Heston Stochastic Volatility Model

Heston model: dS = μS dt + √v·S dW_S; dv = κ(θ−v) dt + σ_v√v dW_v, with corr(dW_S, dW_v) = ρ. Stochastic volatility creates volatility smile/skew — implied vol varies with strike K, unlike Black-Scholes (flat). Negative ρ (leverage effect) creates the observed downward skew in equity markets. Mean reversion speed κ controls clustering; vol-of-vol σ_v controls smile curvature.