Binomial Model
Quick Definition
An options pricing model that uses a discrete-time tree of possible price paths to value options, especially useful for American-style options.
What Is Binomial Model?
The binomial options pricing model, developed by Cox, Ross, and Rubinstein in 1979, values options by constructing a recombining tree of possible future stock prices. At each time step, the underlying price can move up or down by a specific factor, creating a lattice of possible outcomes. The model works backward from expiration, calculating option values at each node based on risk-neutral probabilities. Its key advantage over Black-Scholes is the ability to handle American-style options with early exercise features, discrete dividends, and changing volatility. As the number of time steps increases, the binomial model converges to the Black-Scholes price for European options. The model is intuitive, flexible, and widely used in practice for pricing complex derivatives.
Binomial Model Example
- 1Using a 100-step binomial tree, a trader prices an American put option on a dividend-paying stock, finding the optimal early exercise boundary at each node
- 2The binomial model shows that an American call on a non-dividend stock should never be exercised early, confirming the theoretical result
Related Terms
Black-Scholes Model
The foundational mathematical model for pricing European options, using stock price, strike, time, volatility, and risk-free rate as inputs.
Options Premium
The price paid by the option buyer to the seller for the rights conveyed by the contract, determined by intrinsic value, time value, and volatility.
American Option
An option contract that can be exercised at any time before or on the expiration date, providing maximum flexibility to the holder.
European Option
An option contract that can only be exercised at expiration, not before, typically found in index options and OTC markets.
Implied Volatility (IV)
The market's forecast of the likely magnitude of future price movements, derived from current option prices using pricing models.
Call Option
A contract giving the holder the right, but not the obligation, to buy an underlying asset at a specified price within a specified time period.
Expand Your Financial Vocabulary
Explore 130+ financial terms with definitions, examples, and formulas
Browse Options & Derivatives Terms