机器学习技术和神经网络审查下的VIX指数
The VIX index under scrutiny of machine learning techniques and neural networks
摘要：
芝加哥期权交易所波动率指数（CBOE Volatility Index），其股票代码VIX，是衡量标普500指数市场预期波动率的常用指标，由芝加哥期权交易所（CBOE）计算和发布。它也经常被称为恐惧指数或恐惧量表。当前的VIX指数价值引用了标准普尔500指数在未来30天内的预期年化变化，基于期权理论和当前期权市场数据。尽管其理论基础是期权价格理论，但CBOE的波动率指数很容易出现无意和故意的错误，因为它是可能缺乏流动性的价外看涨期权和看跌期权的加权平均值。近年来，许多关于市场操纵的指控都是针对波动率指数提出的。本文讨论了几种方法来复制波动率指数以及波动率指数期货，通过使用一个子集的相关选项以及神经网络，训练自动学习的基础公式。在原始CBOE方法的基础上使用子集选择方法，以及构建机器学习和神经网络模型，包括随机森林，支持向量机，前馈神经网络和长短期记忆（LSTM）模型，我们将证明少量选项足以复制VIX指数。一旦我们能够使用少量的标普期权实际复制VIX指数，我们将能够利用VIX指数及其基础衍生品之间的潜在套利机会。调查结果将帮助投资者更好地了解期权市场，更重要的是，为美国监管机构和芝加哥期权交易所提供指导，这些机构多年来一直在调查这些操纵指控。
英文摘要：
The CBOE Volatility Index, known by its ticker symbol VIX, is a popular measure of the market's expected volatility on the SP 500 Index, calculated and published by the Chicago Board Options Exchange (CBOE). It is also often referred to as the fear index or the fear gauge. The current VIX index value quotes the expected annualized change in the SP 500 index over the following 30 days, based on options-based theory and current options-market data. Despite its theoretical foundation in option price theory, CBOE's Volatility Index is prone to inadvertent and deliberate errors because it is weighted average of out-of-the-money calls and puts which could be illiquid. Many claims of market manipulation have been brought up against VIX in recent years. This paper discusses several approaches to replicate the VIX index as well as VIX futures by using a subset of relevant options as well as neural networks that are trained to automatically learn the underlying formula. Using subset selection approaches on top of the original CBOE methodology, as well as building machine learning and neural network models including Random Forests, Support Vector Machines, feed-forward neural networks, and long short-term memory (LSTM) models, we will show that a small number of options is sufficient to replicate the VIX index. Once we are able to actually replicate the VIX using a small number of SP options we will be able to exploit potential arbitrage opportunities between the VIX index and its underlying derivatives. The results are supposed to help investors to better understand the options market, and more importantly, to give guidance to the US regulators and CBOE that have been investigating those manipulation claims for several years.
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