Mastering Python for Finance - Second Edition

The Cox–Ross–Rubinstein model

In the preceding examples, we assumed that the underlying stock price would increase by 20 percent and decrease by 20 percent in the respective u up state and d down state. The Cox-Ross-Rubinstein (CRR) model proposes that, over a short period of time in the risk-neutral world, the binomial model matches the mean and variance of the underlying stock. The volatility of the underlying stock, or the standard deviation of returns of the stock, is taken into account as follows: