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TANG YAN · 2022年09月12日

三叉树

NO.PZ2017092702000095

问题如下:

A call option on a stock index is valued using a three-step binomial tree with an up move that equals 1.05 and a down move that equals 0.95. The current level of the index is $190, and the option exercise price is $200. If the option value is positive when the stock price exceeds the exercise price at expiration and $0 otherwise, the number of terminal nodes with a positive payoff is:

选项:

A.

one.

B.

two.

C.

three.

解释:

A is correct.

Only the top node value of $219.9488 exceeds $200

没有看明白答案中三叉树数字是怎么算出来的

1 个答案

星星_品职助教 · 2022年09月12日

同学你好,

“an up move that equals 1.05 and a down move that equals 0.95”指的是上涨和下降的倍数。

例如当前价格是190,下一个阶段的价格就是:1)上涨:190×1.05=199.5;2)下降:190×0.95=180.5;

同理,从199.5出发的两个价格即为199.5×1.05和199.5×0.95;从180.5出发的价格分别为180.5×1.05和180.5×0.95.

其中199.5×0.95和180.5×1.05必然相等,所以只需要写一个价格即可。(因为199.5×0.95=190×1.05×0.95;180.5×1.05=190×0.95×1.05)。

以此类推即可得到二叉树各个节点上的所有价格。


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