Black-Scholes
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Closed-form
Price an option three ways
Move any input and every model reprices instantly. Black-Scholes is exact for European options, the binomial tree also handles early exercise, and Monte Carlo estimates the price by simulating the stock.
Binomial tree
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CRR
Monte Carlo
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Simulating…
Value vs spot
Today At expiry Current spot
Inside the Monte Carlo
The stock follows geometric Brownian motion under the risk-neutral measure. Each path ends somewhere; the option's price is the discounted average payoff over all of them. More paths, tighter confidence interval.
Simulated price paths
Finishes in the money Finishes out of the money Strike
Convergence
Build a strategy
Combine options and stock. Legs are priced at Black-Scholes fair value using the inputs above, and breakevens and maximum profit or loss are solved exactly from the payoff's kinks.
| Side | Qty | Instrument | Strike | Premium | Remove |
|---|
Profit and loss
At expiry Today Breakeven