Solving the Stock Option Forecast problem by a numerical method for the Black-Scholes Equation with Machine Learning Classification Model

TL;DR

The paper tackles the challenge of forecasting short-term option movements under the ill-posedness of the Black-Scholes framework by applying the Quasi-Reversibility Method (QRM) to obtain a minimizer and forecast prices one day ahead. It then combines these QRM-derived features with multiple classification models—decision trees, gradient boosting, random forests, KNN, and neural networks—evaluated on a real Bloomberg dataset of 23,548 options across five days. Results show gradient-boosted trees achieving the highest precision (about 75.18%), with other models also performing strongly, suggesting improved profitability potential over prior neural-network baselines while noting practical limits like transaction costs and the short forecasting horizon. The study demonstrates a viable strategy for integrating PDE-regularization with ensemble classifiers to generate trading signals and outlines future work on predicting percentage changes, adaptive regularization for QRM, and capturing temporal patterns beyond one-day ahead predictions.

Abstract

We proposed classification models that utilize the result from the Quasi-Reversibility Method, which solves the Black-Scholes equation to forecast the option prices one day in advance. Combining the minimizer from QRM with our machine learning classifications, we can classify the option as an increase or decrease in value. Based on the different classifications of the options, we can apply various trading strategies which we aim to figure out ways to improve the results from QRM's extrapolations. To further test the viability of our model, we collected 23548 options data from the real-world market for our model, and we will then feed in the data along with the minimizer from QRM to form decision trees and random forests, which we will later test for accuracy, precision, and recall.

Figures (13)

• Figure 1: Binary Decision Tree example
• Figure 2: Example of Gradient descent for convergence
• Figure 3: Confusion Matrix for option price predictions
• Figure 4: Decision Tree for option movement
• Figure 5: Confusion Matrix for option price predictions