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我们 · 2021年05月04日

请问这里折现的时候,为什么不用加上coupon7呢?

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

请问这里折现的时候,为什么不用加上coupon7呢?
1 个答案

小刘_品职助教 · 2021年05月05日

同学你好,

因为这个题目是在算option的价值,在算B2+-的时候已经把coupon算进去了,但是在算option的时候和债券无关,所以不能再加coupon,这边如果不太理解的话建议回去再听听基础班的课,是个很重要的考点。 1.5倍速21分钟左右,例题可以再学习一下

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