قارن الطرق

	اليونانيات عبر التفاضل والتكامل التلقائي	التقلب المحلي (Dupire)	التقييم المحايد للمخاطر
المجال	التمويل الكمي	التمويل الكمي	التمويل الكمي
العائلة	Machine learning	Regression model	Regression model
سنة النشأة	2008	1994	1979
صاحب الطريقة	Mike Giles, Iman Homescu	Bruno Dupire	John Harrison and David Kreps
النوع	Sensitivity Analysis	Equity/FX Model	Fundamental Principle
المصدر التأسيسي	Giles, M. B. (2008). Adjoint code by automatic differentiation. Journal of Computational Finance, 12(1), 1-18.	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.
الأسماء البديلة	AD Greeks, Algorithmic Differentiation, Autodiff	Deterministic Volatility Function, DVF	Risk-Neutral Measure, Q-Measure
ذات صلة	3	4	4
الملخص	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.