قارن الطرق

	نموذج هول-وايت	إطار عمل HJM
المجال	التمويل الكمي	التمويل الكمي
العائلة	Regression model	Regression model
سنة النشأة	1990	1992
صاحب الطريقة	John C. Hull and Alan White	David Heath, Robert Jarrow, and Andrew Morton
النوع	Interest Rate Model	Interest Rate Framework
المصدر التأسيسي	Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. Review of Financial Studies, 3(4), 573-592.	Heath, D., Jarrow, R. A., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60(1), 77-105.
الأسماء البديلة	Extended Vasicek, Generalized Vasicek	Forward Rate Model, No-Arbitrage Drift Condition
ذات صلة	4	4
الملخص	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 Heath-Jarrow-Morton (HJM) framework (1992) is a general no-arbitrage approach to modeling the entire term structure of forward rates. Unlike short-rate models, HJM works directly with forward rates f(t,T) and specifies their volatility; the drift is then determined by arbitrage constraints. This flexibility enables multi-factor modeling and accurate calibration to swaption matrices.