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六姑娘 · 2021年11月29日

这题的公式最后面为什么2%要除以根号12

NO.PZ2020033001000069

问题如下:

In the Vasicek model, if the current short-term rate equals 5.2% and the annual volatility of the interest rate process is 2%. The long-run mean- reverting level is assumed to be 12% with a speed of adjustment of 0.5. What are the upper and lower node rates after the first month in the binomial interest rate tree?

选项:

Upper node
Lower node
A.
6.67%
4.91%
B.
6.67%
5.24%
C.
6.06%
5.24%
D.
6.06%
4.91%

解释:

D is correct.

考点:Vasicek model

解析:

Upper  node=5.2%+(0.5)(12%5.2%)12+2%12=6.06%Lower  node=5.2%+(0.5)(12%5.2%)122%12=4.91%Upper\;node=5.2\%+\frac{{(0.5)}{(12\%-5.2\%)}}{12}+\frac{2\%}{\sqrt{12}}=6.06\%\\Lower\;node=5.2\%+\frac{{(0.5)}{(12\%-5.2\%)}}{12}-\frac{2\%}{\sqrt{12}}=4.91\%

这题的公式最后面为什么2%要除以根号12

1 个答案

李坏_品职助教 · 2021年11月30日

嗨,爱思考的PZer你好:


题干问的是在第一个月之后的利率是多少?


给你的volatility是年化的数据(2%),所以要除以根号12,这个是时间的平方根法则。

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