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:
The option value in the lower node at the end of year 1 is computed as:
The option value today is computed as:
Bond value 具体计算过程