About subordinated generalizations of 3 classical models of option pricing

• Autorzy: Balcerek Michał , Krzyżanowski Grzegorz Piotr , Magdziarz Marcin

Identyfikatory

DOI

10.14708/ma.v52i1.7256

Warianty tytułu

PL

O subordynowanych uogólnieniach 3 klasycznych modeli wyceny opcji

• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the inverse subordinators. Such models, in contrast to their classical equivalents, can be used in markets where periods of stagnation are observed. We introduce the subordinated Cox-Ross-Rubinstein model and prove that the price of the underlying in that model converges in distribution and in Skorokhod space to the price of underlying in the subordinated Black-Scholes model defined in [24]. Motivated by this fact we price the selected option contracts using the binomial trees. The results are compared to other numerical methods.

PL

W tym artykule badamy relację pomiędzy modelami Bacheliera i Blacka-Scholesa zależnymi od odwrotnego subordynatora. Modele te, w przeciwieństwie do swoich klasycznych odpowiedników mogą być wykorzystane na rynkach gdzie zauważalne są okresy stagnacji. Ponadto, wprowadzamy subordynowany model Coxa-Rossa-Rubinsteina i pokazujemy zbieżność instrumentu podstawowego w tym modelu według rozkładu i w przestrzeni Skorochoda do ceny instrumentu podstawowego w subordynowanym modelu Blacka-Scholesa zdefiniowanym w [25]. Zmotywowani tym faktem wyceniamy wybrane kontrakty opcyjne za pomocą drzewek dwumianowych. Wyniki porównujemy do innych metod numerycznych.

Słowa kluczowe

EN

subdiffusion; subordinator; option contracts; Monte Carlo; Bachelier model; Black-Scholes model

PL

subdyfuzja; subordynator; kontrakt opcyjny; Monte Carlo; model Bacheliera; model Blacka-Scholesa

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2024
• Tom: Vol. 52, no. 1
• Strony: 3--25
• Opis fizyczny: Bibliogr. 34 poz., wykr.

Twórcy

autor

Balcerek Michał

• Wrocław University of Science and Technology & Hugo Steinhaus Center Faculty of Pure and Applied Mathematics Wybrzeże Wyspiańskiego 27, PL-50–370 Wrocław

• https://orcid.org/0000-0003-3637-5501

autor

Krzyżanowski Grzegorz Piotr

• Wrocław University of Science and Technology & Hugo Steinhaus Center Faculty of Pure and Applied Mathematics Wybrzeże Wyspiańskiego 27, PL-50–370 Wrocław

• https://orcid.org/0000-0001-9413-3434

autor

Magdziarz Marcin

• Wrocław University of Science and Technology & Hugo Steinhaus Center Faculty of Pure and Applied Mathematics Wybrzeże Wyspiańskiego 27, 50–370 Wrocław

• https://orcid.org/0000-0002-2239-7155

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