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| Greci tramite differenziazione automatica× | Volatilità Locale (Dupire)× | Valutazione neutrale al rischio× | |
|---|---|---|---|
| Campo | Finanza quantitativa | Finanza quantitativa | Finanza quantitativa |
| Famiglia≠ | Machine learning | Regression model | Regression model |
| Anno di origine≠ | 2008 | 1994 | 1979 |
| Ideatore≠ | Mike Giles, Iman Homescu | Bruno Dupire | John Harrison and David Kreps |
| Tipo≠ | Sensitivity Analysis | Equity/FX Model | Fundamental Principle |
| Fonte seminale≠ | Giles, M. B. (2008). Adjoint code by automatic differentiation. Journal of Computational Finance, 12(1), 1-18. link ↗ | Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20. link ↗ | Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408. DOI ↗ |
| Alias≠ | AD Greeks, Algorithmic Differentiation, Autodiff | Deterministic Volatility Function, DVF | Risk-Neutral Measure, Q-Measure |
| Correlati≠ | 3 | 4 | 4 |
| Sintesi≠ | Automatic differentiation (AD) is a computational technique for computing derivatives (Greeks) by differentiating the computer code that computes the option price. AD avoids manual derivation of formulas and finite-difference approximations, yielding exact sensitivities with machine precision. It has become essential for real-time risk management in modern trading systems. | 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. |
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