Application of Convolutional Neural Networks with Quasi-Reversibility Method Results for Option Forecasting

TL;DR

This paper combines the Quasi-Reversibility Method with Convolutional Neural Networks to improve stock option price forecasting by solving the Black-Scholes equation as an inverse problem, validated on extensive market data.

Contribution

It introduces a novel integration of QRM and CNN for option forecasting, enhancing predictive accuracy over previous models.

Findings

CNN models outperform previous approaches in profit rate

QRM effectively addresses ill-posedness in Black-Scholes equation

Large-scale empirical validation on 92,846 companies

Abstract

This paper presents a novel way to apply mathematical finance and machine learning (ML) to forecast stock options prices. Following results from the paper Quasi-Reversibility Method and Neural Network Machine Learning to Solution of Black-Scholes Equations (appeared on the AMS Contemporary Mathematics journal), we create and evaluate new empirical mathematical models for the Black-Scholes equation to analyze data for 92,846 companies. We solve the Black-Scholes (BS) equation forwards in time as an ill-posed inverse problem, using the Quasi-Reversibility Method (QRM), to predict option price for the future one day. For each company, we have 13 elements including stock and option daily prices, volatility, minimizer, etc. Because the market is so complicated that there exists no perfect model, we apply ML to train algorithms to make the best prediction. The current stage of research combines QRM with Convolutional Neural Networks (CNN), which learn information across a large number of data points simultaneously. We implement CNN to generate new results by validating and testing on sample market data. We test different ways of applying CNN and compare our CNN models with previous models to see if achieving a higher profit rate is possible.