مقایسهٔ روش‌ها

	ارزش‌گذاری بی‌خطر نسبت به ریسک	مدل بازار لیبور
حوزه	مالی کمّی	مالی کمّی
خانواده	Regression model	Regression model
سال پیدایش	1979	1997
پدیدآور	John Harrison and David Kreps	Alan Brace, Dariusz Gatarek, and Marek Musiela
نوع	Fundamental Principle	Interest Rate Model
منبع بنیادین	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.
نام‌های دیگر	Risk-Neutral Measure, Q-Measure	BGM Model, LMM
مرتبط	4	4
خلاصه	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.