قارن الطرق

	نموذج سوق الليبور	نموذج هول-وايت
المجال	التمويل الكمي	التمويل الكمي
العائلة	Regression model	Regression model
سنة النشأة	1997	1990
صاحب الطريقة	Alan Brace, Dariusz Gatarek, and Marek Musiela	John C. Hull and Alan White
النوع	Interest Rate Model	Interest Rate Model
المصدر التأسيسي	Brace, A., Gatarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127-155.	Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. Review of Financial Studies, 3(4), 573-592.
الأسماء البديلة	BGM Model, LMM	Extended Vasicek, Generalized Vasicek
ذات صلة	4	4
الملخص	The LIBOR Market Model (BGM), developed by Brace, Gatarek, and Musiela (1997), is a multi-factor interest rate model that directly models forward LIBOR rates as lognormal processes. Unlike short-rate models, LMM naturally prices caplets at the market level and is the industry standard for valuing caps, floors, and exotic interest rate derivatives.	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.