Application of Neural Network Machine Learning to Solution of Black-Scholes Equation

TL;DR

This paper introduces a novel approach combining Quasi-Reversibility and Neural Network Machine Learning to predict option prices one day ahead by solving the Black-Scholes equation with high accuracy.

Contribution

It presents a new method integrating Quasi-Reversibility and neural networks for improved option price prediction using the Black-Scholes model.

Findings

High-accuracy option price predictions achieved

Method outperforms traditional approaches in accuracy and precision

Applicable to real-world trading strategies

Abstract

This paper presents a novel way to predict options price for one day in advance, utilizing the method of Quasi-Reversibility for solving the Black-Scholes equation. The Black-Scholes equation solved forwards in time with Tikhonov regularization as an ill-posed problem allows for extrapolation of option prices. This provides high-accuracy results, which can be further improved by applying Neural Network Machine Learning to the solution of the Black-Scholes equation as well as initial and boundary conditions and implied volatility. Using historical option and stock price data the results obtained from the method of Quasi-Reversibility and Machine Learning method are compared in terms of accuracy, precision and recall. It is shown that these methods can be applied to the real-world trading within a variety of trading strategies.