Linganisha mbinu

	Uthamini wa Chaguo la Binomiali (Cox-Ross-Rubinstein)	Mchanganuo wa Kutokuwa na Utulivu wa Kimahesabu (Heston)
Nyanja	Fedha	Fedha
Familia	Regression model	Regression model
Mwaka wa asili	1979	1993
Mwanzilishi	John Cox, Stephen Ross & Mark Rubinstein	Steven L. Heston
Aina	Discrete-time lattice option-pricing model	Continuous-time stochastic volatility model
Chanzo asilia	Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.	Heston, S. L. (1993). A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Studies, 6(2), 327-343.
Majina mbadala	binomial tree model, Cox-Ross-Rubinstein model, CRR model, lattice option pricing	Heston model, SV model, continuous-time stochastic volatility, Stokastik Volatilite Modeli (Heston, SV)
Zinazohusiana	4	5
Muhtasari	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.	The stochastic volatility model is a continuous-time option-pricing and risk framework in which volatility follows its own random process rather than staying constant. The Heston model, introduced by Steven Heston in 1993, gives the variance a mean-reverting square-root (CIR) dynamic and yields a closed-form option price; it is the continuous-time counterpart of GARCH.