# Binomial Option Pricing Calculator > Free binomial option pricing calculator using a Cox Ross Rubinstein tree. Price American or European calls and puts and see the early exercise premium. Source: https://learn.tradelabsai.com/tools/binomial-calculator/ Track: Calculators · Level: Beginner · Updated: 2026-10-03 Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice. Cite as: TradeLabs Learn, "Binomial Option Pricing Calculator", https://learn.tradelabsai.com/tools/binomial-calculator/ Binomial trees price options by modelling the underlying price as a series of up and down steps until expiry, then working backwards to today. Their great advantage over Black Scholes is that they handle American options, which can be exercised at any time: at each step, the tree checks whether exercising early is worth more than holding. This calculator uses the Cox Ross Rubinstein tree, published in 1979, and compares its result with the Black Scholes European price, so you can see the value of the early exercise right directly. ## Calculator *Interactive calculator: use it at https://learn.tradelabsai.com/tools/binomial-calculator/* ## How it works ``` Δt = T / Steps Up factor u = e^(σ × √Δt), Down factor d = 1 / u Risk neutral probability p = (e^((r - q) × Δt) - d) / (u - d) Value at each node = max(Exercise value, e^(-r × Δt) × [p × Value up + (1 - p) × Value down]) ``` The max with the exercise value applies only to American options. More steps give more accurate prices; a few hundred steps is usually enough. See [Binomial and Trinomial Trees](https://learn.tradelabsai.com/options/binomial-and-trinomial-trees/). **Example: An American put** A one year at the money put on a $100 stock, with a 4% rate, 20% volatility and no dividends, is worth about $6.00 as a European option under Black Scholes. As an American option, priced with a 500 step tree, it is worth about $6.40. The extra 40 cents is the early exercise premium: if the stock falls far enough, exercising early to receive the strike and earn interest on it beats waiting. For an American call on a stock with no dividends, the tree gives the same price as Black Scholes, because early exercise is never optimal. See [Early Exercise](https://learn.tradelabsai.com/options/early-exercise/) and [American Option Pricing](https://learn.tradelabsai.com/options/american-option-pricing/). ## When early exercise matters | Option | Early exercise worth considering? | |---|---| | American call, no dividends | No; its price equals the European call | | American call before a large dividend | Sometimes, just before the ex dividend date. See [Dividends](https://learn.tradelabsai.com/fundamentals/dividends/) | | American put, deep in the money | Yes, especially with higher interest rates | | European options | Not allowed | ## Steps and accuracy | Steps | Typical accuracy | |---|---| | 10 | Rough; visibly off | | 50 | Within a few cents for typical options | | 200 to 500 | Close to the true model price | | 2,000 | Very precise, slower | Binomial prices oscillate slightly as steps change between odd and even numbers; averaging two neighbouring step counts smooths this. ## Binomial versus Black Scholes | | Binomial tree | Black Scholes | |---|---|---| | American options | Yes | No | | Speed | Slower | Instant | | Discrete dividends | Easy to add | Awkward | | Intuition | Shows the path of prices | A single formula | Many trading platforms use binomial or similar models for American equity options. See [Black-Scholes and Greeks Calculator](https://learn.tradelabsai.com/tools/black-scholes-calculator/) and [American vs European Options](https://learn.tradelabsai.com/options/american-vs-european-options/). ## Trying scenarios Set the style to European and confirm the binomial price converges to the Black Scholes price as you raise the steps. Then switch back to American and raise the interest rate from 4% to 8%: the early exercise premium on the put grows, because receiving the strike early and earning interest on it becomes more valuable. Try a call with a dividend yield of 5% to see that early exercise can also matter for calls when the stock pays a large income. Watching these changes is a quick way to understand when American options are worth more than European ones. ## Frequently asked questions ### What is a binomial option pricing model? A method that models the underlying price as a tree of up and down moves until expiry, then works backwards to value the option, allowing for early exercise. ### Why is an American put worth more than a European put? Because it can be exercised early when that is more valuable than holding, which happens when the put is deep in the money. ### How many steps should a binomial tree have? A few hundred steps usually gives prices within a cent or two of the model's limit. Next, compare futures with spot prices using the [Futures Basis and Forward Price Calculator](https://learn.tradelabsai.com/tools/futures-basis-calculator/). ## Continue learning - Next lesson: [Futures Basis and Forward Price Calculator](https://learn.tradelabsai.com/tools/futures-basis-calculator/) - Previous lesson: [Implied Volatility Calculator](https://learn.tradelabsai.com/tools/implied-volatility-calculator/) - Related: [Implied Volatility Calculator](https://learn.tradelabsai.com/tools/implied-volatility-calculator/): Free implied volatility calculator. Enter an option's market price, strike, expiry and rate to find the volatility the market is pricing in, plus the expected move. - Related: [Binomial and Trinomial Trees](https://learn.tradelabsai.com/options/binomial-and-trinomial-trees/): Binomial and trinomial trees price options by stepping prices up and down through time. Learn how the Cox Ross Rubinstein model works, with a worked example. - Related: [American Option Pricing](https://learn.tradelabsai.com/options/american-option-pricing/): American options can be exercised early, so they need special pricing methods. Learn trees, finite differences, approximations and Longstaff Schwartz simulation. - Related: [Early Exercise](https://learn.tradelabsai.com/options/early-exercise/): Early exercise is using an American option before it expires. Learn why it usually loses money and the dividend and interest cases where it makes sense. - Related: [Black-Scholes and Greeks Calculator](https://learn.tradelabsai.com/tools/black-scholes-calculator/): Free Black Scholes calculator. Enter stock price, strike, days to expiry, rate, volatility and dividend yield to get call and put prices and the Greeks. - Related: [American vs European Options](https://learn.tradelabsai.com/options/american-vs-european-options/): American options can be exercised any time before expiry; European options only at expiry. Learn the differences, which markets use each and how pricing differs.