Calculator Inputs
Example Data Table
| Spot | Strike | Years | Rate % | Volatility % | Dividend % | Steps | Type | Style | Price |
|---|---|---|---|---|---|---|---|---|---|
| 100 | 95 | 0.5 | 4.00 | 25.00 | 0.00 | 4 | Call | European | 11.001856 |
| 100 | 105 | 1 | 5.00 | 20.00 | 1.00 | 5 | Put | American | 9.062639 |
| 120 | 110 | 1.5 | 3.00 | 30.00 | 2.00 | 6 | Call | American | 22.826477 |
Formula Used
How to Use This Calculator
- Enter the current stock price and strike price.
- Provide the time to maturity in years.
- Input the annual risk-free rate and volatility.
- Add dividend yield when the stock pays dividends.
- Choose the number of binomial steps.
- Select call or put, then choose European or American style.
- Press the calculate button to build the tree.
- Review the option price, graph, terminal payoffs, and node table.
- Use CSV or PDF export for reporting or review.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates the present value of a call or put option using a binomial tree. The model breaks the option life into steps and discounts future values back to today.
2. What is the difference between European and American styles?
European options can only be exercised at maturity. American options can be exercised earlier. The calculator checks both continuation and intrinsic values when American style is selected.
3. Why does the step count matter?
More steps create a finer price tree and often improve approximation quality. Higher steps also increase processing and create larger output tables for review.
4. What does the risk-neutral probability mean?
It is the model probability used for pricing, not a real market forecast. It adjusts the expected stock movement so discounting produces an arbitrage-free option value.
5. Why can the probability become invalid?
Extreme assumptions or too few steps can push the model outside valid bounds. When that happens, review rates, volatility, maturity, and the number of steps.
6. Does the calculator support dividends?
Yes. You can enter a continuous dividend yield. That yield affects the growth term and can lower call values while supporting early exercise analysis for some cases.
7. What does the root delta show?
Root delta approximates the option sensitivity to a small stock price change at the initial node. It helps explain hedge behavior near the current market state.
8. What do the CSV and PDF exports include?
The exports include the pricing summary, terminal node payoffs, and the full node detail table. They are useful for audit trails, reports, or classroom review.