The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255692" target="_blank" >RIV/61989100:27740/24:10255692 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1140/epjp/s13360-024-05435-1" target="_blank" >https://link.springer.com/article/10.1140/epjp/s13360-024-05435-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1140/epjp/s13360-024-05435-1" target="_blank" >10.1140/epjp/s13360-024-05435-1</a>
Alternative languages
Result language
angličtina
Original language name
The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model
Original language description
In this study, the coupled nonlinear volatility and option pricing model is examined. A leverage effect is produced, indicating a negative correlation between stock returns and volatility, and a confined Brownian motion linked to the nonlinear Schrödinger equation is exhibited. This model is considered a coupled nonlinear wave substitute for the Black-Scholes option pricing model. A mathematical strategy is introduced to comprehend market price fluctuations for the suggested model. Consequently, the necessary parameters for the existence of these solutions are revealed. The obtained numerical results of market price are discussed through graphs to illustrate and validate the theoretical findings. The generalized mapping approach of Riccati equations is applied to the model under consideration. Several periodic and singular soliton solutions are successfully constructed for the model. When appropriate parameters are chosen, both 2- and 3-dimensional plots that graphically represent some of the observed waveform solutions are included. Additionally, bifurcation, chaotic analysis, Lyapunov exponents, and multi-stability are performed to gain deeper insights into the related dynamical system. Phase portraits of market price fluctuations are shown for various parametric values of the corresponding dynamical system and at the equilibrium points. The results demonstrate that slight changes in initial conditions lead to price fluctuations in the model. (C) The Author(s), under exclusive licence to Societa Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
O - Projekt operacniho programu
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Physical Journal Plus
ISSN
2190-5444
e-ISSN
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Volume of the periodical
139
Issue of the periodical within the volume
7
Country of publishing house
DE - GERMANY
Number of pages
21
Pages from-to
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UT code for WoS article
001277799300007
EID of the result in the Scopus database
2-s2.0-85199780507