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	Model wyceny opcji Blacka-Scholesa-Mertona	Model dwumianowy wyceny opcji (Cox-Ross-Rubinstein)
Dziedzina	Finanse	Finanse
Rodzina	Regression model	Regression model
Rok powstania	1973	1979
Twórca	Fischer Black, Myron Scholes & Robert Merton	John Cox, Stephen Ross & Mark Rubinstein
Typ	Continuous-time option-pricing model	Discrete-time lattice option-pricing model
Źródło pierwotne	Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.	Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.
Inne nazwy	Black-Scholes formula, Black-Scholes-Merton model, BSM model, Black-Scholes opsiyon fiyatlama modeli	binomial tree model, Cox-Ross-Rubinstein model, CRR model, lattice option pricing
Pokrewne	4	4
Podsumowanie	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 binomial option pricing model, introduced by John Cox, Stephen Ross, and Mark Rubinstein in 1979, prices options by modelling the underlying as a discrete tree in which the price moves up or down by fixed factors at each step. Working backward from the option's payoff at maturity using risk-neutral probabilities, it produces a no-arbitrage price that converges to Black-Scholes as the number of steps grows — while naturally handling American early exercise, which the closed-form formula cannot.