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| Rýchla Fourierova transformácia Carr-Madan× | Valuácia neutrálna voči riziku× | |
|---|---|---|
| Odbor | Kvantitatívne financie | Kvantitatívne financie |
| Rodina≠ | Machine learning | Regression model |
| Rok vzniku≠ | 1999 | 1979 |
| Tvorca≠ | Peter Carr and Dilip B. Madan | John Harrison and David Kreps |
| Typ≠ | Valuation Algorithm | Fundamental Principle |
| Pôvodný zdroj≠ | Carr, P., & Madan, D. B. (1999). Option valuation using the fast Fourier transform. Journal of Computational Finance, 2(4), 61-73. DOI ↗ | Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408. DOI ↗ |
| Ďalšie názvy | FFT Pricing, Characteristic Function Method | Risk-Neutral Measure, Q-Measure |
| Príbuzné≠ | 3 | 4 |
| Zhrnutie≠ | 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. | 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. |
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