An Evaluation of novel method of Ill-Posed Problem for the Black-Scholes Equation solution

TL;DR

This paper evaluates a novel regularization-based method for solving the ill-posed Black-Scholes equation, demonstrating its effectiveness in stock option forecasting and profitability when combined with machine learning and a new trading strategy.

Contribution

It introduces a new empirical regularization technique for the Black-Scholes equation and applies it to real market data, showing improved trading profitability over trivial methods.

Findings

Significant profit achieved with the new method and trading strategy.

The regularization approach outperforms trivial extrapolation techniques.

Parallelized implementation on supercomputers enabled processing of large datasets.

Abstract

It was proposed by Klibanov a new empirical mathematical method to work with the Black-Scholes equation. This equation is solved forwards in time to forecast prices of stock options. It was used the regularization method because of ill-posed problems. Uniqueness, stability and convergence theorems for this method are formulated. For each individual option, historical data is used for input. The latter is done for two hundred thousand stock options selected from the Bloomberg terminal of University of Washington. It used the index Russell 2000. The main observation is that it was demonstrated that technique, combined with a new trading strategy, results in a significant profit on those options. On the other hand, it was demonstrated the trivial extrapolation techniques results in much lesser profit on those options. This was an experimental work. The minimization process was performed by Hyak Next Generation Supercomputer of the research computing club of University of Washington. As a result, it obtained about 50,000 minimizers. The code is parallelized in order to maximize the performance on supercomputer clusters. Python with the SciPy module was used for implementation. You may find minimizers in the source package that is available on GitHub. Chapter 7 is dedicated to application of machine learning. We were able to improve our results of profitability using minimizers as new data. We classified the minimizer's set to filter for the trading strategy. All results are available on GitHub.