مقایسهٔ روش‌ها

	چارچوب HJM	مدل هال-وایت
حوزه	مالی کمّی	مالی کمّی
خانواده	Regression model	Regression model
سال پیدایش	1992	1990
پدیدآور	David Heath, Robert Jarrow, and Andrew Morton	John C. Hull and Alan White
نوع	Interest Rate Framework	Interest Rate Model
منبع بنیادین	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.	Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. Review of Financial Studies, 3(4), 573-592.
نام‌های دیگر	Forward Rate Model, No-Arbitrage Drift Condition	Extended Vasicek, Generalized Vasicek
مرتبط	4	4
خلاصه	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.	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.