So sánh phương pháp

	Biến đổi Fourier Nhanh Carr-Madan	Mô hình Bates	Biến động cục bộ (Dupire)
Lĩnh vực	Tài chính định lượng	Tài chính định lượng	Tài chính định lượng
Họ	Machine learning	Regression model	Regression model
Năm ra đời	1999	1996	1994
Người khởi xướng	Peter Carr and Dilip B. Madan	David S. Bates	Bruno Dupire
Loại	Valuation Algorithm	Equity/FX Model	Equity/FX Model
Công trình gốc	Carr, P., & Madan, D. B. (1999). Option valuation using the fast Fourier transform. Journal of Computational Finance, 2(4), 61-73.	Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies, 9(1), 69-107.	Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20.
Tên gọi khác	FFT Pricing, Characteristic Function Method	SVJ Model, Jump Diffusion	Deterministic Volatility Function, DVF
Liên quan	3	4	4
Tóm tắt	The Carr-Madan Fast Fourier Transform (1999) is a highly efficient method for computing option prices across a range of strikes using characteristic functions and FFT. It enables rapid pricing of European options under any model with a known characteristic function (Heston, Merton jumps, Variance Gamma), with computational complexity that scales logarithmically in the number of strikes.	The Bates model (1996) combines stochastic volatility and jump diffusion to capture both the volatility smile and the implied volatility skew observed in equity and currency option markets. It extends the Heston model by adding a Poisson jump component to returns, making it suitable for pricing options when sudden price moves are expected.	Dupire's local volatility model (1994) is a deterministic framework that extracts a term and strike-dependent volatility function from market option prices. Unlike constant volatility, local volatility perfectly fits the observed implied volatility smile and is implemented via finite difference methods for European and American option pricing.