Solving the Ivancevic Pricing Model Using the He's Frecuency Amplitude Formulation

Abstract

In financial mathematics, option pricing theory remains a core area of interest that requires effective models. Thus, the Ivancevic option pricing model (IOPM) is a nonlinear adaptive-wave alternative for the classical Black-Scholes option pricing model; it represents a controlled Brownian motion (BM) in an adaptive setting with relation to nonlinear Schr\"{o}dinger equation. The importance of the IOPM cannot be overemphasized; though, it seems difficult and complex to obtain the associated exact solutions if they exist. Therefore, this paper provides exact solutions of the IOPM by means of a proposed analytical method referred to as He's frequency amplitude formulation. Cases of nonzero adaptive market potential are considered. The method is shown to effective, efficient, simple and direct in application, even without loss of generality.