What is the relation between the binomial option pricing model and the Black-Scholes formula? There is no relation (other than that they both price options), these are two different models The Black Scholes formula is the same as a binomial model with a very large number of up-down periods (and very small delta t) The Black Scholes formula is the same as a binomial model with a very small number of up-down periods (and very large delta t) The Black Scholes formula and the binomial model are the same for at-the-money options