A review of the binomial and trinomial models for option pricing and their convergence to the Black-Scholes model determined option prices

• Authors: Josheski Dushko , Apostolov Mico

Title variants

PL

Przegląd dwumianowych i trójmianowych modeli wyceny opcji i ich zbieżność do modelu Blacka-Scholesa określającego wycenę opcji

• Languages of publication: EN

Abstracts

EN

This paper reviews the binomial and trinomial option pricing models and their convergence to the Black-Scholes model result. These models are generalized for the European and American options. The trinomial models are said to be more accurate than the binomial when fewer steps are modelled. These models are widely used for the usual vanilla option types, European or American options, that respectively can be exercised only at the expiration date and at any time before the expiration date. The results are supportive of the conventional wisdom that trinomial option pricing models such as the Kamrad-Ritchken model and the Boyle model are converging faster than the binomial models. When binomial models are compared in terms of convergence, the most efficient model is the Jarrow-Rudd model. This paper concludes that improved binomial models such as the Haahtela model are converging faster to the BS model result. After some trials, binomial distribution follows log-normal distribution assumed by the Black-Scholes model.

PL

W artykule dokonano przeglądu modeli wyceny opcji dwumianowych i trójmianowych oraz ich zbieżności z wynikami zastosowania modelu Blacka-Scholesa (BS). Przeprowadzono uogólnienie modeli dla opcji europejskich i amerykańskich. W literaturze wskazuje się, że modele trójmianowe w przypadku mniejszej liczby kroków dają bardziej dokładne wyniki niż modele dwumianowe. Modele te są szeroko stosowane dla zwykłych typów opcji waniliowych, opcji europejskich lub amerykańskich, które odpowiednio można wykonać tylko w dniu wygaśnięcia i w dowolnym momencie przed datą wygaśnięcia. Otrzymane wyniki potwierdzają konwencjonalną teorię, że trójmianowe modele wyceny opcji, takie jak model Kamrada-Ritchkena i model Boyle’a, są szybciej zbieżne niż modele dwumianowe. W porównaniu modeli dwumianowych pod względem konwergencji najbardziej efektywnym modelem jest model Jarrowa-Rudda. W artykule zaprezentowano wyniki wskazujące, że ulepszone modele dwumianowe, takie jak model Haahtela, są szybciej zbieżne do wyników uzyskanych z modelu BS. Po przeprowadzeniu kilku prób wskazano, że rozkład dwumianowy

Keywords

EN

Black-Scholes-Merton model; Leisen-Reimer model; Cox-Ross-Rubinstein model; Tian model; Trigeorgis model

PL

model Blacka-Scholesa-Mertona; model Leisena-Reimera; model Coxa-Rossa-Rubinsteina; model Tiana; model Trigeorgisa

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Econometrics. Ekonometria. Advances in Applied Data Analytics
• Year: 2020
• Issue: vol. 24, nr 2
• Pages: 53-85

Contributors

author

Josheski Dushko

author

Apostolov Mico

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