قارن الطرق

	التقييم المحايد للمخاطر	نموذج سوق الليبور
المجال	التمويل الكمي	التمويل الكمي
العائلة	Regression model	Regression model
سنة النشأة	1979	1997
صاحب الطريقة	John Harrison and David Kreps	Alan Brace, Dariusz Gatarek, and Marek Musiela
النوع	Fundamental Principle	Interest Rate Model
المصدر التأسيسي	Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408.	Brace, A., Gatarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127-155.
الأسماء البديلة	Risk-Neutral Measure, Q-Measure	BGM Model, LMM
ذات صلة	4	4
الملخص	Risk-neutral valuation (1979) is the fundamental principle that derivative prices equal the expected payoff discounted at the risk-free rate, computed under a risk-neutral probability measure (Q-measure). This principle, formalized by Harrison and Kreps, eliminates the need to estimate risk premia and is the foundation of modern derivatives pricing.	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.