Dynamically-rebalanced self-financing portfolio in the underlying (Δ_t shares) and risk-free bond that exactly matches an option's payoff at expiry. In a complete market the cost of replication equals the no-arbitrage price: V_0 = mathbbE^mathbbQ[e^-rT,payoff]. The constructive content of the BSM PDE — every option is, in continuous time, a synthetic position in the underlying. In incomplete markets (jumps, stochastic vol with two-sided unhedged risk) perfect replication fails and one resorts to super-replication, quadratic hedging, or utility-indifference pricing.