Take a look at John Hull 8ed, p266

If you set the mean and variance of the binomial tree equal to that of the Geometric Brownian motion, you have two equations so that you can solve it, but maybe it need some approximation which is mentioned in the footnote.

For more clear derivation, see CRR's original paper "Option Pricing: A Simplified Approach"(1979)

Here is the a picture from Hull's book,


best,

谢谢Chemist-MZ，先消化一下，给你敬个礼！

可以参考 CRR（1979）经典论文

这是最简单的推导，如果你是硕士的话自己推导出来应该一点问题都没有，这个都搞不出来的话干脆别做研究了

我的思路是将u用二次方程解出来，然后用泰勒公式展开，但是问题是发现u在二阶导没有实数解，我的思路是不是有问题，另外，我看了原文，里面貌似没有直接推导的地方