قارن الطرق

	تسعير كرنك-نيكلسون	التقلب المحلي (Dupire)	نموذج SABR
المجال	التمويل الكمي	التمويل الكمي	التمويل الكمي
العائلة	Machine learning	Regression model	Regression model
سنة النشأة	1947	1994	2002
صاحب الطريقة	John Crank and Phyllis Nicolson	Bruno Dupire	Patrick S. Hagan
النوع	PDE Solver	Equity/FX Model	Interest Rate Model
المصدر التأسيسي	Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society, 43(1), 50-67.	Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20.	Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk. Wilmott Magazine, 1, 84-108.
الأسماء البديلة	CN Method, Implicit Finite Difference	Deterministic Volatility Function, DVF	Stochastic Volatility Model
ذات صلة	3	4	4
الملخص	The Crank-Nicolson method is a widely-used implicit finite difference scheme for solving PDEs in option pricing. It provides second-order accuracy in both space and time, unconditional stability, and can efficiently price derivatives with early exercise features (American options) or complex boundary conditions.	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.	The SABR (Stochastic Alpha-Beta-Rho) model is a stochastic volatility framework introduced by Hagan et al. in 2002 for valuing interest rate derivatives. It captures the smile effect in implied volatility through correlated Brownian motions and has become industry standard for swaption and caplet pricing.