# Binomial Tree Option Pricing Visualizer

Free CFA binomial option pricing visualizer with stock tree, option tree, risk-neutral probability, delta, and American exercise highlighting.

Canonical URL: https://exclam.ai/cfa/binomial-option-pricing-calculator/

CFA derivatives tool

Build a Cox-Ross-Rubinstein stock lattice, option value tree, delta tree, and terminal payoff table from the same inputs you use in CFA derivatives practice.

Examples

## Load a binomial scenario

Baseline

European at-the-money call

Load

Clean CRR setup for seeing u, d, p, backward induction, and root delta without early exercise noise.

Best first example for understanding the lattice mechanics.

Exercise

American put with early exercise

Load

Deep in-the-money put where immediate exercise beats continuation at selected nodes.

Look for amber exercise badges in the option value tree.

Carry

Dividend-sensitive call

Load

High dividend yield lowers the forward growth rate and changes the risk-neutral probability.

Use this to connect q, p, and the stock tree drift.

Convergence

12-step price with 6-step visual

Load

Prices more steps than the visual tree can usefully show, preserving readability while showing convergence behavior.

Headline price uses 12 steps; tree view caps at 6.

## Inputs

Option typeExercise styleStock priceStrike priceTime to expiration

years

Risk-free rate

%

Dividend yield

%

Volatility

%

Steps

Option price

$11.04

european call

Root delta

0.6141

Hedge ratio at node 0

Risk-neutral p

54.38%

CRR probability

Steps priced

3

Full tree shown

Live interpretation

- The model prices a european call at $11.04 with root delta 0.6141.
- Risk-neutral probability is 54.38%; values outside 0-100% mean the inputs are internally inconsistent for this step size.
- European exercise style disables early exercise, so all interior nodes use continuation value.
- The full priced tree is visible in the lattice.

u

1.1224

Up factor

d

0.89095

Down factor

p

54.38%

Risk-neutral

dt

0.3333

Years per step

discount

0.98347

Per step

root delta

0.6141

First hedge

## Stock and option trees

Branches move forward; option values are solved backward. American exercise nodes are highlighted in amber.

Figure: CRR stock price tree

Hover or focus a node to inspect the tree value.

Figure: Backward induction option value tree

Hover or focus a node to inspect the tree value.

Figure: Delta tree

Hover or focus a node to inspect the tree value.

## Terminal payoff table

The terminal nodes show the final stock price and intrinsic value before backward induction.

| Node | Stock price | Payoff | Binomial probability |
| --- | --- | --- | --- |
| 0 | $70.72 | $0.00 | 9.50% |
| 1 | $89.09 | $0.00 | 33.95% |
| 2 | $112.24 | $12.24 | 40.47% |
| 3 | $141.40 | $41.40 | 16.08% |

## CFA use case

Use the tree to connect the formulas to the hedge portfolio intuition: the risk-neutral probability prices the branch values, while delta shows the local hedge ratio between the up and down states.

- Compare European and American exercise decisions.
- Inspect why American puts can exercise early.
- Check how a larger step count changes headline price.

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## FAQ

What model does this binomial option calculator use?

It uses the Cox-Ross-Rubinstein model with up factor u, down factor d, risk-neutral probability p, and backward induction.

Can it price American options?

Yes. Switch the exercise style to American and the option tree highlights nodes where immediate exercise is better than continuation value.

Why is the visual tree limited to six steps?

Large binomial trees become too dense for a useful browser diagram. The calculator still prices more steps, but the visual lattice is capped for readability.