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| Carr-Madan FFT× | Lokale Volatilität (Dupire)× | |
|---|---|---|
| Fachgebiet | Quantitative Finanzwirtschaft | Quantitative Finanzwirtschaft |
| Familie≠ | Machine learning | Regression model |
| Entstehungsjahr≠ | 1999 | 1994 |
| Urheber≠ | Peter Carr and Dilip B. Madan | Bruno Dupire |
| Typ≠ | Valuation Algorithm | Equity/FX Model |
| Wegweisende Quelle≠ | Carr, P., & Madan, D. B. (1999). Option valuation using the fast Fourier transform. Journal of Computational Finance, 2(4), 61-73. DOI ↗ | Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20. link ↗ |
| Aliasnamen | FFT Pricing, Characteristic Function Method | Deterministic Volatility Function, DVF |
| Verwandt≠ | 3 | 4 |
| Zusammenfassung≠ | 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. |
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