three years to maturity with 7% annual coupon. It is known that the risk-neutral probability of an downward move is 0.3 in year 1 and 0.4 in year 2. The current interest rate is 3.00% At the end of year l, the rate will either be 5.88% or 4.66%. If the rate in year 1 is 5.88%, it will either rise to 8.56% or rise to 6.34% in year 2. If the rate in year 1 is 4.66%, it will either rise to 6.34% or decrease to 4.58%. The value of the put option today is closest to:

选项：

A.

$1.10.

B.

$1.32.

C.

$1.48.

D.

$1.99.

解释：

A is correct.

考点：Option on bond

解析：

先求出两年后的 bond value 在利率为 8.56%, 6.34%, 4.58% 时分别为 98.56, 100.62, 102.31，对应 put option value 分别为 2.44, 0.38, 0

The option value in the upper node at the end of year 1 is computed as:

($2.44×0.6)+($0.38×0.4)1.0588=$1.52\frac{{(\$2.44\times0.6)}+{(\$0.38\times0.4)}}{1.0588}=\$1.52

The option value in the lower node at the end of year 1 is computed as:

($0.38×0.6)+($0.00×0.4)1.0466=$0.22\frac{{(\$0.38\times0.6)}+{(\$0.00\times0.4)}}{1.0466}=\$0.22

The option value today is computed as:

($1.52×0.7)+($0.22×0.3)1.0300=$1.10\frac{{(\$1.52\times0.7)}+{(\$0.22\times0.3)}}{1.0300}=\$1.10


解析中的bond price是不是错了?


我的计算是

N=3, I/Y=8.56, PMT=7, FV=100 求出PV=96.02

N=3, I/Y=6.34, PMT=7, FV=100 求出PV=101.753

N=3, I/Y=4.58, PMT=7, FV=100 求出PV=106.64


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pzqa27 · 2023年08月17日

嗨，从没放弃的小努力你好：


题目的价格没有算错，这里是利率2叉树，所以解析计算的是2年后的bond price，您写的那个是bond的PV，我们求期权价值用不到PV

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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