Stochastic-volatility model: dS_t = μ S_t,dt + √(v_t),S_t,dW_t^S, dv_t = κ(θ - v_t),dt + xi√(v_t),dW_t^v, with dlangle W^S, W^vrangle_t = ρ,dt. Closed-form characteristic function admits semi-analytical option pricing via Carr-Madan FFT or Lewis-Lipton contour integration. Captures volatility clustering and (via ρ < 0) the equity-index skew; struggles with very short-dated steep skew, motivating rough-volatility extensions.