Stochastic and Statistical Analysis of Cnoidal, Snoidal, Dnoidal, Hyperbolic, Trigonometric and Exponential Wave Solutions of a Coupled Volatility Option-Pricing System
L. M. Abdalgadir, Shabir Ahmad, Bakri Youniso, Khaled Aldwoah
TL;DR
This paper explores wave solutions in a financial model that combines market behavior and volatility using stochastic and statistical methods.
Contribution
A new methodology is introduced to derive and analyze wave solutions in a coupled volatility option-pricing system with stochastic effects.
Findings
The system's solutions include cnoidal, snoidal, and exponential wave forms with distinct statistical properties.
Stochastic volatility influences the amplitude and phase dynamics of the solutions, showing non-stationary behavior.
Phase velocity cross-correlation and amplitude cross-correlation reveal coupling dynamics between price and volatility components.
Abstract
We investigate a stochastic coupled nonlinear Schrödinger (Manakov-type) system for option price and volatility wave fields within the Ivancevic adaptive-wave option-pricing paradigm, and derive exact wave families together with statistical diagnostics of the resulting dynamics. This system combines behavioral market effects with classical efficient-market dynamics and incorporates a controlled stochastic volatility component. Randomness in both the option price and volatility is incorporated via white noise, and a system of stochastic partial differential equations (PDEs) is developed that governs the joint evolution of option prices and stock price volatility. We derive advanced solutions of the proposed system using a newly created methodology. The obtained solutions are expressions of cnoidal, snoidal, dnoidal, hyperbolic, trigonometric, and exponential functions. The stochastic…
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Taxonomy
Topicsstochastic dynamics and bifurcation · Stochastic processes and financial applications · Complex Systems and Time Series Analysis