问一道题：NO.PZ2016070201000069

问题如下：

Using the Vasicek model, assume a current short-term rate of 6.2% and an annual volatility of the interest rate process of 2.5%. Also assume that the long-run mean- reverting level is 13.2% with a speed of adjustment of 0.4. Within a binomial interest rate tree, what are the upper and lower node rates after the first month?

选项：

解释：

D is correct. Using a Vasicek model, the upper and lower nodes for time 1 are computed as follows:

${l}Upper\;node=6.2\%+\frac{{(0.4)}{(13.2\%-6.2\%)}}{12}+\frac{2.5\%}{\sqrt{12}}=7.16\%\\Lower\;node=6.2\%+\frac{{(0.4)}{(13.2\%-6.2\%)}}{12}-\frac{2.5\%}{\sqrt{12}}=5.71\%$