Exploring chaos and sensitivity in the Ivancevic option pricing model through perturbation analysis
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Exploring chaos and sensitivity in the Ivancevic option pricing model through perturbation analysis
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Exploring chaos and sensitivity in the Ivancevic option pricing model through perturbation analysis
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10100 - Mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
O - Projekt operacniho programu
Ostatní
Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
PLoS One
ISSN
1932-6203
e-ISSN
1932-6203
Svazek periodika
19
Číslo periodika v rámci svazku
11
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
35
Strana od-do
—
Kód UT WoS článku
001364424600041
EID výsledku v databázi Scopus
2-s2.0-85210364629