Binomial tree (CRR)
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
Cox-Ross-Rubinstein discretisation of GBM on a recombining lattice: at each step the price moves to Su or Sd with u = e^σ√(Δ t), d = 1/u, risk-neutral probability p = (e^rΔ t - d)/(u - d). American options priced by backward induction with max(continuation, exercise) at each node. Converges to BSM at rate O(1/n), accelerated by Richardson extrapolation; trinomial extension gives better convergence and natural extension to interest-rate trees (Hull-White).
Binomial tree (CRR) in plain English
This is the friendliest way to price an option: instead of fancy math, you imagine that in each short time step the stock can only do one of two things — tick up by a factor u or down by a factor d — building a branching tree of possible futures. The clever part (from Cox, Ross and Rubinstein) is choosing u, d, and the up-probability p so this coin-flipping world matches the real stock's volatility, so nearby paths reunite and the tree stays manageable. To price the option you start at the far-future tips where the payoff is obvious, then work backward step by step, at each node taking the better of "cash in now" versus "hold and wait" — which is exactly why it handles American options (ones you can exercise early) so naturally. Add more steps and it homes in on the exact Black-Scholes price.
Also called: CRR
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