Model in which instantaneous volatility is a deterministic function σ_loc(S,t) of spot and time, calibrated to perfectly reproduce the observed implied-vol surface via Dupire's formula: σ_loc^2(K,T) = dfracpartial C/partial T + r K partial C/partial Ktfrac12 K^2 partial^2 C/partial K^2. The unique 1-factor Markovian completion of an arbitrage-free option surface. Mis-prices forward-skew and barrier options because the model's future skew flattens (counterfactually). Stochastic-local-volatility hybrids (SLV) are the dealer-grade fix.