قارن الطرق

	تحويل فورييه السريع لكار-مادان	نموذج بيتس
المجال	التمويل الكمي	التمويل الكمي
العائلة	Machine learning	Regression model
سنة النشأة	1999	1996
صاحب الطريقة	Peter Carr and Dilip B. Madan	David S. Bates
النوع	Valuation Algorithm	Equity/FX Model
المصدر التأسيسي	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.
الأسماء البديلة	FFT Pricing, Characteristic Function Method	SVJ Model, Jump Diffusion
ذات صلة	3	4
الملخص	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.