Financial Rogue Waves Appearing in the Coupled Nonlinear Volatility and Option Pricing Model

Abstract

The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black-Scholes option pricing model. In this short report, we analytically propose the two-component financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The two-component financial rogue wave solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of rogue waves in the financial markets and other related fields.