New Financial Research Program: General Option-Price Wave Modeling

TL;DR

This paper introduces a new research program aiming to develop a comprehensive wave-based model for option pricing, building on previous nonlinear Schrödinger equation approaches and extending them with rogue wave solutions for improved financial prediction.

Contribution

It proposes a novel general wave model for option pricing, expanding the nonlinear Schrödinger framework with rogue wave solutions for better financial analysis.

Findings

Successful fit of wave solutions to Black-Scholes data

Extension of wave models with rogue wave solutions

Foundation for a new comprehensive option-pricing model

Abstract

Recently, a novel adaptive wave model for financial option pricing has been proposed in the form of adaptive nonlinear Schr\"{o}dinger (NLS) equation [Ivancevic a], as a high-complexity alternative to the linear Black-Scholes-Merton model [Black-Scholes-Merton]. Its quantum-mechanical basis has been elaborated in [Ivancevic b]. Both the solitary and shock-wave solutions of the nonlinear model, as well as its linear (periodic) quantum simplification are shown to successfully fit the Black-Scholes data, and define the financial Greeks. This initial wave model (called the Ivancevic option pricing model) has been further extended in [Yan], by providing the new NLS solutions in the form of rogue waves (one-rogon and two-rogon solutions). In this letter, I propose a new financial research program, with a goal to develop a general wave-type model for realistic option-pricing prediction and control. Keywords: General option-price wave modeling, new financial research program