Binomial Option Pricing, one-step and two-step trees by hand
Two equations, one process: build the stock price forward, then the option backward. A worked one-step (p = 0.6523, $0.633) and two-step tree ($1.2823).
A 6-minute animated lesson on the binomial option pricing model, built for FIN301 Derivatives students at Western Sydney University and for anyone meeting option pricing for the first time. A binomial tree is really just two equations and one simple process: build the stock price forward, from left to right, then price the option backward, from right to left.
Working a $20 stock that moves up 10 percent (u = 1.1) or down 10 percent (d = 0.9), a $21 strike call, and a 12 percent per year rate, the video prices the option entirely by hand. The one-step tree gives a risk-neutral probability p = 0.6523 and a call value of $0.633. The two-step recombining tree then folds three terminal payoffs back through backward induction to a call value of $1.2823.
The lesson clears up the single most common confusion, that u and d are magnitude, how far the stock moves, while p is likelihood, so how far is not the same as how likely. It closes on the surprise that the option price never depends on the stock's real-world expected return, only on the rate, the up and down factors, and the payoffs, which is the seed of no-arbitrage pricing and Black-Scholes. Pair the video with the Atlas concept pages for the full derivation, worked examples, a quick quiz, and citations to Hull (2022) and Cox-Ross-Rubinstein (1979).