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正则化 Black–Scholes 期权交易预测

文章 arXiv papers · 作者: Kirill V. Golubnichiy et al.
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总结

本文介绍一种实证方法，通过向前求解 Black–Scholes 方程来预测期权价格。由于该问题不适定，方法采用正则化；研究提出了关于唯一性、稳定性和收敛性的定理。研究使用单个期权的历史数据，实证分析涵盖大量期权和 Russell 2000 指数。

作者报告称，将该方法与交易策略结合后，利润高于简单外推；对计算所得极小值应用机器学习，通过过滤交易进一步提高了盈利能力。证据来自针对这一特定历史期权样本的实验。本文在此未提供交易成本、样本外稳健性、风险或具体交易规则的细节，因此所报告的盈利能力不应被视为实盘表现的证明。

核心观点

  • 该方法通过向前求解 Black–Scholes 方程来预测期权价格。
  • 研究使用正则化处理方程的不适定反问题。
  • 研究报告称，在其历史期权样本中，交易结果优于简单外推。
  • 研究使用机器学习，根据计算所得的极小值筛选交易。

标签

期权衍生品定价机器学习统计学回测
全文
# 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.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。