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	Real Options Valuation	Model dwumianowy wyceny opcji (Cox-Ross-Rubinstein)
Dziedzina	Ekonomia	Finanse
Rodzina	Process / pipeline	Regression model
Rok powstania	1994	1979
Twórca	Stewart Myers (term); Dixit & Pindyck, Trigeorgis (theory)	John Cox, Stephen Ross & Mark Rubinstein
Typ	Valuation of managerial flexibility under uncertainty	Discrete-time lattice option-pricing model
Źródło pierwotne	Dixit, A. K., & Pindyck, R. S. (1994). Investment Under Uncertainty. Princeton University Press. ISBN: 9780691034102	Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.
Inne nazwy	Real Options Analysis, ROV, Real Option Pricing, Investment Under Uncertainty	binomial tree model, Cox-Ross-Rubinstein model, CRR model, lattice option pricing
Pokrewne	3	4
Podsumowanie	Real options valuation applies the theory of financial options to real (physical, strategic) investment decisions, valuing the managerial flexibility to defer, expand, contract, switch, or abandon a project as uncertainty resolves over time. Where standard discounted-cash-flow analysis assumes a now-or-never commitment to a fixed plan, real options recognize that managers hold rights — not obligations — to act, and that this flexibility has value precisely because the future is uncertain. Using option-pricing and dynamic-programming methods, the approach values these embedded options and identifies the optimal timing and conditions for exercising them.	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.