# Binomial Option Pricing Model

Binomial Option Pricing Model

The binomial option pricing model proceeds from the assumption that the value of the underlying asset follows an evolution such that in each period it increases by a fixed proportion (the up factor) or decreases by another (the down factor). Using a binomial tree one can project all possible values of the underlying asset at the option's expiration date, and from them, all possible final values for the option. To find the current value of the option, one needs to work backwards through the tree starting with the known final option values. The key is to recognize that it is always possible to create a portfolio made up of a position in the underlying asset combined with a position in the lending market that will have the same next period value as the option. The restricted assumptions about the movements in the value of the underlying asset imply that there is enough information to determine the portfolio weights and thus the value of the replicating portfolio. Under the assumption of no-arbitrage, the replicating portfolio must have the same value as the option.