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.
Load a binomial scenario
Inputs
european call
Hedge ratio at node 0
CRR probability
Full tree shown
- 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.
Stock and option trees
Branches move forward; option values are solved backward. American exercise nodes are highlighted in amber.
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.