Exploring chaos and sensitivity in the Ivancevic option pricing model through perturbation analysis
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10256077" target="_blank" >RIV/61989100:27740/24:10256077 - isvavai.cz</a>
Result on the web
<a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0312805" target="_blank" >https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0312805</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1371/journal.pone.0312805" target="_blank" >10.1371/journal.pone.0312805</a>
Alternative languages
Result language
angličtina
Original language name
Exploring chaos and sensitivity in the Ivancevic option pricing model through perturbation analysis
Original language description
This study explores the Ivancevic Option Pricing Model, a nonlinear wave-based alternative to the Black-Scholes model, using adaptive nonlinear Schrödingerr equations to describe the option-pricing wave function influenced by stock price and time. Our focus is on a comprehensive analysis of this equation from multiple perspectives, including the study of soliton dynamics, chaotic patterns, wave structures, Poincaré maps, bifurcation diagrams, multistability, Lyapunov exponents, and an in-depth evaluation of the model's sensitivity. To begin, a wave transformation is applied to convert the partial differential equation into an ordinary differential equation, from which soliton solutions are derived using the (Formular Presented) method. We explore various forms of the option price function at different time points, including singular-kink, periodic, hyperbolic, trigonometric, exponential, and complex solutions. Furthermore, we simulate 3D surface plots and 2D graphs for the real, imaginary, and modulus components of some of the obtained solutions, assigning specific parameter values to enhance visualization. These graphical representations offer valuable insights into the dynamics and patterns of the solutions, providing a clearer understanding of the model's behavior and potential applications. Additionally, we analyze the system's dynamic behavior when a perturbing force is introduced, identifying chaotic patterns using the Lyapunov exponent, Sensitivity, multistability analysis, RK4 method, wave structures, bifurcation diagrams, and Poincaré maps.
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
10100 - 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
PLoS One
ISSN
1932-6203
e-ISSN
1932-6203
Volume of the periodical
19
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
35
Pages from-to
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UT code for WoS article
001364424600041
EID of the result in the Scopus database
2-s2.0-85210364629