Key quantities of the model
The binomial model prices an option by letting the underlying move up or down by fixed factors over discrete steps. Working backwards from the payoffs at expiry with risk-neutral probabilities gives the option value at every node. This interactive tree also shows the replicating portfolio of stock and bond that reproduces the option at each step.
It is the probability q = (1 + r − d) / (u − d) under which the expected return of the stock equals the risk-free rate. It is not a forecast; it is the weight that makes discounted prices consistent with no arbitrage.
As the number of steps grows and the up and down factors are chosen to match the volatility, the binomial price of a European option converges to the Black–Scholes price.