Build valuations using stepwise stock paths and payoffs. Test volatility, rates, dividends, and exercise choices. Generate clear results, graphs, tables, and downloadable reports instantly.
| Case | Spot | Strike | Time | Rate | Volatility | Dividend | Steps | Type | Style | Price |
|---|---|---|---|---|---|---|---|---|---|---|
| Example A | 100.000000 | 95.000000 | 1.000000 | 0.050000 | 0.220000 | 0.010000 | 50 | Call | American | 13.319358 |
| Example B | 120.000000 | 125.000000 | 0.750000 | 0.040000 | 0.180000 | 0.020000 | 60 | Put | American | 9.370326 |
| Example C | 80.000000 | 85.000000 | 1.500000 | 0.030000 | 0.250000 | 0.000000 | 75 | Call | European | 9.218533 |
A binomial tree option pricing calculator estimates derivative value by splitting time into many small decision points. At every step, the model assumes the underlying asset can move up or down by known factors. This makes the method practical for engineering style modeling, structured analysis, and repeatable scenario testing. It is especially useful when you want a transparent pricing path instead of relying on one closed form result.
The calculator supports call and put contracts, along with European and American exercise styles. European contracts can only be exercised at maturity. American contracts can be exercised at any earlier step, so the tree compares continuation value with intrinsic value during backward induction. That feature matters when early exercise can change the final contract value.
Inputs include spot price, strike price, maturity, volatility, risk free rate, dividend yield, and number of tree steps. More steps usually improve model resolution, although they also increase computation and output size. The terminal node table shows possible ending stock prices and final payoffs. The displayed trees show how asset values and option values evolve across the first portion of the lattice.
This page also reports a practical set of tree based sensitivities. Delta estimates price response to small asset moves. Gamma shows how delta changes across the tree. Theta gives a time decay estimate based on nearby node values. These values are approximations, but they help with comparison, stress testing, and hedging reviews.
The graph adds a visual payoff view, while CSV and PDF downloads help with documentation and sharing. Engineers, analysts, students, and decision modelers can use this layout to study discrete time pricing behavior, compare assumptions, and produce a clean calculation record for reports or classroom work.
Step Length: dt = T / N
Up Factor: u = e^(σ × √dt)
Down Factor: d = 1 / u
Risk Neutral Probability: p = (e^((r - q) × dt) - d) / (u - d)
Discount Factor: e^(-r × dt)
Call Intrinsic Value: max(S - K, 0)
Put Intrinsic Value: max(K - S, 0)
Continuation Value: e^(-r × dt) × [p × Vup + (1 - p) × Vdown]
American Rule: max(Intrinsic Value, Continuation Value)
European Rule: Continuation Value only before maturity
It breaks the contract life into many small steps. At each step, the asset price moves up or down. The model then works backward from maturity payoffs to estimate the current option price.
American contracts allow early exercise, while European contracts only allow exercise at maturity. Early exercise can add value in some situations, especially for puts or dividend sensitive cases.
More steps usually give a finer approximation of price behavior. The result often becomes more stable, but the tree grows larger and calculation output becomes heavier to inspect.
Volatility controls the size of upward and downward moves in the tree. Higher volatility expands the range of possible future prices and often increases option value.
Dividend yield adjusts the risk neutral growth assumption. It can reduce expected upward drift in the tree and may affect early exercise decisions for some contracts.
No. They are practical tree based estimates derived from nearby nodes. They are useful for analysis and comparison, but they remain approximations.
Some combinations can produce an invalid risk neutral probability. When that happens, adjust the inputs or use more steps so the discrete tree remains mathematically consistent.
Yes. It shows the price summary, payoff graph, terminal node values, displayed tree sections, and export tools. That makes it suitable for study, demonstrations, and documentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.