六姑娘 · 2021年11月29日
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：
解释：
D is correct.
考点：Vasicek model
解析：
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 mol, if the current short-term rate equals 5.2% anthe annuvolatility of the interest rate process is 2%. The long-run mean- reverting level is assumeto 12% with a speeof austment of 0.5. Whare the upper anlower no rates after the first month in the binomiinterest rate tree? Upper no Lower no A.6.67% 4.91% B.6.67% 5.24% C.6.06% 5.24% 6.06% 4.91% is correct. 考点Vasicek mol解析Upper no=5.2%+(0.5)(12%−5.2%)12+2%12=6.06%Lower no=5.2%+(0.5)(12%−5.2%)12−2%12=4.91%Upper\;no=5.2\%+\frac{{(0.5)}{(12\%-5.2\%)}}{12}+\frac{2\%}{\sqrt{12}}=6.06\%\\Lower\;no=5.2\%+\frac{{(0.5)}{(12\%-5.2\%)}}{12}-\frac{2\%}{\sqrt{12}}=4.91\%Upperno=5.2%+12(0.5)(12%−5.2%)+122%=6.06%Lowerno=5.2%+12(0.5)(12%−5.2%)−122%=4.91% 讲义上的公式後半部是σ*，李老师写的後半部是εσ*()^，也就是说=ε*()^那这题题干为啥没给ε，而是直接让我们用σ*()^来计算?
NO.PZ2020033001000069 6.67% 5.24% 6.06% 5.24% 6.06% 4.91% is correct. 考点Vasicek mol 解析 Upper no=5.2%+(0.5)(12%−5.2%)12+2%12=6.06%Lower no=5.2%+(0.5)(12%−5.2%)12−2%12=4.91%Upper\;no=5.2\%+\frac{{(0.5)}{(12\%-5.2\%)}}{12}+\frac{2\%}{\sqrt{12}}=6.06\%\\Lower\;no=5.2\%+\frac{{(0.5)}{(12\%-5.2\%)}}{12}-\frac{2\%}{\sqrt{12}}=4.91\%Upperno=5.2%+12(0.5)(12%−5.2%)+12 2%=6.06%Lowerno=5.2%+12(0.5)(12%−5.2%)−12 2%=4.91% 这题公式是什么呢？不记得了
