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陶婧 · 2024年01月18日

Bond value具体计算过程

  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

Bond value 具体计算过程

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1 个答案

李坏_品职助教 · 2024年01月18日

嗨，努力学习的PZer你好：


The underlying bond has three years to maturity with 7% annual coupon. 意思是这是一个3年期限的、票面利息7%的债券。但是这道题要求的期权只有2年期限，所以我们要先求出2年后这个债券的value。


由于2年后的利率有3种可能：8.56%, 6.34%, 4.58% , 所以分三种情况讨论：

  1. 如果2年后利率为8.56%，那么2年后的债券value = 107 / (1+8.56%) = 98.56.
  2. 如果2年后利率为6.34%，那么2年后的债券value = 107/(1+6.34%) = 100.62.
  3. 如果2年后利率为4.58%，那么2年后的债券value = 107/(1+4.58%) = 102.31.

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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.PZ2018122701000063 问题如下 A Europeput option, whiwoulexpirein two years, ha strike priof $101.00. The unrlying bonhthree years to maturity with 7% annucoupon. It is known ththe risk-neutrprobability of wnwarmove is 0.3 in ye1 an0.4 in ye2. The current interest rate is 3.00% the enof yel, the rate will either 5.88% or 4.66%. If the rate in ye1 is 5.88%, it will either rise to 8.56% or rise to 6.34% in ye2. If the rate in ye1 is 4.66%, it will either rise to 6.34% or crease to 4.58%. The value of the put option toy is closest to: A.$1.10. B.$1.32. C.$1.48. $1.99. A is correct.考点Option on bon析先求出两年后的 bonvalue 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, 0The option value in the upper no the enof ye1 is computeas:($2.44×0.6)+($0.38×0.4)1.0588=$1.52\frac{{(\$2.44\times0.6)}+{(\$0.38\times0.4)}}{1.0588}=\$1.521.0588($2.44×0.6)+($0.38×0.4)​=$1.52The option value in the lower no the enof ye1 is computeas:($0.38×0.6)+($0.00×0.4)1.0466=$0.22\frac{{(\$0.38\times0.6)}+{(\$0.00\times0.4)}}{1.0466}=\$0.221.0466($0.38×0.6)+($0.00×0.4)​=$0.22The option value toy is computeas:($1.52×0.7)+($0.22×0.3)1.0300=$1.10\frac{{(\$1.52\times0.7)}+{(\$0.22\times0.3)}}{1.0300}=\$1.101.0300($1.52×0.7)+($0.22×0.3)​=$1.10 如题

2024-03-08 00:36 2 · 回答

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2023-08-17 10:57 1 · 回答

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2021-08-07 16:29 1 · 回答

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2021-05-04 22:05 1 · 回答