Binomial Option Pricing Calculator
The binomial model prices an option by stepping the underlying through a tree of up and down moves and discounting the payoff back to today under risk-neutral probabilities. It handles American early exercise that the Black-Scholes formula cannot. This calculator uses the standard Cox-Ross-Rubinstein parameterisation. Enter the spot, strike, time, volatility, risk-free rate and number of steps to price a call or put.
Cox-Ross-Rubinstein formula
dt = T / steps
u = e^(sigma * sqrt(dt)), d = 1 / u
p = (e^(r * dt) - d) / (u - d) (risk-neutral up probability)
Terminal price at node j = S * u^j * d^(steps - j)
Payoff (call) = max(0, price - K); (put) = max(0, K - price)
Backward step: value = e^(-r * dt) * (p * V_up + (1 - p) * V_down)
American: value = max(value, immediate exercise payoff)
Worked example
Single step (steps = 1), S = 100, K = 100, T = 1, sigma = 20%, r = 5%. dt = 1, u = e^0.20 = 1.2214, d = 0.8187. p = (e^0.05 - 0.8187) / (1.2214 - 0.8187) = (1.0513 - 0.8187) / 0.4027 = 0.5776. Up payoff = max(0, 122.14 - 100) = 22.14; down payoff = 0. Call value = e^(-0.05) * (0.5776 * 22.14 + 0.4224 * 0) = 0.9512 * 12.79 = $12.16. With 100 steps the European call converges toward the Black-Scholes value near $10.43.
Binomial pricing: frequently asked questions
What is the binomial option pricing model?
The binomial model values an option by building a tree of possible underlying prices over discrete time steps. At each step the price moves up by a factor u or down by a factor d. The Cox-Ross-Rubinstein (CRR) parameterisation sets u = e^(sigma * sqrt(dt)) and d = 1/u. Option values are computed at expiry then discounted back through the tree using the risk-neutral probability.
How does it handle American options?
At each node the model compares the discounted expected value of holding the option with the value of exercising immediately, and takes the larger. This captures the early-exercise premium that the European Black-Scholes formula cannot. For European options it only applies the payoff at expiry.
How many steps should I use?
More steps give a more accurate price and converge toward the Black-Scholes value for European options. 50 to 200 steps is typically enough for a smooth estimate. This calculator caps steps at 500 to keep the computation fast in the browser.
Sources and method
- U.S. Securities and Exchange Commission investor education on options: Investor.gov: Options.
- Method: Cox, Ross and Rubinstein (1979) binomial tree, a standard public option-pricing model. No proprietary data is used.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.