Black-Scholes-Merton, one formula that priced the option market
A continuously hedged stock-and-bond portfolio replicates an option, so it has one no-arbitrage price, and the expected return of the stock drops out entirely.
A 3 minute animated lesson on the Black-Scholes-Merton model. Built for FIN301 and ECON3003 students who have already seen the binomial tree.
Before 1973 traders priced options by feel. Black, Scholes, and Merton showed that a continuously rebalanced portfolio of stock and bond can replicate a European option, so the option has a single no-arbitrage price. The video builds the call price C = S0 N(d1) − K e^(−rT) N(d2) term by term, shows N(d1) and N(d2) as areas under the normal curve, and prices a one-year call on a A$50 stock at about A$7.12.
The surprising part is that the price does not depend on the expected return of the stock. The delta hedge cancels the directional risk, so the drift drops out of the formula. The lesson also shows how the binomial tree becomes Black-Scholes in the limit. Citations to Black and Scholes (1973), Merton (1973), and Hull (2022) sit on the Atlas concept page.