Binomial Tree (Cox-Ross-Rubinstein)
Prices an option with the Cox-Ross-Rubinstein binomial tree, the most teachable numerical method for options. At each step, the price moves up or down by factors calibrated to the volatility, and the option value is computed backward, from expiry to today. Unlike Black-Scholes, the tree prices American options, checking early exercise at each node. Choose call or put, European or American, and enter the price, strike, rate, volatility, term and number of steps.
Result
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Binomial Tree (Cox-Ross-Rubinstein)
Prices an option with the Cox-Ross-Rubinstein binomial tree, the most teachable numerical method for options. At each step, the price moves up or down by factors calibrated to the volatility, and the option value is computed backward, from expiry to today. Unlike Black-Scholes, the tree prices American options, checking early exercise at each node. Choose call or put, European or American, and enter the price, strike, rate, volatility, term and number of steps.
The tree that teaches how options work
The Cox-Ross-Rubinstein binomial model is, for many people, the gateway to option theory. The idea is disarmingly simple: at each small time interval, the asset price can only do two things, move up or down by fixed factors. Repeating that many times builds a tree of possible prices to expiry.
The option value is computed backward. At expiry, the payoff at each node is known; stepping back, each node is worth the discounted average of the two future nodes, weighted by the risk-neutral probability. The big advantage over Black-Scholes is pricing American options: at each node, you just compare the value of holding with that of exercising on the spot.
Choose call or put, European or American style, and enter the spot price, the strike, the rate, the volatility, the term and the number of steps. The tool returns the tree price. The more steps, the closer a European option's result gets to Black-Scholes; for Americans, the tree is the practical reference.
Related Tools
No-Touch Option
Computes the price of a no-touch option: it pays a fixed amount if the asset does NOT touch a barrier before expiry, and nothing if it touches. It's the opposite bet to the one-touch — you win as long as the price behaves and stays away from the barrier. The two are complementary: the sum of a one-touch and a no-touch with the same barrier is always the discounted payout. Enter the spot price, the barrier, the rate, the volatility, the term and the payout.
Trinomial Tree (Boyle)
Prices an option with the Boyle trinomial tree, an evolution of the binomial where the price, at each step, can move up, down or stay flat. That third path gives the tree more flexibility and faster, more stable convergence than the binomial for the same number of steps. It's widely used for options whose features demand numerical precision. Choose call or put and enter the price, strike, rate, volatility, term and number of steps.
American Call (Bjerksund-Stensland)
Computes the price of an American call option with the Bjerksund-Stensland (1993) approximation, valid when the asset pays dividends (cost of carry below the interest rate). It defines an exercise trigger price and, below it, combines exponential terms to approximate the value with early exercise. It's faster than a binomial tree and widely used in practice for American calls on dividend-paying stocks. Enter the spot price, the strike, the rate, the cost of carry, the volatility and the term.
American Call with Dividend (Roll-Geske-Whaley)
Computes the price of an American call option on a stock paying a discrete dividend, with the Roll-Geske-Whaley model. Unlike the European call, the American one can be exercised early, and that's only optimal precisely an instant before the dividend, when the price will drop. The model finds the critical exercise price and combines probabilities via the bivariate normal. Enter the spot price, the strike, the rate, the volatility, the term, the dividend and the date it's paid.
American Put (Barone-Adesi-Whaley)
Computes the price of an American put option with the Barone-Adesi-Whaley quadratic approximation. Unlike the European put, the American one can be exercised at any time, and that right has value — the so-called early-exercise premium. The method iteratively finds the critical price below which exercising already pays off, and adds that premium to the European put value. It's fast and accurate, with no need for a binomial tree. Enter the spot price, the strike, the rate, the cost of carry, the volatility and the term.
Complex Chooser Option (Rubinstein)
Computes the price of a complex chooser option with the Rubinstein (1991) formula: on the choice date, the holder decides between a call and a put that may have different strikes and expiries. It's the general version of the simple chooser, and because it allows distinct parameters for each side it requires the bivariate normal and a search for a critical price. When the call and put share the same strike and expiry, it collapses to the simple chooser. Enter the spot price, the call and put strikes, the choice date, the two expiries, the rate and the volatility.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.