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	Carr-Madan FFT	Lokal volatilitet (Dupire)	Riskneutralvärdering
Ämnesområde	Kvantitativ finans	Kvantitativ finans	Kvantitativ finans
Familj	Machine learning	Regression model	Regression model
Ursprungsår	1999	1994	1979
Upphovsperson	Peter Carr and Dilip B. Madan	Bruno Dupire	John Harrison and David Kreps
Typ	Valuation Algorithm	Equity/FX Model	Fundamental Principle
Ursprungskälla	Carr, P., & Madan, D. B. (1999). Option valuation using the fast Fourier transform. Journal of Computational Finance, 2(4), 61-73.	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	Deterministic Volatility Function, DVF	Risk-Neutral Measure, Q-Measure
Närliggande	3	4	4
Sammanfattning	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.	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.