قارن الطرق

	تغيير المقياس	إطار عمل HJM
المجال	التمويل الكمي	التمويل الكمي
العائلة	Regression model	Regression model
سنة النشأة	1995	1992
صاحب الطريقة	Hélyette Geman, Nicole El Karoui, Jean-Charles Rochet	David Heath, Robert Jarrow, and Andrew Morton
النوع	Measure Theory	Interest Rate Framework
المصدر التأسيسي	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.	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.
الأسماء البديلة	Numeraire Switching, Measure Change	Forward Rate Model, No-Arbitrage Drift Condition
ذات صلة	3	4
الملخص	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.	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.