In 1973, Fischer Black and Myron Scholes published the most famous formula in finance. It answered the question traders had asked for decades: what is a stock option worth? The model earned Scholes and Robert Merton the 1997 Nobel Prize and transformed derivatives from a niche instrument into a $600+ trillion global market.

Call = S × N(d₁) − K × e^(−rT) × N(d₂). Five inputs: S (stock price), K (strike), σ (volatility), T (time), r (risk-free rate). N(·) = cumulative normal CDF. d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T). d₂ = d₁ − σ√T. Put-Call Parity: Call + PV(K) = Put + S — if this holds, no arbitrage exists between puts, calls, and the stock. The Greeks: Delta (Δ) ≈ N(d₁) — hedge ratio; Vega — sensitivity to σ; Theta — time decay; Gamma — rate of delta change.