مقایسهٔ روش‌ها

	ارزش‌گذاری بی‌خطر نسبت به ریسک	SABR Model
حوزه	مالی کمّی	مالی کمّی
خانواده	Regression model	Regression model
سال پیدایش	1979	2002
پدیدآور	John Harrison and David Kreps	Patrick S. Hagan
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.	Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk. Wilmott Magazine, 1, 84-108.
نام‌های دیگر	Risk-Neutral Measure, Q-Measure	Stochastic Volatility Model
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 SABR (Stochastic Alpha-Beta-Rho) model is a stochastic volatility framework introduced by Hagan et al. in 2002 for valuing interest rate derivatives. It captures the smile effect in implied volatility through correlated Brownian motions and has become industry standard for swaption and caplet pricing.