قارن الطرق

	تسعير كرنك-نيكلسون	نموذج هول-وايت	نموذج SABR
المجال	التمويل الكمي	التمويل الكمي	التمويل الكمي
العائلة	Machine learning	Regression model	Regression model
سنة النشأة	1947	1990	2002
صاحب الطريقة	John Crank and Phyllis Nicolson	John C. Hull and Alan White	Patrick S. Hagan
النوع	PDE Solver	Interest Rate 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.	Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. Review of Financial Studies, 3(4), 573-592.	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	Extended Vasicek, Generalized Vasicek	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.	The Hull-White model (1990) is a one-factor short-rate model with time-dependent mean reversion and volatility, designed to fit the initial yield curve exactly. It generalizes the Vasicek model to allow better calibration to observed bond and derivative prices, and is widely used for pricing interest rate exotics and managing interest rate risk.	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.