Black–Scholes
Constant-volatility dynamics plus continuous hedging yield a closed-form option price and the message that options are manufactured, not bet on.
Black–Scholes assumes the stock follows geometric Brownian motion with constant volatility, a constant risk-free rate, continuous trading, and no frictions. Itô's lemma applied to a continuously rebalanced hedge then removes the randomness, leaving a PDE whose solution prices a European call or put in closed form. The economic message matters more than the formula: an option is not a bet on direction but a package manufactured by dynamically hedging the underlying, so its fair value is the cost of that hedge. Its known weaknesses, constant volatility and continuous paths, are precisely what the final two nodes confront.