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| Изчисляване на гръцките букви чрез автоматично диференциране× | Модел на Бейтс× | Безрискова оценка× | |
|---|---|---|---|
| Област | Количествени финанси | Количествени финанси | Количествени финанси |
| Семейство≠ | Machine learning | Regression model | Regression model |
| Година на възникване≠ | 2008 | 1996 | 1979 |
| Създател≠ | Mike Giles, Iman Homescu | David S. Bates | John Harrison and David Kreps |
| Тип≠ | Sensitivity Analysis | Equity/FX Model | Fundamental Principle |
| Основополагащ източник≠ | Giles, M. B. (2008). Adjoint code by automatic differentiation. Journal of Computational Finance, 12(1), 1-18. link ↗ | Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies, 9(1), 69-107. DOI ↗ | Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408. DOI ↗ |
| Други названия≠ | AD Greeks, Algorithmic Differentiation, Autodiff | SVJ Model, Jump Diffusion | Risk-Neutral Measure, Q-Measure |
| Свързани≠ | 3 | 4 | 4 |
| Резюме≠ | 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. | 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. | 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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