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	FFT di Carr-Madan	Modello di Bates	Volatilità Locale (Dupire)	Valutazione neutrale al rischio
Campo	Finanza quantitativa	Finanza quantitativa	Finanza quantitativa	Finanza quantitativa
Famiglia	Machine learning	Regression model	Regression model	Regression model
Anno di origine	1999	1996	1994	1979
Ideatore	Peter Carr and Dilip B. Madan	David S. Bates	Bruno Dupire	John Harrison and David Kreps
Tipo	Valuation Algorithm	Equity/FX Model	Equity/FX Model	Fundamental Principle
Fonte seminale	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.	Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408.
Alias	FFT Pricing, Characteristic Function Method	SVJ Model, Jump Diffusion	Deterministic Volatility Function, DVF	Risk-Neutral Measure, Q-Measure
Correlati	3	4	4	4
Sintesi	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.	Risk-neutral valuation (1979) is the fundamental principle that derivative prices equal the expected payoff discounted at the risk-free rate, computed under a risk-neutral probability measure (Q-measure). This principle, formalized by Harrison and Kreps, eliminates the need to estimate risk premia and is the foundation of modern derivatives pricing.