قارن الطرق

	تسعير الخيارات الثنائية (كوكس-روس-روبنشتاين)	نماذج أسعار الفائدة (فاسيتشيك، سي آي آر، نيلسون-سيغل)
المجال	التمويل	التمويل
العائلة	Regression model	Regression model
سنة النشأة	1979	1977
صاحب الطريقة	John Cox, Stephen Ross & Mark Rubinstein	Vasicek (1977); Nelson & Siegel (1987)
النوع	Discrete-time lattice option-pricing model	Term-structure / short-rate model
المصدر التأسيسي	Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.	Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5(2), 177–188.
الأسماء البديلة	binomial tree model, Cox-Ross-Rubinstein model, CRR model, lattice option pricing	term structure models, short-rate models, yield curve models, Vasicek model
ذات صلة	4	5
الملخص	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.	Interest rate models are structural models that describe how interest rates evolve over time within a stochastic differential equation framework. The family covers Vasicek's normal short-rate process (1977), the CIR square-root process, the adjustable Hull-White extension, and the Nelson-Siegel approach to fitting the yield curve (1987).