Price an option on a binomial or trinomial tree
American or European, call or put. Watch the tree work node by node, see where early exercise pays, and check the answer against Black-Scholes. Everything updates as you type.
How the trees work
Binomial (CRR)
Each step the price moves up by u = eσ√Δt or down by d = 1/u. The risk-neutral up probability is p = (e(r−q)Δt − d)/(u − d). Option values are discounted back from expiry; an American option takes the larger of holding and exercising at every node.
Jarrow-Rudd
The moves carry the drift: u, d = e(r−q−σ²/2)Δt ± σ√Δt, so the probability sits close to one half. Here p is solved exactly so the tree stays arbitrage-free and put-call parity holds to the last digit.
Trinomial
Three branches per step: up by eσ√(2Δt), flat, or down. The probabilities come from two half-steps of a binomial, so a European price on N trinomial steps equals a binomial on 2N half-steps. The extra middle branch smooths convergence.
Greeks: Delta, Gamma and Theta are read from the first steps of the tree; Vega and Rho reprice the tree with volatility and rate nudged up and down. Theta is per calendar day (365), Vega per one volatility point, Rho per one percentage point of rate. Black-Scholes values a European option only, so for an American option the gap to Black-Scholes includes the early-exercise premium.