So sánh phương pháp

	Khung HJM	Thay đổi Numeraire
Lĩnh vực	Tài chính định lượng	Tài chính định lượng
Họ	Regression model	Regression model
Năm ra đời	1992	1995
Người khởi xướng	David Heath, Robert Jarrow, and Andrew Morton	Hélyette Geman, Nicole El Karoui, Jean-Charles Rochet
Loại	Interest Rate Framework	Measure Theory
Công trình gốc	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.	Geman, H., El Karoui, N., & Rochet, J. C. (1995). Changes of numeraire, changes of probability measure and option pricing. Journal of Applied Probability, 32(2), 443-458.
Tên gọi khác	Forward Rate Model, No-Arbitrage Drift Condition	Numeraire Switching, Measure Change
Liên quan	4	3
Tóm tắt	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.	Change of numeraire is a mathematical technique for simplifying option pricing by changing the choice of discount factor (numeraire). By selecting a numeraire aligned with the payoff structure, complex problems become simple. The technique is essential for LIBOR market models and multi-currency derivatives.