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Regularized Black–Scholes Forecasting for Option Trading

Article arXiv papers · Author: Kirill V. Golubnichiy et al.
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Summary

The document describes an empirical method for forecasting option prices by solving the Black–Scholes equation forward in time. Because the problem is ill-posed, the method uses regularization; the work formulates theorems concerning uniqueness, stability, and convergence. Historical data for individual options is used, with an empirical study drawing on a large set of options and the Russell 2000 index.

The authors report that combining the method with a trading strategy produced higher profits than simple extrapolation, and that machine learning applied to computed minimizers improved profitability further by filtering trades. The evidence is experimental and comes from this particular historical option sample. The document provides no details here about transaction costs, out-of-sample robustness, risk, or the specific trading rules, so the reported profitability should not be treated as proof of performance in live markets.

Key ideas

  • The approach forecasts option prices by solving the Black–Scholes equation forward in time.
  • Regularization is used to address the equation’s ill-posed inverse problem.
  • The study reports better trading results than trivial extrapolation on its historical option sample.
  • Machine learning is used to filter the strategy using computed minimizers.

Tags

OptionsDerivatives pricingMachine learningStatisticsBacktesting
Full text
# An Evaluation of novel method of Ill-Posed Problem for the Black-Scholes Equation solution


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.