Ivancevic Option Pricing Model modulational instability through the variational approach

TL;DR

This paper investigates the instability of the Ivancevic option pricing model using variational and numerical methods, deriving dispersion relations for different volatility models and analyzing their stability properties.

Contribution

It introduces an analytical derivation of dispersion relations for the Ivancevic model under various volatility assumptions and applies numerical simulations to study its instability.

Findings

Derived dispersion relations for constant and time-dependent volatility models.

Numerical analysis confirms the instability characteristics predicted analytically.

Provides insights into the modulational instability in option pricing models.

Abstract

The instability of the Ivancevic option pricing model is studied through the variational method. We have analytically derived the dispersion relation of the IOPM for both constant volatility and Landau coefficient model and time-dependent volatility and Landau coefficient model. Also the IOPM was studies numerically using the 4th order Runge-Kutta method.