Linganisha mbinu

	Modeli wa Soko wa Libor	Mfumo wa HJM
Nyanja	Fedha za Kiidadi	Fedha za Kiidadi
Familia	Regression model	Regression model
Mwaka wa asili	1997	1992
Mwanzilishi	Alan Brace, Dariusz Gatarek, and Marek Musiela	David Heath, Robert Jarrow, and Andrew Morton
Aina	Interest Rate Model	Interest Rate Framework
Chanzo asilia	Brace, A., Gatarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127-155.	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.
Majina mbadala	BGM Model, LMM	Forward Rate Model, No-Arbitrage Drift Condition
Zinazohusiana	4	4
Muhtasari	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 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.