题目
A non-dividend-paying stock has a current price of $10 and a volatility of 12% per annum. The risk-free rate is 4.0%. We use a twelve-step binomial model to value a one-year European-style put option on the stock; i.e., each step is one month. What is the second-largest stock price among all of the nodes on the binomial tree?
选项
A.$14.64
B.$19.68
C.$23.29
D.$97.15
答案
A
解析
The largest value is the top-most node at the end of the year: S(0)u^12. The second largest must be the one month's prior node, S(0)u^11, as it must be higher than the second-highest node at maturity which is S(0)u^11 d. Keep in mind we assume a recombining tree, and in a recombining tree the communicative property applies; e.g. S(0)×u×d = S(0)×d×u. As u= 1.0352, this node given by: S(0)u^11=$14.638 最大价值的时间节点在年末发生： S(0)u^12，第二大的节点必定是一个月前的节点：S(0)u^11，因为最大节点一定大于第二大的节点。请记住我们假定一个重组树，在树叉间的属性应用结合起来制成。 当u= 1.0352，这个节点为S(0)u^11=$14.638