Binomial Option Pricing 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#

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.

When early exercise matters#

Steps and accuracy#

Binomial prices oscillate slightly as steps change between odd and even numbers; averaging two neighbouring step counts smooths this.

Binomial versus Black Scholes#

Many trading platforms use binomial or similar models for American equity options. See Black-Scholes and Greeks Calculator and 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.