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| Model dwumianowy wyceny opcji (Cox-Ross-Rubinstein)× | Model zmienności stochastycznej (Heston)× | |
|---|---|---|
| Dziedzina | Finanse | Finanse |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 1979 | 1993 |
| Twórca≠ | John Cox, Stephen Ross & Mark Rubinstein | Steven L. Heston |
| Typ≠ | Discrete-time lattice option-pricing model | Continuous-time stochastic volatility model |
| Źródło pierwotne≠ | Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263. DOI ↗ | 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. DOI ↗ |
| Inne nazwy≠ | 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) |
| Pokrewne≠ | 4 | 5 |
| Podsumowanie≠ | 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. |
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