مقایسهٔ روش‌ها

	مدل قیمت‌گذاری اختیار معامله بلک-شولز-مرتون	مدل پرش-انتشار مرتون
حوزه	مالی	مالی
خانواده	Regression model	Regression model
سال پیدایش	1973	1976
پدیدآور	Fischer Black, Myron Scholes & Robert Merton	Robert C. Merton
نوع	Continuous-time option-pricing model	Continuous-time asset price model (diffusion plus Poisson jumps)
منبع بنیادین	Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.	Merton, R. C. (1976). Option Pricing When Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3(1–2), 125–144.
نام‌های دیگر	Black-Scholes formula, Black-Scholes-Merton model, BSM model, Black-Scholes opsiyon fiyatlama modeli	Merton jump-diffusion, jump-diffusion process, Atlama Difüzyon Modeli (Merton Jump-Diffusion)
مرتبط	4	4
خلاصه	The Black-Scholes-Merton model, published by Fischer Black and Myron Scholes in 1973 with the theoretical framework extended by Robert Merton, gives a closed-form no-arbitrage price for European options. By assuming the underlying asset follows geometric Brownian motion with constant volatility, it derives a partial differential equation whose solution expresses the option price in terms of the stock price, strike, time to maturity, risk-free rate, and volatility — transforming option pricing from intuition into a rigorous, tractable formula.	The Merton Jump-Diffusion model, introduced by Robert C. Merton in 1976, extends Geometric Brownian Motion by adding sudden price jumps generated by a Poisson process. It captures the volatility smile and the fat-tailed return behaviour that standard Black-Scholes cannot explain, and is widely used in option pricing and risk management.