قارن الطرق

	نموذج سوق الليبور	التقييم المحايد للمخاطر
المجال	التمويل الكمي	التمويل الكمي
العائلة	Regression model	Regression model
سنة النشأة	1997	1979
صاحب الطريقة	Alan Brace, Dariusz Gatarek, and Marek Musiela	John Harrison and David Kreps
النوع	Interest Rate Model	Fundamental Principle
المصدر التأسيسي	Brace, A., Gatarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127-155.	Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408.
الأسماء البديلة	BGM Model, LMM	Risk-Neutral Measure, Q-Measure
ذات صلة	4	4
الملخص	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.	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.