Binomial Option Pricing (Cox-Ross-Rubinstein)

The binomial option pricing model, introduced by John Cox, Stephen Ross, and Mark Rubinstein in 1979, prices options by modelling the underlying as a discrete tree in which the price moves up or down by fixed factors at each step. Working backward from the option's payoff at maturity using risk-neutral probabilities, it produces a no-arbitrage price that converges to Black-Scholes as the number of steps grows — while naturally handling American early exercise, which the closed-form formula cannot.