Linganisha mbinu

	Mfumo wa HJM	Modeli ya Hull-White
Nyanja	Fedha za Kiidadi	Fedha za Kiidadi
Familia	Regression model	Regression model
Mwaka wa asili	1992	1990
Mwanzilishi	David Heath, Robert Jarrow, and Andrew Morton	John C. Hull and Alan White
Aina	Interest Rate Framework	Interest Rate Model
Chanzo asilia	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.
Majina mbadala	Forward Rate Model, No-Arbitrage Drift Condition	Extended Vasicek, Generalized Vasicek
Zinazohusiana	4	4
Muhtasari	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.