Binomial Option Pricing

The Binomial Option Pricing Model is a flexible, discrete-time framework for valuing options — developed by Cox, Ross, and Rubinstein in 1979 as an alternative to the continuous-time Black-Scholes model. The binomial model constructs a price tree for the underlying asset over the life of the option, where at each time step the asset price can move to one of two possible values — up or down — by predetermined factors. Working backward from the known payoffs at expiry, the model discounts expected option values at the risk-free rate to calculate the option's fair value at each node, arriving at the present value at the root of the tree. Unlike Black-Scholes (which only applies to European options), the binomial model can price American options — options that can be exercised at any point before expiry — by checking at each node whether early exercise is optimal. The binomial model also handles dividend payments, variable volatility assumptions, and barrier conditions more naturally than closed-form models. In India, the binomial model is used for pricing American-style stock options, employee stock options (ESOPs), and complex structured products where path dependency or early exercise features make closed-form pricing formulas unavailable or impractical.