CFA derivatives tool

Binomial Tree Option Pricing Visualizer

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

Inputs

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.

CRR stock price tree100.00t089.09t1112.24t179.38t2100.00t2125.98t270.72t389.09t3112.24t3141.40t3
Hover or focus a node to inspect the tree value.
Backward induction option value tree11.04S 100.003.50S 89.0917.71S 112.240.00S 79.386.55S 100.0027.63S 125.980.00S 70.720.00S 89.0912.24S 112.2441.40S 141.40
Hover or focus a node to inspect the tree value.
Delta tree0.614S 100.00.317S 89.10.812S 112.20.00S 79.40.529S 100.01.00S 126.0
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.

NodeStock pricePayoffBinomial probability
0$70.72$0.009.50%
1$89.09$0.0033.95%
2$112.24$12.2440.47%
3$141.40$41.4016.08%

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.

Related calculators

CFA finance tools

CFA hub

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.