To do this, (in their simplest, though widely used form) both approaches assume a "binomial model" for the behavior of the underlying instrument, which allows for only two states – up or down. If S is the current price, then in the next period the price will either be "S up" or "S down". Here, the value of the share in the up-state is S × u, and in the down-state is S × d (where u and d are multipliers with d < 1