Binomial pricing is a method for valuing options by assuming that, over each small time step, the underlying asset can move to one of two prices: up or down.
How the model works
Start with a current price S. After one step, the asset becomes either:
uSin the up state, ordSin the down state.
If the option payoff in those two states is Cu and Cd, the no-arbitrage price is the discounted expected payoff under the risk-neutral probability:
q = (1 + r - d) / (u - d)
and
Option value = [qCu + (1-q)Cd] / (1 + r)
The key logic is not that investors are literally risk neutral. It is that a replicating portfolio and no-arbitrage condition pin down the fair price.
Why economists and practitioners use it
The binomial approach is especially useful when:
- dividends matter,
- early exercise is possible,
- the payoff structure is more complicated than a simple European option.
That is why it remains a practical complement to the Black-Scholes framework. With enough time steps, the tree can approximate continuous-time pricing while still being intuitive.
Strengths and limits
Its main strength is flexibility. Its main limit is that the model still depends on assumptions about volatility, interest rates, and how finely time is divided.